SUBSONIC WIND-TUNNEL WALL CORRECTIONS ON A … · SUBSONIC WIND-TUNNEL WALL CORRECTIONS ON A WING WITH A ... 2D Airfoil Data (Pressure) ... 78 Figure 5.4 Values

SUBSONIC WIND-TUNNEL WALL CORRECTIONS ON A WING WITH A CLARK Y-14 AIRFOIL

A Masters Project

Presented to

The Faculty of the Department of

Mechanical and Aerospace Engineering

San Jose State University

In Partial Fulfillment

Of the Requirements for a Degree

Master of Science

In

Aerospace Engineering

By

Tommy James Blackwell

May 2011

ii

© 2011

Tommy James Blackwell

ALL RIGHTS RESERVED

iv

ABSTRACT

As our civilization relies more heavily on aircrafts and rockets, the use of wind-tunnels has increasing been integrated as an important aeronautical tool in their design. Even though wind-tunnels are great scientific tools, they do have their flaws. Based on the specific wind-tunnel design, one of the main negatives is that wind-tunnels cannot simulate free-flight conditions without having to correct the data for wall effects and other flow phenomena.

Both two and three-dimensional flows need to have corrections applied that are unique to that wind-tunnels design. For two dimensional flows, corrections that can be obtain are for the

with direct corrections available for . The

corrections are developed from the buoyancy, solid and wake blockages, and streamline curvature corrections. For tree-dimensional flows, corrections can be obtain are ,

These corrections depend on the methods applied to the two-dimensional cases along with the method of images.

The experiments contained in this project are utilizing an AEROLAB wind-tunnel along with a ClarkY-14 airfoil and wing. The wind-tunnel was set up to have inlet velocities of 6, 30, 68 and 102 mph and outlet atmospheric environmental conditions. The data collected with the correction factors applied was then compared with free-flight CFD models to compare corrections effectiveness

v

ACKNOWLEDGEMENTS

I would like to take the opportunity to thank Dr. Mourtos and Dr. Papadopoulos for their support throughout this project. Their assistance has been invaluable during the process of finishing this project. I would also like to thank San Jose State University for the use of their wind tunnel facility. A special thanks goes to my mom, dad and family, who have stood by me with encouragement and moral support. Also to my Aunt Helen and Jim Lyons, who provided editing assistance, I thank you so much for your time and effort. Finally, I thank Hai Le, Albert Rios and Paul Linggi for being a sounding board and encouragement throughout the project.

vi

Table of Contents

List of Figures ................................................................................................................................. 1

List of Variables .............................................................................................................................. 6

Chapter 1: Introduction ................................................................................................................. 11

1.1 Background ......................................................................................................................... 11

1.1.1 Development of Wind-Tunnels .................................................................................... 11

1.1.2 Wind-Tunnel Design .................................................................................................... 13

1.1.3 Wall Effects ................................................................................................................. 16

1.1.4 Wall Effect Corrections ............................................................................................... 19

A. The Method of Images ..................................................................................................... 19

Chapter 2: Clark Y-14 Airfoil and Wing ...................................................................................... 24

2.1 Development of Airfoils and Wings ................................................................................... 24

2.2 Development of the Clark Y-14 .......................................................................................... 27

2.3 Characterizing the Clark Y-14 ............................................................................................ 28

2.3.1 Aerodynamic Forces .................................................................................................... 29

2.3.2 Low-Speed Aerodynamics ........................................................................................... 30

2.3.3 Characterizing Airfoil Performance ............................................................................. 31

2.3.4 Characterizing Wing Performance ............................................................................... 32

2.4 Obtaining Airfoil Characteristics from Data ....................................................................... 32

2.4.1 Airfoil control Volume Analysis ................................................................................. 32

vii

2.4.2 Test Section Control Volume Analysis........................................................................ 33

2.4.3 Wing Direct Force Measurement ................................................................................. 34

Chapter 3: AEROLAB Low-Speed Wind Tunnel ........................................................................ 36

3.1 General AEROLAB Wind Tunnel Specifications .............................................................. 36

3.2 Test Section and Instrumentation ........................................................................................ 37

3.3 Clark Y-14 Airfoil and Wing Models ................................................................................. 39

Chapter 4: Two-Dimensional Wall Corrections for the Clark Y-14 Airfoil ................................ 40

4.1 Buoyancy Correction .......................................................................................................... 40

4.1.1 Theory .......................................................................................................................... 40

4.1.2 Approach ...................................................................................................................... 42

4.1.3 Results .......................................................................................................................... 49

4.1.4 Discussion .................................................................................................................... 51

4.2 Solid Blockage Correction .................................................................................................. 52

4.2.1 Theory .......................................................................................................................... 52

4.2.2 Approach ...................................................................................................................... 53

4.2.3 Results .......................................................................................................................... 55

4.2.4 Discussion .................................................................................................................... 57

4.3 Wake Blockage Correction ................................................................................................. 58

4.3.1 Theory .......................................................................................................................... 58

4.3.2 Approach ...................................................................................................................... 59

viii

4.3.3 Results .......................................................................................................................... 61

4.3.4 Discussion .................................................................................................................... 66

4.4 Streamline Curvature Correction ........................................................................................ 67

4.4.1 Theory .......................................................................................................................... 67

4.4.2 Approach ...................................................................................................................... 69

4.4.3 Results .......................................................................................................................... 71

4.4.4 Discussion .................................................................................................................... 75

Chapter 5: Three-Dimensional Wall Corrections for the Clark Y-14 Wing ................................ 77

5.1 Buoyancy Correction .......................................................................................................... 77

5.1.1 Theory .......................................................................................................................... 77

5.1.2 Approach ...................................................................................................................... 78

5.1.3 Results .......................................................................................................................... 78

5.1.4 Discussion .................................................................................................................... 79

5.2 Solid Blockage Correction .................................................................................................. 79

5.2.1 Theory .......................................................................................................................... 79

5.2.3 Results .......................................................................................................................... 80

5.2.4 Discussion .................................................................................................................... 81

5.3 Wake Blockage Correction ................................................................................................. 82

5.3.1 Theory .......................................................................................................................... 82

5.3.2 Approach ...................................................................................................................... 82

ix

5.3.3 Results .......................................................................................................................... 84

5.3.4 Discussion .................................................................................................................... 85

5.4 Method of Images ............................................................................................................... 85

5.4.1 Theory .......................................................................................................................... 85

5.4.2 Approach ...................................................................................................................... 89

5.4.3 Results .......................................................................................................................... 91

5.4.4 Discussion .................................................................................................................... 92

5.5 Streamline Curvature Correction ........................................................................................ 93

5.5.1 Theory .......................................................................................................................... 93

5.5.2 Approach ...................................................................................................................... 93

5.5.3 Results .......................................................................................................................... 94

Chapter 6: Computational Fluid Dynamics of the Clark Y-14 Airfoil ........................................ 98

6.1 Grids .................................................................................................................................... 98

6.2 Setup ................................................................................................................................. 100

6.3 Results ............................................................................................................................... 101

6.4 Discussion ......................................................................................................................... 111

Chapter 7: Conclusion................................................................................................................ 112

Works Cited ................................................................................................................................ 113

Appendix A ................................................................................................................................. 115

Appendix B ..................................................................................................................................... 1

x

2D Airfoil Data (Pressure) .......................................................................................................... 1

2D Airfoil Calculations ............................................................................................................. 59

Appendix C ................................................................................................................................... 71

3D Wing Data ........................................................................................................................... 71

3D Wing Calculations ............................................................................................................... 89

1

List of Figures

Figure 1.1 - Benjamin Robins�’ Whirling Arm .......................................................................8

Figure 1.2 - Example of open-circuit wind-tunnel .................................................................11

Figure 1.3 - Example of closed-circuit wind-tunnel ..............................................................12

Figure 1.4a - Example of model maintained on the centerline of test section .......................13

Figure 1.4b - Example of model mounted on test section wall .............................................14

Figure 1.5 - Example of 3D image system utilizing lifting line and a pair

of trailing vortices ..............................................................................................15

Figure 1.6 - Shape factor to determine ...............................................................................18

Figure 2.1 - Early patented airfoil shapes by H.F. Phillips31 ................................................21

Figure 2.2 - Airfoil Nomenclature .........................................................................................24

Figure 2.3 - Clark Y Airfoil ...................................................................................................25

Figure 2.4 - Aerodynamic Forces ..........................................................................................27

Figure 2.5 - Pressure distribution over an airfoil ...................................................................30

Figure 2.6 - Control volume on a 2D body ............................................................................31

Figure 2.7 - Schematic of Forces on Sting balance ...............................................................31

Figure 3.1 - AEROLAB Educational Wind Tunnel ...............................................................33

Figure 3.2 - AEROLAB Wind Tunnel Test Section ..............................................................34

Figure 3.3 - Clark Y-14 Airfoil ..............................................................................................36

Figure 3.4 - Clark Y-14 Wing with and without Flaps and slats deployed ...........................36

Figure 4.1 - Cross-sectional area in percentage of length ......................................................38

Figure 4.2 �– Static Pressure Gradient in the test section for a velocity of 6.5 MPH .............39

2

Figure 4.3 - Body shape factor for different shapes...............................................................40

Figure 4.4 - Plot of thickness ratios for a category of airfoils vs. ......................................41

Figure 4.5 �– Laminar and turbulent boundary layer over a flat plate ....................................42

Figure 4.6 �– Test section diagram for calculation of P2 and V2 .............................................44

Figure 4.7 �– Effective cross-sectional exit area of the test section with the boundary layer

displacement removed ........................................................................................45

Figure 4.8 �– Effective cross-sectional area at exit of test section for various airspeeds ........46

Figure 4.9 - Static pressure gradient through the test section from 0 to 334 ....................47

Figure 4.10 - 2D Buoyancy Correction for 0 �– 334 .........................................................48

Figure 4.11 �– Plot of vs. Fineness ratio ..........................................................................50

Figure 4.12 �– Model volume plotted with airfoil angle attack ..............................................53

Figure 4.13a �– Solid Blockage for the Clark Y-14 for M < .3 ...............................................53

Figure 4.13b �– Solid Blockage for the Clark Y-14 for V <90 ft/sec .....................................54

Figure 4.14: Diagram of the velocity profiles in a test section with wake ............................55

Figure 4.15 �– �“Wake�” rake behind the Clark Y-14 airfoil .....................................................57

Figure 4.16 �– Profile of wake at 6.5MPH ..............................................................................59

Figure 4.17 �– Profile of wake at 30 MPH ..............................................................................60

Figure 4.18 �– Profile of wake at 68 MPH ..............................................................................61

Figure 4.19 �– Plot of the coefficient of drag vs. angle of attack ............................................62

Figure 4.20 �– Plot of the wake blockage vs. angle of attack .................................................62

Figure 4.21 �– Image system needed for the streamline curvature correction ........................64

Figure 4.22 �– Translation of moment to quarter-chord point on the Clark Y-14 ..................67

3

Figure 4.23 �– Plot of Cl vs. uncorrected angle of attack .....................................................69

Figure 4.24 �– Plot of mc/4 vs. uncorrected angle of attack ..................................................69

Figure 4.25 �– Plot of L' vs. uncorrected angle of attack ......................................................70

Figure 4.26 �– Plot of vs. uncorrected angle of attack .......................................................70

Figure 4.27�– Plot of corrected Cl vs. uncorrected angle of attack .........................................71

Figure 4.28 �– Plot of corrected angle of attack vs. uncorrected angle of attack ....................71

Figure 4.29 �– Plot of corrected coefficient of moment vs. uncorrected angle of attack ........72

Figure 5.1 �– Values of vs. fineness ratio ..........................................................................75

Figure 5.2 �– Plot of the buoyancy correction vs. the test section airspeed ............................76

Figure 5.3 �– Plot of the solid blockage for the Clark Y-14 wing ...........................................78

Figure 5.4 �– Values of K3 and K3 for a number of bodies .....................................................80

Figure 5.5 �– Plot of the angle of attack vs. the coefficient of drag ........................................81

Figure 5.6 �– Plot of the angle of attack vs. wake blockage ...................................................81

Figure 5.7 - The effects of downwash on a finite wing to produce induced drag .................83

Figure 5.8 - Single vortex arrangement for simulation with vertical boundaries ..................84

Figure 5.9 - Vortex image system for the horizontal simulation of wing in a rectangular test

section .................................................................................................................85

Figure 5.10 - Vortex image system for the vertical simulation of wing in a rectangular test

section .................................................................................................................86

Figure 5.11 �– Vortices image setup to calculate the induced velocity ...................................87

Figure 5.12 �– Plot of vs. the u .........................................................................................89

Figure 5.13 �– Plot of cdi vs. the u .......................................................................................89

Figure 5.14 �– Wing lift slope curves for 6.5 MPH ................................................................91

4

Figure 5.15 �– Wing lift slope curves for 30 MPH .................................................................92

Figure 5.16 �– Wing lift slope curves for 68 MPH .................................................................92

Figure 5.14 �– Wing lift slope curves for 102 MPH ...............................................................93

Figure 5.18 �– Plot of the change in the angle of attack vs. uncorrected angle of attack ........93

Figure 5.19 �– Plot of the change in coefficient of lift vs. uncorrected angle of attack ..........94

Figure 5.20 �– Plot of the change in moment coefficient vs. uncorrected angle of attack ......94

Figure 6.1 �– Orthogonal grid around the Clark Y-14 Airfoil ................................................95

Figure 6.2 �– Free flight grid with 5 sub-domains for the Clark Y-14 ....................................96

Figure 6.3 �– Grid modeling the flow inside the wind-tunnel with the Clark Y-14 ................97

Figure 6.4 �– CFD Results for the Clark Y-14 at -4 aoa .........................................................98

Figure 6.5 �– CFD Results for the Clark Y-14 at 0 aoa ..........................................................98



Figure 6.8 �– CFD Results for the Clark Y-14 at 12 aoa ........................................................100

Figure 6.9 �– CFD Results for the Clark Y-14 at 16 aoa ........................................................100

Figure 6.10 �–Plot of the Cp over the Clark Y-14 at -4 aoa .....................................................101

Figure 6.11 �–Plot of the Cp over the Clark Y-14 at 0 aoa ......................................................101



Figure 6.14 �–Plot of the Cp over the Clark Y-14 at 12 aoa ....................................................103

Figure 6.15 �–Plot of the Cp over the Clark Y-14 at 16 aoa ....................................................103

Figure 6.16 �– Plot of the Cl at a velocity of 44 ft/sec comparing uncorrected, corrected, expected

and CFD results ..................................................................................................104

5

Figure 6.17 �– Plot of the Cl at a velocity of 99.73 ft/sec comparing uncorrected, corrected,

expected and CFD results ...................................................................................104


expected and CFD results ...................................................................................105

Figure 6.19 �– Streamlines over the Clark Y-14 at -4 aoa ......................................................105

Figure 6.20 �– Streamlines over the Clark Y-14 at 0 aoa ........................................................106



Figure 6.23 �– Streamlines over the Clark Y-14 at 12 aoa ......................................................108

Figure 6.24 �– Streamlines over the Clark Y-14 at 16 aoa ......................................................108

6

List of Variables

Abbreviation Description

c Chord

h Test Section Height

S Planform Area

DB Change in Drag due to Buoyancy

Body Shape Factor

t Body Thickness

LE Leading Edge

TE Trailing Edge

Induced velocity

eff Effective Angle of Attack

i Induced Angle of Attack

i Change in Induced Angle of Attack

Angle of Attack

c Corrected Angle of Attack

u Uncorrected Angle of Attack

cd Coefficient of Drag for an Airfoil

cdu Uncorrected Coefficient of Drag for an Airfoil

cdc Corrected Coefficient of Drag for an Airfoil

cd0 Coefficient of Drag at 0 Lift Condition

CD Coefficient of Drag for a Wing

CDu Uncorrected Coefficient of Drag for a Wing

7

CDc Corrected Coefficient of Drag for a Wing

CDi Coefficient of Induced Drag

CDi Change in the Coefficient of Induced Drag

Cl Coefficient of Lift for an Airfoil

Clu Uncorrected Coefficient of Lift for an Airfoil

Clc Corrected Coefficient of Lift for an Airfoil

CL Coefficient of Lift for a Wing

CLu Uncorrected Coefficient of Lift for a Wing

CLc Corrected Coefficient of Lift for a Wing

Re Reynolds Number

Reu Uncorrected Reynolds Number

Rec Corrected Reynolds Number

Recr Critical Reynolds Number

Cm Moment Coefficient for an Airfoil

Cmu Uncorrected Moment Coefficient for an Airfoil

Cmc Corrected Moment Coefficient for an Airfoil

Cm c Corrected Moment Coefficient for an Airfoil at Chord

Cm u Uncorrected Moment Coefficient for an Airfoil at Chord

CM Moment Coefficient for a Wing

CMu Uncorrected Moment Coefficient for a Wing

CMc Corrected Moment Coefficient for a Wing

N Normal Force

A Axial Force

8

CN Normal Force Coefficient

Cp Pressure Coefficient

Cpu Uncorrected Pressure Coefficient

Cpc Corrected Pressure Coefficient

q Dynamic Pressure

qu Uncorrected Dynamic Pressure

qc Corrected Dynamic Pressure

Pt Total Pressure

P Pressure

Ps Static Pressure

P Freestream Pressure

Vortex Strength

M Pitching Moment

Mu Pitching Moment on Upper Surface

Ml Pitching Moment on Lower Surface

Density

V Velocity

V Freestream Velocity

Vu Uncorrected Velocity

Vc Corrected Velocity

B Tunnel Width

b Wing Span

r Vortex Spacing

9

Change in Induced Velocity

a Cylinder Radius

u Local Velocity

C Test Section Cross-sectional Area

Boundary Layer Thickness

* Boundary Layer Displacement

Turbulent Boundary Layer Displacement

Laminar Boundary Layer Displacement

Static Pressure Curve Slope

Wing Lift Curve Slope

Sx Airfoil Cross-Sectional Area

l Length of Leading Edge

2 Body Shape for 2D Bodies

3 Body Shape for 3D Bodies

Doublet Strength

ltc Length of Test Section

Fineness Ratio

P0 Initial Pressure

xcr Distance where the flow transitions

cmodel Model Chord

vmodel Model Volume

sb Solid Blockage

wb Wake Blockage

10

total Total Blockage

Q Mass Flow Rate

hs Spacing between sources

Yw Wake Width

v Induced Velocity in the Vertical Direction

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Cayley used a whirling arm that could produce velocities of 10 to 20 feet per second but was not

modified in any way to correct for the model going through its own wake. (Theodorsen, 1933)

Over the years since Robins�’ first whirling arm, they had gotten bigger and able to produce faster

velocities to the point that researchers were able to obtain tip velocities in excess of 100 mph.

Since the times of Leonardo da Vinci and Sir Isaac Newton as well as Benjamin Robins and Sir

George Cayley, engineers realized that there was a need for a device to create and maintain a

steady, controllable flow of air. It wasn�’t till the 1870�’s that the Aeronautical Society of Great

Britain began development of the first enclosed wind tunnel that could maintain a steady,

controlled air flow. The society invented, designed and operated with the help of Francis Herbert

Wenham, who is credited with many aeronautical fundamental discoveries including the

measurement of lift-to-drag ratios and the importance of a high aspect ratio. (NASA,2005) Along

with other experiments that were completed using the new technology, Osborne Reynolds

demonstrated that the airflow pattern over a scale model would be the same as for a full-scale

model if certain parameters were the same with the scaled and full�–scale model. The flow

parameter became known as the Reynolds Number which is a description for all fluid-flow

situations, including the shapes of flow pattern, the ease of heat transfer and the onset of

turbulence. However there are limitations on the conditions in which dynamic similarity are

based upon the Reynolds Number alone. (Theodorsen, 1933) With the advent of the Reynolds

Number, the wind-tunnel became a more powerful research tool which allowed the Wright

brothers to test their variously designed airfoils which revolutionized manned flight. Since the

Wright brothers, the use of wind-tunnels has exploded and the science of aerodynamics was

born.

13

Wind-tunnels are often limited to the volume and the speed of airflow which could be delivered

by the flow environment and power plant respectively. The wind-tunnels used by the Germans

during WWII are an interesting example of the difficulties associated with extending the useful

range of large wind-tunnels. To overcome the limit in volume that kept large wind-tunnels from

operating effectively, the Germans used caves which were excavated to be even larger to store

air which could be diverted to their wind-tunnels when needed. The caves allowed for an

increase in air volume which in turn allowed the research labs to explore the high-speed regimes

and greatly accelerated the number of aircraft advances that German held over the Allies. By the

end of the war, Germany had three different supersonic wind-tunnels that were able to sustain

velocities of Mach 4.4. (NASA, 2005) Since the time of the war, metal vessels which can hold

very high pressure and handle higher volumes of air where developed and are used as a substitute

to the German design. Later research focused on more powerful power plants, turbine blade

design, tunnel shape and test section design. Wind-tunnels and other types of tunnels were the

best aerodynamic research tool until computer power increased enough for the development of

CFD (Computational Fluid Dynamics) programs to take over for the expensively run wind-

tunnels. Even with CFD solvers being used, wind-tunnels still have their place in research today.

1.1.2 Wind-Tunnel Design

The design of wind-tunnels can be open-circuit or closed-circuit. Open-circuit tunnels (Figure

1.2) can also be �“suckdown�” or �“blower�” tunnels. A �“Suckdown�” tunnel is open to the

atmosphere (open-circuit) and has the axial fan or centrifugal blower downstream of the test

section which sucks the fluid through the test section. A �“Blower�” tunnel is also open to the

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solid blocka

moments at a

s usually neg

n closed test

wake blocka

ncreases the

sually neglig

n closed test

ncreased exc

- Example

peed Wind T

walls in the t

st section, a

ge�” and cau

a given angle

gligible since

sections, a l

age.�” The �“w

drag on the

gible since th

section, the

cessively, ma

of model m

Tunnel Testi

test section.

lateral const

ses an increa

e of attack. In

e the flow is

lateral constr

wake blockag

model. In an

he flow is al

angle of att

aking the tip

17

mounted on t

ing�”, the auth

The issues o

traint to the

ase of dynam

n an open te

allowed to e

raint to the f

ge�” effect inc

n open test s

llowed to exp

ack near the

p stall start ea

test section

hor produce

one needs to

flow pattern

mic pressure

est section, th

expand in a

flow pattern

creases the w

section, the e

pand in a no

e wingtips of

arly. The eff

wall. (NASA

s a list of iss

consider are

n about a bod

, increasing

he effect of �“

normal matt

about the w

wake size wh

effect of �“wa

ormal matter

f a model wi

fect of an op

A, 2005)

sues produce

e listed below

dy is known

all forces an

�“solid block

ter.

wake is know

hich in turn

ake blockage

r.

ith a large sp

pen jet is opp

ed by

w;

n as

nd

age�”

wn as

e�” is

pan is

posite

18

where the tips are unstalled. In both cases the effect is diminished to the point of

negligibility by keeping model span less than .8 of the tunnel width

An alteration to the normal curvature of the flow about a wing so that the wing moment

coefficient, wing lift and angle of attack are increased in a closed wind tunnel and is

decreased with an open jet.

The normal downwash is altered so that the measured lift and drag are in error. The

closed jet makes the lift too large and the drag too small at a given geometric angle of

attack. An open jet has just the opposite effect.

The normal downwash is altered so that behind the wing is the measured tail setting and static

stability are in error In a closed jet, the model has too much stability and an excessively high

wake location. In an open jet, the stability effect is large.

The normal flow pattern is altered so that the hinge moments are too large in a closed test

section and too small in an open test section.

The normal flow is altered about an asymmetrically loaded wing such that the boundary

effects become asymmetric and the observed rolling and yawing moments are in error.

The flow is altered by a thrusting propeller such that a given thrust occurs at a speed

lower than it would be in free-flowing air when in a closed test section. With the

propeller braking, the effect is opposite. Wake effects such as these are negligible when a

free jet is employed.

In most instances, corrections for all the above will not be used at once. With these corrections

listed above, extraneous corrections are needed due to wind tunnel design which includes

angularity of flow, local variations in velocity, tare, and interference.

19

1.1.4 Wall Effect Corrections

Wall effects that need to be corrected depend on the model that is placed in the tunnel. With an

airfoil spanning the test section, wall to wall, 2D wall effect corrections will be utilized. Other

shapes that are not considered 2D will employ 3D wall effect corrections.

A. The Method of Images

The method of images approach allows for the flow pattern about the wing to be closely

simulated mathematically by replacing the wing with a system of vortices composed of a lifting

line vortex and a pair of trailing vortices. (Theodorsen, 1933) Similarly, a solid body may be

represented by a source-sink system and a wake by source. The simulation of a course, sink,

doublet or vortex behind the boundary to be represented. �“Solid boundaries are formed by the

addition of an image system which produces a zero streamline matching the solid boundary.

Figure 1

An open

matches

test sectio

the corre

velocities

viscous f

correctly

(Gustafso

B. Buoya

Like the

the buoya

fuselage

1.5 - Examp

n boundary r

the boundary

on becomes

cted values f

s. In the boo

flow, that the

y. This will e

on and Sethi

ancy Correc

other correc

ancy correct

experiences

le of 3D ima

equires an im

y. (Pope, 19

a doubly inf

for the induc

ok written by

e normal bou

nsure you ha

ian, 1991)

ction

ction factors

tion is need f

significantly

age system u(P

mage system

84) After th

finite system

ced drag coe

y Gustafson,

undary cond

ave an accur

needed to an

for all parts

y higher dra

20

utilizing liftope, 1984)

m that produc

e image syst

m of vortices

efficient, ind

he discusses

dition for the

rate solution

nalyze the da

of an aircraf

ag due to buo

ting line and

ces a zero ve

tem is establ

. This metho

duced angle o

s the need, in

solid walls

n when calcu

ata returned

ft, especially

oyancy force

d a pair of t

elocity poten

lished, a clos

od can be us

of attack and

n both the in

to set the sy

ulating the co

from wind t

y the fuselag

e than a wing

trailing vort

ntial line whi

sed rectangu

ed to determ

d the induced

nviscid and

ystem of ima

orrection fac

tunnel testin

ge. While the

g or airfoil, t

tices.

ich

ular

mine

d

ages

ctors.

ng,

e

the

developm

immersed

the test s

between

buoyancy

where

Values o

provided

model be

mitigate

ment of the c

d body in a w

ection. In or

the test secti

y, and is def

f can be f

d as some pre

efore analysi

the buoyanc

F

correction fa

wind tunnel

rder to conse

ion walls an

fined (Hahn,

found in figu

essure. The h

is can comm

cy force that

Figure 1.6 -

ctor for a wi

test section,

erve mass, th

nd the flow n

2004) as

ure 1.6. The

horizontal bu

mence. Some

is projected

Shape facto

21

ing or airfoil

the flow wo

he flow there

near the test s

derivative o

uoyancy mu

wind tunnel

onto the bo

or to determ

l is still nece

ould like to e

efore must ac

section is ref

of pressure w

ust be subtrac

ls have sligh

dy in the flo

mine (Pop

essary. As th

expand beyo

ccelerate. Th

ferred to as h

with respect t

cted from the

htly expandin

ow field. (Po

pe, 1984)

he flow passe

ond the walls

his interactio

horizontal

to x was

e drag of the

ng walls to

ope, 1984)

es an

s of

on

(1.1)

(1.2)

e

22

C. Wake Blockage Corrections

Any real body without suction-type boundary layer control will have a wake behind it and this

wake will have a mean velocity lower than the free stream. The velocity outside the wake in a

closed tunnel must be higher than free stream in order that a constant volume of fluid may pass

through the test section. Maskell�’s theory of wake blockage in closed tunnels was originally

intended for use with aircraft models. The theory applies to large blockages arising in the testing

of bluff models, particularly those mounted on the floor. �“Maskell has derived expressions for

the correction of force and pressure coefficients measured in a closed wind tunnel on bluff

models subject to separated flow. For symmetrical models, normal to the wind direction, the

relationships given�” (Gould, 1970) are shown in equation 1.2.

(1.3)

These relationships are the key to developing the corrected values for wake blockage and can be

verified through experimental methods using a flat plate.

D. Solid Blockage Corrections

The presence of a model in the test section reduces the area through which the air can flow and

by continuity and Bernoulli�’s equation increases the velocity of the air as it flows over the

model. This increase of velocity is called solid blockage. �“Its effect is a function of model

thickness, thickness distribution, model size and is independent of the camber.�” (Herriot, 1950)

To determine the blockage correction for a symmetrical body at zero attack, it is only necessary

to consider only the basic profile of the airfoil. The wing can be represented by a series of finite

23

lines of sources and sinks. The lines will thin down at the extreme tip and the planform will not

be exactly rectangular. The actual wing is represented quite well by this method and enables a

calculation to be made of the induced velocity along the tunnel axis by images of the wing. The

velocity induced by the images which represents the effect of the tunnel walls on the velocity at

the model is known as the solid-blockage correction.

Chapte

2.1 Deve

The earli

Although

some sus

produce m

1884 afte

(were) pr

1933) Oc

experime

the differ

sustainin

(Theodor

er 2: Clark

elopment o

iest serious w

h it was know

spected that

more lift or

er testing the

roduced from

ctave Chanut

ents be made

rence betwee

ng effect betw

rsen, 1933)

Figure 2.1

k Y-14 Air

of Airfoils a

work on the

wn that flat p

shapes with

do so more e

em in one of

m induction b

te writes in

e on concavo

en success an

ween a plane

1 - Early pa

rfoil and W

and Wings

developmen

plates would

curvature, w

efficiently. H

f the earliest

by a steam j

1893, "...it s

o-convex sur

nd failure of

e surface and

atented airfo

24

Wing

nt of airfoil s

d produce lif

which more c

H.F. Phillips

wind tunnel

et in a wood

eems very d

rfaces of var

f a proposed

d one proper

oil shapes b

sections bega

ft when set a

closely resem

s patented a s

ls in which "

den trunk or

desirable that

rying shapes

d flying mach

rly curved to

by H.F. Phill

an in the late

at an angle of

mbled bird w

series of airf

"artificial cur

conduit." (T

t further scie

s, for it is not

hine will dep

o get a maxim

lips (CTIE,

e 1800's.

f incidence,

wings would

foil shapes in

rrents of air

Theodorsen,

entific

t impossible

pend upon th

mum of 'lift'.

2004)

d

n

e that

he

."

25

At nearly the same time, Otto Lilienthal had similar ideas. (Lilienthal, 2000) Lilienthal had a

clear interest in the physical basis of flight: He wanted to fly. He realized quickly and correctly

that the knowledge of his time was absolutely insufficient for his aim. So he put his main aim

aside for decades in order to concentrate on an extensive aerodynamic measurement program.

After more than 20 years of experiments in physics without a single practical attempt to fly,

Lilienthal summarized his knowledge in the book �“Bird flight as the basis of aviation�” in 1889.

Lilienthal describes the technique of flight as a stomping ground for amateurs, �“emotion-

mechanics�” and only a few specialists (Lilienthal, 2000). His book is for all of them. It is a

popular book about physics which guides in a clear line of thought to from Lilienthal�’ achieved

newest state of research. The book is still a standard for the research of bird flight today.

Lilienthal combined theoretical and technical skills and skills in craft and athletics in a very

special way which enabled him to become the first flying human. He worked out the theoretical

stock-in-trade for human flight, constructed a suitable flying apparatus and built it mostly by

himself. He had the physical constitution, courage and dexterity in order to test his flying

apparatus. He was designer and testing pilot in one person. So it was easier for him to improve

his construction during the testing period. The diversity of Lilienthal`s skills, the broadness of his

interests and his interdisciplinary approach are certainly essential reasons for his success.

No one equaled him in the power to draw new recruits to the cause; no one equaled him in

fullness and desire of understanding of the principles of flight; no one did so much to convince

the world of the advantages of curved wing surfaces; and no one did so much to transfer the

problem of human flight to the open air where it belonged.

As a missionary, he was wonderful. He presented the cause of human flight to his readers so

earnestly, so attractively, and so convincingly that it was difficult for anyone to resist the

26

temptation to make an attempt at it himself, �… he was without question the greatest of the

precursors, and the world owes to him a great debt. With these words in 1912, Wilbur

Wright described the man who was the most important influence on practical flying and flight

theory before the Wright brothers: the German engineer, Otto Lilienthal.

Airfoils used by the Wright Brothers closely resembled Lilienthal's sections: thin and highly

cambered. (Lilienthal, 2000) This was quite possibly because early tests of airfoil sections were

done at an extremely low Reynolds number, where such sections behave much better than

thicker ones. The erroneous belief that efficient airfoils had to be thin and highly cambered was

one reason that some of the first airplanes were biplanes. The use of such sections gradually

diminished over the next decade. A wide range of airfoils were developed, based primarily on

trial and error. Some of the more successful sections such as the Clark Y and Gottingen 398 were

used as the basis for a family of sections tested by the NACA in the early 1920's. (NASA, 2005)

In 1939, Eastman Jacobs at the NACA in Langley, designed and tested the first laminar flow

airfoil sections. These shapes had extremely low drag and the section shown here achieved a lift

to drag ratio of about 300. A modern laminar flow section, used on sailplanes, illustrates that the

concept is practical for some applications. It was not thought to be practical for many years after

Jacobs demonstrated it in the wind tunnel. Even now, the utility of the concept is not wholly

accepted and the "Laminar Flow True-Believers Club" meets each year at the homebuilt aircraft

fly-in. One of the reasons that modern airfoils look quite different from one another and

designers have not settled on the one best airfoil is that the flow conditions and design goals

change from one application to the next. On the right are some airfoils designed for low

Reynolds numbers. Unusual airfoil design constraints can sometimes arise, leading to some

unconventional shapes. The airfoil here was designed for an ultra-light sailplane requiring very

high max

solution:

Today, a

commerc

can be in

transfer a

economy

main con

for subso

design ph

skin frict

Different

(TE), thic

2.2 Deve

Clark Y-

purpose a

designed

ximum lift co

a variable g

irfoils are co

cial, military

ncreased to e

at high speed

y at specific o

nsideration in

onic, transon

hilosophies (

tion drag and

t airfoils are

ckness (t), ch

elopment o

14 is the nam

aircraft desig

d in 1922 by

oefficients w

geometry airf

ontinuously r

y, and scienti

nable lower

ds. In these a

operating co

n airfoil desi

nic, superson

(John. D. An

d low speed

defined by v

hord (c), and

Figure 2.

of the Clark

me of a parti

gns, and muc

Virginius E.

with small pi

foil with flex

re-evaluated

ific applicati

speed flight

applications,

onditions def

ign is the rel

nic, and hype

nderson). Hi

airfoils will

various para

d camber, as

2 - Airfoil N

k Y-14

icular airfoil

ch studied in

. Clark. The

27

itching mom

xible lower s

d in order to

ions. Drag ca

t; profiles ca

, airfoils are

fined by altit

lative velocit

ersonic flow

gh speed air

tend to have

ameters such

s seen in Figu

Nomenclatu

l profile, wid

n aerodynam

airfoil has a

ments at high

surface.

meet the gro

an be reduce

an be redesig

optimized f

tude, temper

ty of the airf

conditions e

rfoils may ha

e more camb

h as leading e

ure 2.2.

ure (NASA,

dely used in

mics over the

a thickness o

speed. One

owing deman

ed to save on

gned to accom

for performan

rature, and v

foil. For this

exhibit striki

ave less cam

ber in order t

edge (LE), tr

2005)

general

e years. The

of 11.7 perce

possible

nd in

n fuel costs;

mmodate he

nce and

velocity. The

s reason, airf

ingly differe

mber to reduc

to maximize

railing edge

profile was

ent and is fla

lift

eat

e

foils

ent

ce

e lift.

at on

the lower

on prope

appealing

The Lock

Clark Y h

ratio, and

optimal f

Louis and

2.3 Cha

The Clar

can be us

that its lo

angle of

low-spee

obtain 2D

In additio

Wing is m

directly.

r surface fro

llers, and ma

g thanks to i

kheed Vega

has been ade

d has gentle

from an aero

d the Piper C

aracterizing

rk Y-14 was

sed for its su

ower surface

attack direct

ed operating

D flow condi

on to the 2D

mounted to a

The data obt

m 30 percen

akes for easy

ts high camb

is one exam

equate; it giv

and relativel

odynamic per

Cub use the C

g the Clark

chosen for t

uperb control

e is parallel t

tly if needed

conditions. A

itions and pr

characteriza

a sting balan

tained from

nt of chord b

y constructio

ber, which p

Figure 2.3

mple of the C

ves reasonab

ly benign sta

rspective, an

Clark Y.

k Y-14

this project d

l at low Rey

o its chord, e

d. For this pro

A full airfoi

ressure distri

ation, a Clar

nce, in a hori

both the 2D

28

back. The fla

on of wings

produces a ve

3 - Clark Y A

lark Y used

ble overall pe

all characteri

nd it is rarely

due to the air

nolds numbe

enabling the

oject, the Cl

l is mounted

ibutions ove

rk Y-14 wing

izontal positi

D and 3D exp

at bottom sim

on a flat sur

ery good lift

Airfoil

in practice.

erformance i

ristics. But th

y used in new

rfoil being a

ers. An addi

e use of an in

lark Y-14 air

d vertically in

er the chord a

g is used for

ion, to meas

periments wi

mplifies angl

rface. The Cl

t-to-drag rati

For many ap

in respect of

he flat lower

w designs. T

a general pur

itional featur

nclinometer

rfoil is chara

n the SJSU w

as well as m

r 3D characte

sure the reac

ill be analyz

le measurem

lark Y is

io.

pplications t

f its lift-to-dr

r surface is s

The Spirit of

rpose design

re of this win

to change th

acterized und

wind tunnel

measure the w

erization. Th

tion forces

ed in order t

ments

the

rag

ub-

f St.

that

ng is

he

der

to

wake.

he

to

29

obtain values for the coefficients; CL, CD, CM and CN. Wind tunnel wall corrections for the SJSU

tunnel are combined with the test data to develop corrected data more similar to free space

conditions. These results will then be compared with the theoretical and excepted data values for

any given angle of attack. The analysis will be building a more rigorous model of the Clark Y-

14�’s behavior under low speed conditions.

2.3.1 Aerodynamic Forces

The aerodynamic forces acting on a body may be described by lift, drag and pitching moment.

Lift is the net vertical force and drag is the net horizontal force with respect to the direction of

motion. The pitching moment reflects the tendency of the airfoil or wing to pitch about a given

reference point. These quantities are derived from the normal force and axial force acting on the

airfoil by equations 2.1 and 2.2;

(2.1)

(2.2)

The normal force (N) is defined as the force perpendicular to the airfoil chord and the axial force

(A) that is acting parallel to the chord. It can be seen in the equations for the lift force ( and the

drag force ( are both derived from the same normal and axial force. However, the angle of

attack ( determines how much of the normal and axial forces transfer into the lift and how

transfer into the drag forces. The pitching moment may be expressed by an integral of the net

moments acting on the airfoil (Equation 2.3).

(2.3)

In Equati

integrate

shown in

2.3.2 Low

In low-sp

Mach .3

idealizati

density v

Another

effects th

assumpti

effect at

and this i

to be stea

to dynam

equation

ion 2.3, the d

d from the le

n Figure 2.4.

w-Speed Ae

peed flows, s

to help simp

ion of the flo

varies by onl

idealization

hat occur in a

on relies on

low Reynold

idealization

ady and the b

mic effects. T

(Equation 2

differential m

eading edge

Figure 2.4

erodynamic

several ideal

plify the fluid

ow is that de

y a few perc

is the flow i

any flow suc

having a hig

ds numbers.

is well supp

body forces

These idealiz

2.4), in the lo

moments are

to the trailin

- Aerodyna

s

lizations can

d dynamics a

ensity remain

cent from a v

is inviscid. I

ch as fraction

gher Reynol

These effec

orted by cur

acting on th

zed condition

ow-speed flo

30

e taken with

ng edge. A g

amic Forces

n be applied w

analysis. On

ns constant (

velocity rang

nviscid flow

n, thermal co

ds number b

cts are know

rrent theory.

he working fl

ns are suffici

ow analysis.

respect to a

graphical rep

s (Anderson

when the fre

ne assumptio

(no compres

ge of 0 to 30

ws are flows

onduction an

because visco

wn to be mini

(Anderson,

luid were as

ient to allow

given refere

presentation

n, 2007)

ee stream ve

on that can b

sibility of th

00 mph (And

that neglect

nd diffusion.

ous effects h

imal for low

2007) The f

sumed to be

w the use of B

ence and the

of these forc

elocity is und

be made from

he fluid) sinc

derson, 2007

the viscous

. Using this

have a signif

w-speed air fl

flow is assum

e minor comp

Bernoulli�’s

n

ces is

der

m the

ce the

)

ficant

lows

med

pared

31

Bernoulli�’s equation may also be derived from the momentum equation by considering a

differential control volume and applying the assumptions made previously. The resulting

equation shows that the sum of the local pressure (p) and the dynamic pressure (q), (Equation

2.5), is constant throughout a given flow. From this Equation, the local velocities may be

computed from knowledge of upstream data and local pressure so that all of the flow

characteristics may be obtained.

(2.4)

(2.5)

Effects of the wind tunnel walls may be ignored by applying the inviscid flow approximation. By

doing so, the flow may be assumed to be uniform except over the airfoil/wing. Uniform flow

simplifies the control volume analysis and allows the consideration of a full length airfoil as a 2D

profile. The assumption of uniform flow is justified due to the smooth wind, the filtered flow and

the controlled entry into the test section.

2.3.3 Characterizing Airfoil Performance

Airfoil performance may be characterized by quantities such as the lift, drag or pitching moment

produced under different operating conditions. These aerodynamic forces are often computed

from the total pressure over the planform area and are then normalized by the dynamic pressure

in order to produce non-dimensional quantities. For example, the lift, drag and normal

coefficients may be expressed as Equation 2.6, 2.7 and 2.8 respectively. The pitching moment

must also be normalized by the chord length in order to produce a non-dimensional moment

coefficient as in Equation 2.9.

(2.6)

32

(2.7)

(2.8)

(2.9)

(2.10)

These non-dimensional quantities are functions of the Reynolds number (Equation 2.10) and the

angle of attack. The Reynolds influence may be seen by the inclusion of the density ( and the

velocity ( terms while the angle of attack influence is implied through the force, moment and

area terms. Thus, in order to appreciate the full range of responses of a given airfoil, it is

necessary to consider a range of Reynolds numbers and angles of attack. Variation in the

Reynolds number produces different lift curves, while variations in the angle of attack will alter

the lift-drag ratio.

2.3.4 Characterizing Wing Performance

Wing performance can be characterized much the same way as an airfoil�’s performance.

2.4 Obtaining Airfoil Characteristics from Data

2.4.1 Airfoil control Volume Analysis

One method of obtaining the lift, drag and pitching moment coefficients of interest is to analyze

a control volume over the surface of the airfoil. In this method, localized pressure measurements

are taken in a plane in the chord wise direction on both the upper and lower surfaces to obtain a

pressure distribution. (Figure 2.5) The difference in the pressure distributions may then be

integrated in order to obtain an expression for the net pressure acting over the surface.

In the pre

represent

arrows to

pressure

leading e

by Berno

pressure

unaccoun

2.4.2 Tes

An altern

streamlin

volume,

Figu

essure distrib

ts a positive

o show negat

distribution

edge where t

oulli�’s equati

data fails to

nted for in th

st Section C

native metho

ne bounded c

it can be ded

ure 2.5 - Pre

bution show

gage pressu

tive gage pre

diagram. It

he velocity i

ion. Howeve

detect the ax

his method.

Control Volu

od of measur

control volum

duced that th

essure distri

wn in Figure 2

ure while the

essure. This

can be seen

is the highes

er, a limitatio

xial forces a

ume Analysi

ring drag for

me. By apply

he body with

33

ibution over

2.5, the arrow

upper press

is clarified i

that the norm

st. This obse

on of this arr

acting on the

is

rce is to perf

ying conserv

hin the contro

r an airfoil (

ws pointing

sure distribut

in the two pl

malized gag

rvation conf

rangement is

e airfoil and t

form a contro

vation of mo

ol volume co

(Pope, 1984

towards the

tion shows o

lots shown b

ge pressure is

firms the beh

s that the sum

the skin frict

ol volume an

omentum to

ontributed to

4)

e wingspan

outward poin

below the

s lowest near

havior predic

mmation of

tion is

nalysis over

this control

o a loss of

nting

r the

cted

a

momentu

shown in

shape du

produced

end of th

pressure

consideri

arrangem

were not

2.4.3 Wi

A more r

mounted

the axial

um. The effe

n Figure 2.6.

e to localize

Figu

d by the airfo

he control vo

measuremen

ing normaliz

ment will pro

measured an

ng Direct F

realistic meth

in the cente

and normal

ects may be v

The inlet flo

ed loss of mo

ure 2.6 - Co

oil and may b

lume. Altern

nts in the wa

zed pressure

ovide sufficie

nd thus lift a

Force Measu

hod of predi

er of the test

reaction for

visualized by

ow is uniform

omentum. Th

ontrol volum

be indirectly

natively, thro

ake may be u

was then us

ent data to ca

and moment

urement

cting airfoil

section. The

rce imposed

34

y marking th

m while the

his loss of m

me on a 2D b

y calculated

ough the use

used instead.

sed to solve f

alculate the

cannot be e

performanc

e 3D airfoil (

on the sting-

he inlet and o

outlet flow

momentum is

body (Ande

by solving t

e of Bernoul

. A non-dim

for the coeff

drag coeffic

valuated fro

ce is to consi

(wing) uses

-airfoil struc

outlet veloci

will have a n

s known as th

erson, 2007)

the velocity p

li�’s equation

mensional ana

ficient of dra

cient but diff

om this data.

ider a finite l

a sting balan

cture due to t

ity profiles a

non-uniform

he drag

)

profiles at ei

n, localized

alysis

ag. This type

ferential forc

length wings

nce that mea

the flow. Th

as

m

ither

e of

ces

span

asures

he

reduced c

width of

Figu

constraints a

the airfoil w

re 2.7: Sche

allow the airf

will allow rot

ematic of Fo

foil to respo

tational flow

35

orces on Stin

nd with the

w over the sid

ng balance

full six degr

des of the wi

(Pope, 1984

rees of freed

ing.

4)

om and the ffinite

Chapte

3.1 Gen

The San

specifica

tunnel wi

used to o

The max

infinite a

fiberglas

rotationa

10HP mo

The tunn

test sectio

contracti

tunnel to

er 3: AERO

eral AERO

Jose State U

ally made for

ith a 12x12x

obtain a varie

Figure 3.

imum veloc

adjustability

s. The blade

al speed in th

otor which is

nel ductings a

on, the diffu

on contour.

achieve hig

OLAB Lo

OLAB Win

University wi

r the educati

x12-inch test

ety of aerody

.1 - AEROL

ity that can b

above 10 mp

es are rated to

he wind tunn

s controlled

are compose

user and then

The contract

gh performan

ow-Speed W

nd Tunnel S

ind tunnel (F

onal environ

t section whe

ynamics data

LAB Educat

be created is

ph with the 9

o a maximum

nel is 2345 rp

by heavy-du

ed of four ma

n fan housing

tion ratio (in

nce and low

36

Wind Tun

Specificatio

Figure 3.1) w

nment. The w

ere a force b

a.

tional Wind

s around 145

9 blade fan w

m rotational

pm. The fan

uty variable f

ajor duct com

g. A propriet

nlet area to o

turbulence l

nnel

ons

was designed

wind tunnel

balance or tab

d Tunnel (A

5 mph with a

which is con

speed of 34

is mounted

frequency dr

mponents wh

tary 9th-orde

outlet area) i

level at low s

d by AEROL

is an open c

ble mounted

AEROLAB,

a clear chann

nstructed of r

437 rpm but m

directly to th

rive.

which are the

er polynomia

s 9.5:1 whic

speeds. Alon

LAB and is

circuit or �“Ei

d models can

2007)

nel with near

reinforced-

maximum

he shaft of a

contraction,

al defines the

ch allows the

ng with the

iffel�”

n be

r-

a

, the

e

e

contracti

area) help

2007). An

uses hexa

hexagona

turbulenc

0.009 inc

smaller ed

eddies.

3.2 Test

The test s

with dive

diverging

layer thic

The test s

mounted

on ratio, the

ps eliminate d

nother contri

agonal matrix

al matrixes do

ce-reducing s

ch stainless st

ddies by the

t Section an

section of th

erging walls

g walls mitig

ckness.

Figure 3.

section is als

to the floor

shallow-ang

diffuser effec

ibuting factor

xes which are

o little to elim

creens imme

teel wire spac

screens. Com

nd Instrum

he AEROLA

that diverge

gate the test

.2 - AEROL

so equipped

of the test se

gle (6º total-i

cts especially

r to the high p

e 4 inches lon

minate small

ediately down

ced at 20 wir

mparatively s

mentation

AB wind tunn

e 0.0625 inch

section buoy

LAB Wind T

with a manu

ection usual

37

included dive

y when large

performance

ng and .25 in

eddies, altho

nstream of th

res per inch.

speaking, sm

nel is 12x12x

hes from the

yancy effect

Tunnel Test

ually-operate

ly for pressu

ergence angl

models are b

e of this tunne

nches wide to

ough the tunn

he hexagonal

Small eddies

maller eddies d

x12-inch (Fi

e test section

resulting fro

t Section (A

ed yaw table

ure models. T

le based on c

being tested (

el is that flow

o straighten th

nel is equipp

l matrixes. Th

s in the air ar

dissipate fast

igure 3.2) an

n inlet to the

om the grow

AEROLAB,

e for models

These mode

ross sectiona

(AEROLAB

w conditionin

he flow. The

ed with two

hey are made

re broken into

ter than large

nd is equippe

outlet. The

wing boundar

2007)

needing to b

ls can be

al

,

ng

e

e of

o yet

er

ed

ry

be

38

connected to a 24-tube multi-manometer that does not require the DAC or to the two solid-state

differential pressure transducers. When using the 24-tube multi-manometer, it only required reading

of the change of pressure from the tubes manually. The vertical glass tubes provide pressure

measurement as well as visualization. Along the bottom, these tubes connect to an anodized

aluminum reservoir. The reservoir remains at atmospheric pressure because the lid does not make a

perfect seal. To use models that require pressure transducers, a data acquisition (DAC) system is

supplied and is used with the pressure transducers and the sting balance. Also, there is a �“sting�”

Force/Moment Balance that is mounted to the top of the MPS (Motion Positioning System)

vertical arms. The wind tunnel�’s three-component sting balance is mounted on a parallelogram-

type model positioning system. The model positioning system was designed specifically for the

EWT sting balance. It was dimensioned such that changes in pitch angle have little effect on

model height �– the forward tip of the balance remains essentially stationary as pitch angle is

changed, therefore keeping the test model centered in the airflow. The pitch angle range is +/-

20°. Prior to shipment, the balance was calibrated (first order only) at AEROLAB.

The maximum load ranges are:

Normal Force (Side Force): 25 lbs. (111.2 N) Axial Force: 10 lbs. (44.5 N) Pitching Moment (Yawing Moment): 50 inch-lbs. (5.65 N-m) The use of the DAC is controlled by a program written in LabVIEW to control all tunnel

functions. This program is connected and used to control the two solid-state differential pressure

transducers and a three-component sting Force/Moment balance.

3.3 Clar

The wind

correctio

3.3) is m

pressure

multi-man

recorded

The Clar

and flaps

and has a

configura

Figur

rk Y-14 Air

d tunnel com

n factors for

ounted verti

tabs are con

nometer. For

through Lab

rk Y-14 wing

s for a wide v

a span of 3.5

ation which

re 3.4 - Clar

rfoil and W

mes with a va

r the wind tu

ically to the y

nnected to the

r this project,

VIEW.

Figure 3.3

g (Figure 3.4

variety of ex

5 inches. For

entails the s

rk Y-14 Win

Wing Mode

ariety of mod

unnel were th

yaw table an

e pressure tr

, the pressure

- Clark Y-1

4) can be mo

xperiments th

r the purpose

lats and flap

ng with and

39

els

dels but the t

he Clark Y-1

nd spans the

ransducer arr

e tabs are con

14 Airfoil (A

ounted on sti

hat can be pe

e of this proj

ps being left

without Fla2007)

two models

14 airfoil and

test section.

ray or can be

nnected to th

AEROLAB

ing balance o

erformed. Th

ect, the wing

un-deployed

aps and slat

used to deve

d wing. The

. The 18 flus

e connected

he DAC to ha

B, 2007)

only and has

he wing is 9

g will be left

d.

ts deployed

elop the

Airfoil (Fig

sh-mounted

to the 24-tub

ave the test ru

s adjustable s

9.875 inches

ft in a clean

(AEROLA

gure

be

uns

slats

long

B,

40

Chapter 4: Two-Dimensional Wall Corrections for the Clark Y-14 Airfoil

For an airfoil, there are several corrections that need to be performed to more accurately model

free-flight conditions. The four main wall corrections for an airfoil are buoyance, wake

blockage, solid blockage and streamline curvature. The buoyance corrections will have an

additive component to the drag force while the wake and solid blockage component are

dimensionless but are used in the correction for the streamline curvature. The streamline

curvature corrections are the most important for correcting airfoil data corrections for , cL,

cm and includes the parameters; Vc, qc, Rec, c, clc, cm c and cd0. The velocities tested in the

wind-tunnel are 6.5, 30, 68 and 102 MPH and the Reynolds numbers are 100,000, 500,000,

1,200,000 and 1,800,000 respectively. Data and calculations for this chapter can be found in

Appendix B

4.1 Buoyancy Correction

4.1.1 Theory

Closed-throat wind-tunnels have a variation of static pressure along the axis of the test section.

The variation of static pressure is due to a thickening of the boundary layer as the flow

progresses through the test section. As the flow approaches the end of the test section, the

pressure progressively becomes more negative. With the pressure turning more negative down

the length of the test section, the model tends to be sucked down the test section. The amount of

buoyancy is usually insignificant for wings and airfoils but the correction becomes more

important for fuselages and nacelles. The buoyancy corrections can be applied in the two-

dimensional or three-dimensional space. For the two-dimensional case, the cross-section area is

41

shown in figure 4.1 and the static pressure variation along the test section length is graphed in

figure 4.2 as an example. It should be noted that for every velocity change, the static pressure

gradient through the test section will change. The static pressure can be determined

experimentally by measuring the pressure distribution over the airfoil or wing or by utilizing

equation 4.1 to determine the slope.

(4.1)

Figure 4.1 - Cross-sectional area in percentage of length

42

Figure 4.2 �– Static Pressure Gradient in the test section for a velocity of 6.5 MPH

Wind tunnel designers employ slanted vertical walls along the test section length to mitigate the

effects of the buoyancy force on the model. The walls slightly widen from the narrowest point at

the mouth of the test section and opens to a determined width through calculations and then

verification of the results to ensure the test section exit has not over expanded.

4.1.2 Approach

It can be seen that the variation of the static pressure in figure 4.2 from any two given station

along the airfoil is linear and therefore the pressure differential acts on the average area. The

resulting drag force for that segment of the airfoil is

(4.2)

Equation 4.2 can be solved by plotting the local static pressure against the cross-section area as

in figure 4.2 and the area under the curve is found to be the buoyancy. If the static pressure

gradient is a straight line, equation 4.2 simplifies to

(4.3)

1.9

1.92

1.94

1.96

1.98

2

2.02

0 2 4 6 8 10 12

Pressure

(lb/ft2)

Distance through Test Section (inches)

Graphing

can be ill

approach

The sque

gradient

where

shape,

,

where

5.4.

g the static p

lustrated by

h the end of t

eezing effect

effect. The t

can be foun

can be de

becomes

Figur

pressure grad

viewing stre

the test secti

t should be a

total drag inc

nd from figur

etermined ea

s

;

re 4.3 - Body

dient shows t

eamlines tran

ion, they are

accounted for

crement per

re 4.3. Witho

asier by repl

y shape fact

43

that the test

nsiting down

closer toget

r in the corre

span length

out experime

acing w

tor for diffe

section is ef

n the test-sec

ther than wh

ected equati

with the inc

ental data to

with . W

, can also

erent shapes

ffectively shr

ction. As the

hen entering

on and adde

cluded squee

find the val

With the sub

o be determin

s (Pope, 198

rinking and t

e streamlines

the test secti

ed to the pres

ezing effect i

lues for the b

stitution of

ned by Figur

84)

this

s

ion.

ssure

is

(4.4)

body

(4.5)

re

Fi

A more r

Bernoull

using Be

the veloc

then dete

To begin

plate, wh

flow is co

Reynolds

igure 4.4 - P

rigorous app

i�’s and conti

rnoulli�’s equ

city and pres

ermined at th

n, the Rec wil

hich taking o

onsidered to

s number for

Plot of thick

roach is nec

inuity equati

uation (Equa

sure at the e

he test sectio

ll need to be

one side of th

o be laminar

r a length is

kness ratios

essary if the

ions are need

ation 4.6) an

entrance of th

on entrance a

determined

he test sectio

and for Re >

found by

44

for a catego

e pressure gr

ded. The pre

d the continu

he wind tunn

and exit.

for a given

on can be ass

> 500,000, th

ory of airfoi

radient is not

essure gradie

uity equation

nel. The velo

for the ex

sumed, is 50

he flow is co

,

ils vs. (Po

t given wher

ent can be de

n (Equation

ocity and pre

xperiment. R

00,000. For R

onsidered to

ope, 1984)

re the use of

etermined by

4.7) by know

essure can be

Recr for a flat

Re < 500,000

be turbulent

f the

y

wing

e

(4.6)

(4.7)

t

0, the

t. The

(4.8)

Once the

laminar o

layer disp

The exit

the exit. T

boundary

For the c

found to

Figure

The trans

e Reynolds n

or turbulent c

placement ca

velocity is n

The cross-se

y layer displa

ase where fl

determine th

4.5 �– Lami

sition point,

number is fou

can be made

an be found

needed at the

ectional area

acement has

low turns tur

he boundary

nar and tur

xcr, is determ

und for the t

e. If the flow

directly from

e test section

a is dependen

s been found

rbulent befor

y layer displa

rbulent boun

mined by usi

45

est section le

w is laminar t

m

n exit which

nt on the bou

d, the effectiv

re exiting th

acement. (Fig

ndary layer

ing the critic

ength, the de

the test secti

depends on

undary layer

ve area at the

e test section

gure 4.3)

r over a flat

cal Reynolds

etermination

ion length, th

the cross-se

r displaceme

e exit can al

n, the xcr wil

t plate (CFD

s number for

n if the flow

he boundary

ctional area

ent. Since the

so be found

(

ll need to be

D Online, 20

r a flat plate

is

y

(4.9)

at

e

by

(4.10)

e

009)

in

46

(4.11)

With the transition point found, the laminar boundary layer displacement can be found at that

point by using equation 4.9. The laminar boundary layer displacement at the transition point can

also be assumed to be the thickness of the turbulent boundary layer displacement. With that

assumption,

(4.12)

Solving for xeq, the starting point of turbulent boundary layer can be found by subtracting xeq

from . Since the turbulent boundary layer start point has been identified, equation 4.12 can be

used to find the turbulent boundary layer displacement at the test section exit by replacing xeq in

the equation with the length of the turbulent boundary layer. Using equation 4.10 and replacing

with , the effective exit area can be found.

The test section exit area can now be used in equation 4.7 but the other parameters also need to

be found. Some assumptions need to be made to simplify the problem 1) by ignoring the losses

through the contraction of the inlet of the test section, 2) ignoring the losses through the flow

screen at the wind-tunnel entrance, 3) assuming incompressible flow and the pressure at the

entrance of the test section is actually lower than the pressure calculated at the test section

entrance. The known parameters for equation 4.6 are which are assumed to be

STD and is 0 .

Since the

utilized t

since it is

but unkn

cross-sec

determin

found is P

calculate

Figu

e boundary c

o find P1 at s

s measured a

own for stat

ctional area t

ning the boun

P2 which can

d, the longit

ure 4.6 �– Tes

conditions at

station 1 but

at station 1 w

tion 2. V2 at

that was calc

ndary layer d

n be easily c

tudinal static

st section di

t the entrance

t realize P1 is

with the DAC

station 2 wil

culated for se

displacement

calculated by

c pressure gr

47

iagram for c

e of the wind

s actually les

C. All variab

ll need to be

ection 2, the

t. (Figure 4.7

y equation 4.

radient can b

calculation

d-tunnel are

ss than P1. (F

bles are now

calculated b

e test section

7) The last v

.6. Once all s

be found for

of P2 and V

known, equ

Figure 4.6) V

w known for

by equation

n exit by the

variable that

six variables

any free-stre

V2

uation 4.6 ca

V1 is also kn

station 0 and

4.7 and the

process of

needs to be

s have been

eam velocity

an be

nown

d 1

y.

Figure

By using

This proc

A code to

excel file

applicatio

4.7 �– Effect

g the P1 and P

cess can be r

o complete t

e. Now that t

on of a simp

tive cross-se

P2, the longit

repeated as m

this task is sh

the pressure

plified equati

ectional exit

displace

tudinal static

many times a

hown in App

gradient thr

ion for the b

48

t area of the

ement remo

c pressure gr

as needed to

pendix A and

ough the tes

uoyancy cor

e test section

oved

radient is ca

o obtain a

d can be use

st section is k

rrection (Equ

n with the b

alculated by

curve for th

ed to output a

known, this

uation 4.14)

boundary la

(

he wind-tunn

a range of

allows for th

for an airfo

(

ayer

(4.13)

nel.

to

he

il.

(4.14)

49

4.1.3 Results

To determine the 2D buoyancy correction, the cross-sectional exit area of the test section is

shown in figure 4.8.

Figure 4.8 �– Effective cross-sectional area at exit of test section for various airspeeds

Equation 4.14 is used along with equation 4.6 and 4.6 to determine the static pressure gradient

through the test section (Figure 4.9).

0.88

0.90

0.92

0.94

0.96

0.98

1.00

0 50 100 150 200 250 300

EffectiveTestS

ectio

nExitArea,A

2eff(ft2 )

Test Section Airspeed, V (ft/sec)

50

Figure 4.9 - Static pressure gradient through the test section from 0 to 334

The airfoil has a model volume of .0068 ft3 by recreating an exact model of the airfoil in

SolidWorks. The 2D buoyancy correction, as shown on the chart below, was calculated for a

velocity range of 0 �– 334 and is plotted in figure 5.6. The maximum velocity plotted

corresponds to at sea level.

70.00

60.00

50.00

40.00

30.00

20.00

10.00

0.000 50 100 150 200 250 300

StaticPressure

Grad

ient

/(lb

/ft2)


51

Figure 4.10 - 2D Buoyancy Correction for 0 �– 334

4.1.4 Discussion

As seen in figure 4.10, the buoyancy drag contributes very little to the overall drag on the airfoil.

The largest amount of drag for what is considered �“low speed�” is approximately .9 lbs. per span

length and could be omitted from the wall corrections if a high degree of fidelity is not required.

With the assumptions that the boundary layer starts at station 1 in figure 4.6, this creates a certain

amount of error in the calculations. Since the boundary layer actually starts at the entrance of the

wind-tunnel, by the time the flow reaches the test section entrance, it could already be turbulent.

The assumption was made because the exact equation used to create the inlet is not known nor

the actually roughness of the inner surface. Also, the wind-tunnel has a flow straightening system

at the entrance. The entering air first passes through a matrix of parallel passages that are shaped as

a hexagonal matrix, like a �“honeycomb�”. The honeycomb cells are 4 inches long and serve to

straighten the flow �– to eliminate most flow angularity. The �“honeycomb�” matrix does little to

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300

2DBu

oyna

cyCo

rrectio

n,D b

(lbs)


52

eliminate small eddies and it is hard to account for these eddies which effects on the boundary layer

thickness. The tunnel is equipped with two turbulence-reducing screens immediately downstream of

the honeycomb and even though they help keep the flow straight, it is hard to calculate the screens

effects on the boundary layer.

The effective cross-sectional exit area of the test section is affected by the wind-tunnel inlet

conditions. The effective area is more susceptible to the inlet conditions at very low speeds as

seen in figure 4.8. At approximately 90 ft/sec, the test section exit turns from laminar to turbulent

which reduces the boundary layer displacement and which causes the pressure gradient slope to

decrease slightly. Once the flow turns turbulent in the test section, the effective cross-sectional

exit area stabilizes and at approximately 140 ft/sec, the area becomes equal to .9962 ft2 for M <

3.

4.2 Solid Blockage Correction

4.2.1 Theory

With a two-dimensional model in the test section, the flow is semi-blocked and the flow area is

reduced. In order for continuity and Bernoulli�’s equation to be satisfied, the flow must increase

in velocity to maintain the same mass flow rate through the test section. The increase of velocity

is considered solid blockage and is a function of model thickness, thickness distribution and

model size. The camber of the airfoil is independent of the solid blockage. �“The solid blockage

velocity increment at the model is much less (about ¼ ) than the increment one obtains from the

direct area reduction.�” (Pope, 1984) The streamlines furthest from the model are also impacted

by the increment velocity since they are displaced more due to the confines of the test section.

53

4.2.2 Approach

In solving solid-blockage problems, it is important to determine the axial velocity. One case to

examine is where a circular cylinder is placed into a two-dimensional test section. The circular

cylinder can be simulated as doublet of certain strength and is contained by an infinite vertical

series of doublets of the same strength. Using this simulation of doublets, the axial velocity can

be found by

(4.15)

Since the velocity produced by a doublet varies inversely with the square of the distance from the

doublet, then doubly infinite doublet series may be summed as

(4.16)

To use a 2-ft diameter cylinder in a tunnel that is 10-ft high would have a solid blockage that

would cause the flow velocity to be increased by 3.3% over the true free-stream velocity. In the

case of an airfoil, the solid-blockage velocity increment (Glauert, 1933) is show be

(4.17)

where values of can be found in figure 4.9. Another variation to determine the solid-blockage

on an air

(Allen an

where

two-dime

where

that is sp

foil is from a

nd Vincenti,

ensional tunn

is .74 for a

anning verti

Figure

a report that

1944). The

;

nel is given

wing spann

ically and a g

e 4.11 �– Plot

t uses some f

following re

. A simpler

by

ning the tunn

good approx

54

t of vs. F

factors assoc

esult is from

r equation fo

nel test sectio

ximation for

Fineness rati

ciated with th

their work w

or the solid-b

on horizonta

an airfoil m

io

he buoyancy

where

blockage cor

ally and is

model volume

y correction

(

rrection for a

(

s .52 for a sp

e is

(

(4.18)

a

(4.19)

pan

(4.20)

55

The approximation of the airfoil model volume is only appropriate at a 0 angle of attack. For

any other angle of attack, the model thickness becomes

(4.21)

where the .49 is the thickness of the airfoil due to the chord line of the Clark Y-14 being the

bottom edge of the airfoil. The model chord becomes

(4.22)

and the model span remains unaffected. The variable, C, can be used but if greater accuracy is

desired, the geometric area of the exit of the test section should be used less the boundary layer

displacement thickness around the perimeter. The boundary layer displacement can be calculated

by using the process in section 4.1. But if an approximation is adequate, the approximation of the

displacement thickness is .6 of the boundary layer thickness, since the boundary layer turns

turbulent at some point in the test section. The boundary layer thickness can be found by

(4.23)

For an example of boundary layer thicknesses, wind tunnels with the general size of 7x10-ft have

displacement thicknesses of inch.

4.2.3 Results

For the 2D solid blockage correction, equation 4.19 is used to determine the correction factor for

the solid blockage. Since the airfoil is mounted vertically in the wind tunnel, a value of .52

was used. C is the effective area at the exit of the test section and figure 4.8 can be used to find

the effective area for a plotted velocity. The model volume is estimated with equations 4.20,

4.21, 4.22 and is plotted in figure 4.12. With the model volume and test section exit effective

area

56

Figure 4.12 �– Model volume plotted with airfoil angle attack

calculated for angle of attacks from -4 to 16 degrees, the solid blockage is calculated and plotted

in figure 4.13a. A more detailed view of solid blockage curve is plotted in figure 4.13b.

Figure 4.13a �– Solid Blockage for the Clark Y-14 for M < .3

0.000

0.005

0.010

0.015

0.020

4 2 0 2 4 6 8 10 12 14 16

Mod

elVo

lume,v m

odel(ft

3 )

Airfoil Angle of Attack, (degrees)

0.0015

0.0035

0.0055

0.0075

0.0095

0.0115

0 50 100 150 200 250 300

2DSolid

Blockage,

sb


sb @0 aoa

sb @4 aoa

sb @4 aoa

sb @8 aoa

sb @12 aoa

sb @16 aoa

57

Figure 4.13b �– Solid Blockage for the Clark Y-14 for V <90 ft/sec

4.2.4 Discussion

The two-dimensional solid blockage is a dimensionless quantity and increases with angle of

attack as seen in figure 4.12 and 4.13. The plot shows the solid blockage at very low speeds

jumps dramatically but continues in a decreasing slope as the flow speed increases. At a velocity

of approximately 83 feet per second, the boundary layer turns turbulent at the exit of the test

section and causes the solid blockage to drop and stay flat for the remainder of the velocities

used in calculations.

A fundamental source of error in the solid blockage used in section 4.2.2 is the simulation of the

body by doublet system to develop the equations. It may be possible to circumvent the error if

the pressure at the tunnel wall is measured with the model in place and then with the model

0.0015

0.0035

0.0055

0.0075

0.0095

0.0115

0 10 20 30 40 50 60 70 80 90

2DSolid

Blockage,

sb


4 aoa

0 aoa

4 aoa

8 aoa

12 aoa

16 aoa

removed

used to c

AEROLA

to measu

lead to a

dependin

4.3 Wak

4.3.1 The

All bodie

not exem

higher th

test sectio

principle

layer gro

neglected

Figur

wake is t

. The resulta

ompute the r

AB wind tun

ure pressure.

reduction in

ng on tunnel

ke Blockag

eory

es create a w

mpt. The law

han the free s

on. (Figure 4

. Bernoulli�’s

owth along th

d for the case

re 4.14: Dia

toward the ax

ant velocity i

ratio betwee

nnel has two

When the p

n the solid bl

conditions.

ge Correctio

wake with the

of continuit

stream veloc

4.14) The ve

s principle st

he model ind

e of open top

agram of the

xial symmet

increment ca

en blockage a

holes in the

itot tube is n

lockage sinc

on

e fluid they a

ty states the v

city in order

elocity in the

tates that a p

duces a veloc

p and bottom

e velocity pr

try which pe

58

an be compu

at the wall a

e walls of the

not installed,

e pressure ca

are moving t

velocity outs

for a constan

e mainstream

pressure grad

city increme

m of the test

rofiles in a t

rmits a singl

uted and the

and at the tun

e test section

, the holes ar

an be natura

through and

side the wak

nt volume of

m will be hig

dient derived

ent on the mo

section. The

test section

le correction

image syste

nnel centerli

n used for pit

re left open a

ally increased

bodies in w

ke in a closed

f fluid to flo

gher due to B

d because of

odel. Wake b

e natural ten

with wake.

n.

m theory can

ne. The

tot tube inse

and can actu

d or decreas

wind tunnels a

d tunnel mus

ow through th

Bernoulli�’s

f the boundar

blockage ma

ndency for th

(Pope, 1984

n be

ertion

ually

ed

are

st be

he

ry

ay be

he

4)

59

4.3.2 Approach

In order to calculate the wake effect due to the model, we must first simulate the wake and the

tunnel boundaries. For the two-dimensional case, a line source is needed to be placed at the

wing�’s trailing edge with some hypothetical different colored fluid which can mark the wake

region. The region to be emitted (Q) may be determined by

(4.24)

To preserve continuity, a sink must be placed at least 4 body lengths downstream. This

simulation of the wake must be contained between the upper and lower surface of the test section

walls by an infinite vertical row of sink-source combinations. The sources will not produce an

axial velocity on the model but the sinks will induce a horizontal velocity in the amount of

(4.25)

where hs is the spacing between sources. The one-half in equation 4.25 is due to half of the sink

velocity increment will be felt upstream and downstream. The incremental velocity is produced

at the model due to the walls and it should be added to the measured velocity. A handy equation

for the incremental velocity is

(2.26)

where . Maskell�’s two-dimensional method calculates the wake blockages correction by

(2.27)

To be able to utilize equation 2.27, the must be known or be able to be calculated. One

method for calculating the is by

(2.28)

This met

measur

only th

total drag

drag. An

This m

when us

figure 4.

then conv

thod requires

red. The AE

he cp availabl

g. The shear

n alternate m

method does

sing only pre

.15. The �“wa

Fi

verted to dyn

s that the she

ROLAB win

le, only the p

r stresses on

method is to c

not have the

essure. To m

ake�” rake me

gure 4.15 �–

namic pressu

ear stresses f

nd-tunnel is

pressure drag

the surface o

calculate the

e additive co

measure the w

easures the p

�“Wake�” ra

ures by

60

from the upp

incapable of

g can be mea

of the airfoil

e from th

omponent of

wake, a �“wak

pressure acro

ake behind t

per and lowe

f measuring

asured which

l dominate th

he wake that

f skin friction

ke�” rake is p

oss 18 pressu

the Clark Y

er surfaces o

the shear str

h is a very sm

he additive c

is created b

n drag but is

laced behind

ure ports, the

Y-14 airfoil

of the airfoil

resses and w

mall part of

component o

ehind the air

(

more accur

d the airfoil

ese pressure

(

to be

with

the

of the

rfoil.

(2.29)

ate

as in

es are

(4.30)

61

Once the dynamic pressures across the rake have been calculated, a plot of the q is needed to

visually see where the wake is located. Taking the q�’s that are in the wake, apply equation 4.31

(4.31)

where the is the distance between the pressure ports to find the area under the curve for each

q value and the area can then be summed to satisfy the in equation 2.29. After the

integration has been completed, the rest of the equation becomes trivial to calculate the

4.3.3 Results

Figures 4.16 through 4.18 were plotted with the calculated data from using equation 2.29.

62

Figure 4.16 �– Profile of wake at 6.5MPH

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.30 0.20 0.10 0.00 0.10 0.20 0.30

Distna

ceon

wakerake,x

(ft)

Dynamic pressure, q (psf)

4 aoa

0 aoa

4 aoa

8 aoa

12 aoa

16 aoa

63

Figure 4.17 �– Profile of wake at 30 MPH

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

1 0 1 2 3 4 5

Distna

ceon

wakerake,x

(ft)


4 aoa

0 aoa

4 aoa

8 aoa

12 aoa

16 aoa

64

Figure 4.18 �– Profile of wake at 68 MPH

Figure 4.19 is developed from the calculated cd of the pressure data corresponding to equation

4.30.

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0 5 10 15 20 25

Distna

ceon

wakerake,x

(ft)


4 aoa

0 aoa

4 aoa

8 aoa

12 aoa

16 aoa

65

Figure 4.19 �– Plot of the coefficient of drag vs. angle of attack

Figure 4.20 is plotted with the calculated wake blockage from equation 2.27.

Figure 4.20 �– Plot of the wake blockage vs. angle of attack

0.006

0.026

0.046

0.066

0.086

0.106

0.126

0.146

0.166

0.186

4 1 6 11 16

Coefficient

ofdrag,c

du

Angle of attack, (degrees)

6.5 MPH

30 MPH

68 MPH

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

4 1 6 11 16

Wakeblockage,

wb

Angle of attack, (degrees)

6.5 MPH

30 MPH

68 MPH

66

4.3.4 Discussion

The wake blockage for a two-dimensional shape depends heavily on the coefficient of drag and it

is important to have complete data relating to the drag (skin friction and pressure). Without all

the components for the drag, it is hard to calculate the correct wake blockage. It is also difficult

to get a complete picture of the drag without developing an equation to model the pressures to

integrate in equations 2.28 and 2.29. This point is illustrated in figure 4.19 where the cd is greater

for the case of the 30 MPH flow compared with the 6.5 MPH flow but both are higher for the 68

MPH flow. This is confusing because it would be expected that the cd would slowly increase

with flow speed to a certain point.

In figure 4.16, flow through the test section is so slow that that pressure sensors have a difficult

time measuring any pressure change over the noise created by the senor itself. Figure 4.17 shows

a more expect profile shape as the flow velocity increases. It can be seen that the flow is

becoming steadier and when the test section velocity is increased to 68 MPH, the wake profile

becomes very smooth and easily distinguishable from the normal flow conditions. Due to tunnel

limitations, a 102 MPH run could not be performed due to the wake and solid blockage

becoming so great, that it would �“choke�” the tunnel flow, and possibly damage some of the

equipment.

Also, a consideration needs to be made that the wake rake did not measure the entire wake and

therefore, the wake correction is left incomplete. This issue will lead to an incorrect cd from

being calculated. Since two of the main contributors of the wake blockage come from the wake

calculations, the error could be significant.

67

4.4 Streamline Curvature Correction

4.4.1 Theory

For the streamlines, the presence of the ceiling and the floor prevents the normal curvature of the

free flow that occurs about any lifting body, and relative to the straightened flow, the body

appears to have more camber than it actually has. This is usually on the order of 1% for

customary sizes. Accordingly, the airfoil in a closed wind tunnel has too much lift and moment

force about the quarter chord at any given angle of attack as well as the angle of attack being too

large itself. This effect is not limited to cambered airfoils but to any lifting body that produces a

general curvature in the airstream.

To gain insight into the streamline curvature effect, it must be assumed that the airfoil in

question is small and may be approximated by a single vortex at its quarter-chord point. The

image system necessary to contain this vortex between the floor and ceiling consists of a vertical

row of vortices about and below the real vortex. The image system extends to infinity both above

and below and has alternating signs according to the section about the method of images that will

be discussed in a later section. With the method of images, it can be seen that by considering the

first image pair as shown in figure 4.22, it is apparent that the vortices induce no horizontal

velocity since the horizontal components cancel but the vertical components add induced

velocity.

Figure

From sim

Substitut

induced u

essentiall

The chor

loading p

from the

the tange

to the lin

attack co

e 4.21 �– Ima

mple vortex t

tion of reason

upwash angl

ly circular.

rdwise load f

plus an ellipt

product of t

ent at the hal

ne connecting

orrection.

age system n

theory, the v

nable values

le varies alm

for an airfoil

tically shape

the slope of t

lf-chord poin

g the ends of

needed for t

vertical veloc

s for x and h

most linearly

l with circula

ed loading. T

the lift curve

nt because fo

f the camber

68

he streamlin

city at a dista

h into the abo

along the ch

ar camber m

The magnitud

e and the bou

or a circular

r line. The lo

ne curvatur

ance x from

ove equation

hord, and he

may be consid

de of the flat

undary-indu

camber the

oad is proper

re correctio

the lifting li

n reveals that

nce the strea

dered to be a

t plate loade

uced increase

curve at this

rly computed

n (Pope, 19

ine will be

(

t the bounda

am curvature

a flat plate

ed is determi

e in the angle

s point is par

d as an angle

84)

(4.31)

ary-

e is

ined

e of

rallel

e of

69

4.4.2 Approach

To complete the corrections for the streamlines, the airfoil will need to be assumed to be a flat

plate. A correction for the angle of attack is developed by

(4.32)

where

(4.33)

assuming that is small compared to h2 which is the first image pair. The second pair of

vortices being twice as far away, will be roughly one-fourth as effective and the third pair, one-

ninth. So that so that for the images above and below the real wing, we have

(4.34)

The additive lift correction is

(4.35)

and the additive moment correction is

(4.36)

The complete low-speed wall effects for two-dimensional wind-tunnel testing are located below

if only the corrected term is needed. The data with the subscript u are uncorrected data and bases

on free-stream, clear tunnel q, with the exception of drag which must have the buoyancy

correction due to the longitudinal static-pressure gradient removed before final correcting.

The velocity correction is

(4.37)

The dynamic pressure is

(4.38)

The Reyn

The angl

where

is fr

taken at a

point of f

Fi

translate

where A

nolds numbe

e of attack is

comes fr

from the win

a different sp

force measur

igure 4.22 �–

it to the qua

is 1.135 inc

er is

s

rom the mom

ng testing and

pot than at th

rement is loc

�– Translation

arter-chord p

hes for this w

ment force m

d needs to ha

he quarter-ch

cated behind

n of momen

(AE

point is

wind-tunnel

70

measured dur

ave its own c

hord point. I

d the quarter

nt to quarter

EROLAB)

. With the

ring wing-tun

correction d

In figure 4.2

r-chord and t

r-chord poi

determine

nnel testing.

due the mom

2, it can seen

the equation

int on the C

ed, find

(

(

The measur

ent force bei

n that the ac

to

Clark Y-14

(

by

(4.39)

(4.40)

re of

ing

ctual

(4.41)

71

(4.42)

is used to calculate

(4.43)

The coefficient of lift is

(4.44)

where the coefficient of lift is derived from the pressure distribution over the wing. The pressure

distribution is calculated by

(4.45)

Once the has been determined, summing the area under the curve created by the on the

upper and lower surface of the airfoil, gives the for a particular angle of attack and velocity.

The coefficient of moment is

(4.46)

The coefficient of drag at 0 lift angle is

(4.47)

4.4.3 Results

The results below are created from equations 4.34 -4.46.

72

Figure 4.23 �– Plot of Cl vs. uncorrected angle of attack

Figure 4.24 �– Plot of mc/4 vs. uncorrected angle of attack

0.025

0.020

0.015

0.010

0.005

0.000

0.005

0.010

0.015

0.020

4 1 6 11 16

,Cha

ngeincoefficient

oflift,

C l

Uncorrected Angle of Attack, u (degrees)

6.5 MPH

30 MPH

68 MPH

102 MPH

2.0

1.5

1.0

0.5

0.04 1 6 11 16

Chan

geincoefficient

ofmom

ent,

mc/4


6.5 MPH

30 MPH

68 MPH

102 MPH

73

Figure 4.25 �– Plot of L' vs. uncorrected angle of attack

Figure 4.26 �– Plot of vs. uncorrected angle of attack

0.01

0.04

0.09

0.14

0.19

4 1 6 11 16

Chan

geinlift,

L'(lb

s)


6.5 MPH

30 MPH

68 MPH

102 MPH

0.020

0.010

0.000

0.010

0.020

0.030

0.040

4 1 6 11 16

Chan

geinan

gleof

attack,

(degrees)


6.5 MPH

30 MPH

68 MPH

102 MPH

74

Figure 4.27�– Plot of corrected Cl vs. uncorrected angle of attack

Figure 4.28 �– Plot of corrected angle of attack vs. uncorrected angle of attack

0.700

0.200

0.300

0.800

1.300

4 1 6 11 16

CorrectedCo

efficient

oflift,c l


30 MPH

68 MPH

102 MPH

6.5 MPH

4

2

0

2

4

6

8

10

12

14

16

4 2 0 2 4 6 8 10 12 14 16

CorrectedAn

gleof

Attack

(degrees)


75

Figure 4.29 �– Plot of corrected coefficient of moment vs. uncorrected angle of attack

The profile drag was created at the zero lift position of -3.5 degrees angle of attack and is in

Table 1.

UncorrectedVelocity, VU

(ft/s)

UncorrectedAngle ofAttack, u

(degrees)

UncorrectedCoefficient ofDrag, Cd0u

CorrectedCoefficient ofDrag, Cd0

9.53 3.46 0.080 0.0844.00 3.67 0.150 0.1599.73 3.51 0.010400 0.0104Table 1 �– Uncorrected and corrected Cd0

4.4.4 Discussion

The correction mainly depends on the calculated cl and the cl comes from the pressure

distribution over the airfoil. The airfoil has pressure ports from the 0 chord line position to the

80% of the chord line. The last 20% of the pressure distribution is not included due to any

pressure readings after the 80% chord length. This introduces an element of error into the

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.04 1 6 11 16

CorrectedCo

efficient

ofmom

ent,c m

c/4

Uncorrected Angle of Attack, u (degrees

6.5 MPH

30 MPH

68 MPH

102 MPH

76

calculations for total Cp and filters through to the calculation of total cl. The corrected angle of

attack vs. uncorrected angle of attack is as expected in that the figure 4.25 shows for any

uncorrected angle of attack; the corrected angle of attack is lower. Also the cl has a negative

slope for most test sections airspeeds and behaves as expected. All the 6.5 MPH cases produced

erratic results due to the flow speed itself and the very low Reynolds number plays an important

role in the results. The corrected coefficient of moment is negative as expected but again, the 6.5

MPH case shows 0 correction factor required.

The Cd0calculations introduce the most error of all the corrections. The correction depends on

the solid blockage and the wake blockage which as discussed previously, the wake blockage has

a large error rate. The error is then multiplied by 3 times due to the equation used to calculate it.

Another source of error is coming from the plotting of the cl vs. cd to determine the initial Cd0 to

correct. From published data for the Clark Y-12 and Clark Y-15, the correction is two orders of

magnitude higher than it should be. Also the wake calculated for the cd is incomplete at high

angles of attack due to the wake rake not being long enough to capture the whole wake.

77

Chapter 5: Three-Dimensional Wall Corrections for the Clark Y-14 Wing

For a wing, there are several corrections that need to be performed to more accurately model

free-flight conditions when data is collected from a wind tunnel. The four main wall corrections

for an airfoil is buoyance, wake blockage, solid blockage and streamline curvature. The

buoyancy corrections will have an additive component to the drag force while the wake and solid

blockage component are dimensionless but are used in the correction for the streamline

curvature. The streamline curvature corrections are the most important for correcting wing data

and includes the corrections for , CL, Cm and CDi. The velocities used in testing in the

wind-tunnel are 6.5, 30, 68 and 102 MPH and the Reynolds numbers are 100,000, 500,000,

1,200,000 and 1,800,000 respectively. The data and calculations are located in Appendix C.

5.1 Buoyancy Correction

5.1.1 Theory

Closed-throat wind-tunnels have a variation of static pressure along the axis of the test section.

The variation of static pressure is due to a thickening of the boundary layer as the flow

progresses through the test section. As the flow approaches the end of the test section, the

pressure progressively becomes more negative. With the pressure turning more negative down

the length of the test section, the model tends to be sucked down the test section. The amount of

buoyancy is usually insignificant for wings and airfoils but the correction becomes more

important for fuselages and nacelles. The buoyancy corrections can be applied in a three-

dimensional space. The philosophy behind the three-dimensional buoyancy correction is the

same as the two-dimensional.

5.1.2 Ap

The appr

process c

correctio

The is

Clark Y-

by the m

5.1.3 Res

The buoy

4.1.2 to d

plotted in

proach

roach to the t

can be follow

n becomes

s determined

14 wing. Th

aximum thic

Fi

sults

yancy correc

determine th

n figure 5.2 f

three-dimen

wed in sectio

d by finding

he fineness ra

ckness of the

igure 5.1 �– V

ction was cal

e pressure g

for M < .3.

sional case i

on 4.1.2 dow

the fineness

atio is calcul

e shape. The

Values of

lculated usin

radient throu

78

is very simil

wn to equatio

ratio of the

lated by the

e ratio is used

vs. finene

ng equation 5

ugh the test

lar to the two

on 4.14. At th

shape being

length of the

d to find the

ess ratio (Po

5.1 and usin

section. The

o-dimension

he point, the

g tested and i

e shape bein

by figure

ope, 1984)

g the method

e buoyancy c

nal one. The

e buoyancy

in this case,

ng tested divi

e 5.1.

ds in section

correction is

(5.1)

the

ided

n

79

Figure 5.2 �– Plot of the buoyancy correction vs. the test section airspeed

5.1.4 Discussion

The buoyancy for the wing is lower than that of the airfoil. This could be due to the airfoil

covering the entire berth of the test section where the wing is only 80% of the test section berth.

The calculated drag due to the buoyancy is a really small component of the overall drag. This

small component is so small that it could be left out of the correction altogether and still

represent less than .1% of the error in drag force.

5.2 Solid Blockage Correction

5.2.1 Theory

With a three-dimensional model in the test section, the flow is semi-blocked and the flow area is

reduced. In order for continuity and Bernoulli�’s equation to be satisfied, the flow must increase

in velocity to maintain the same mass flow rate through the test section. The increase of velocity

0

0.005

0.01

0.015

0.02

0.025

0 50 100 150 200 250 300

3DBu

oyan

cyCo

rrectio

n,D b

(lbs)


80

is considered solid blockage and is a function of model thickness, thickness distribution and

model size. The camber of the airfoil is independent of the solid blockage. �“The solid blockage

velocity increment at the model is much less (about ¼ ) than the increment one obtains from the

direct area reduction.�” (Pope, 1984) The streamlines furthest from the model are also impacted

by the increment velocity since they are displaced more due to the confines of the test section.

5.2.2 Approach

The solid blockage correction for a three-dimensional body follows the same procedures as in

section 4.2.2. The approach for solid-blockage of a wing defined by Thom�’s short-form equation

is

(5.2)

where k is .90 for a wing and .96 for a body of revolution. Solid-blockage for a wing-body

system is a combination of simply the sum of each component as determined from their

respective equations. This will give you the total solid blockage for the entire system.

5.2.3 Results

Applying equation 5.2 to the Clark Y-14 wing and using a k value of .90, the solid blockage is

plotted in figure 5.3 for test section velocities of M < .3. The cross-sectional area was derived

from the process used in 4.1 and those C values were used in the solid blockage for a wing.

81

Figure 5.3 �– Plot of the solid blockage for the Clark Y-14 wing

5.2.4 Discussion

The solid blockage is greater for the wing compared with the airfoil�’s solid blockage in section

4.2. This makes sense because the wing blocks more area in the flow as the angle of attack

increases than an airfoil. But wing�’s solid blockage follows the same pattern as the airfoil as the

velocity increases.

0.0025

0.0075

0.0125

0.0175

0.0225

0 50 100 150 200 250 300

3DSolid

Blockage,

sb


sb @4 aoa

sb @0 aoa

sb @4 aoa

sb @8 aoa

sb @12 aoa

sb @16 aoa

82

5.3 Wake Blockage Correction

5.3.1 Theory

All bodies, two-dimensional and three-dimensional, create wake with the fluid they are moving

through and bodies in wind tunnels are not exempt. The law of continuity states the velocity

outside the wake in a closed tunnel must be higher than the free stream velocity in order for a

constant volume of fluid to flow through the test section. For the three-dimensional case,

Maskell�’s three-dimensional method is utilized. The Maskell�’s method accounts for the effects of

momentum outside the wake when separated flow occurs. This added effect from the momentum

is added by the lateral wall constraint on the wake and results in lower wake and model base

pressure than what would occur in the free flow condition. (Maskell, 1965) Maskell

demonstrates that wake blockage yields results similar to their higher speed counter parts on the

same model. The natural tendency for the wake is toward the axial symmetry which permits a

single correction.

5.3.2 Approach

The wake blockage correction for streamline flow follows the loci for the two-dimensional case

in section 4.3.2 as far as the wake is simulated by a source of strength

(5.3)

which is matched for continuity by adding a downstream sink of the same strength. However for

the three-dimensional case, the image system consists of a doubly infinite course-sink system

space a tunnel height apart vertically and a tunnel width apart horizontally. The axial velocity

induced at the model by the image source system is again zero, and due to the image sink system

is

The incre

pressure

where K1

The Cdu f

AEROLA

balance.

convert t

eased drag d

draw by

1 is derived f

Fi

for the wing

AB wind-tun

The normal

he raw data

due to the pre

from figure 5

igure 5.4 �– V

is calculated

nnel. The for

and axial fo

to a drag for

essure gradie

5.4

Values of K

d by using th

rce data is ge

orces measur

rce. To conv

83

ent may be s

K3 and K3 for

he force data

enerated by

red by the sti

vert the drag

subtracted by

r a number

a generated b

the 3-compo

ing balance h

to into its co

y removing t

r of bodies

by test comp

onent force/m

had equation

oefficient fo

the wing wa

pleted in the

moment stin

n 2.2 applied

orm, apply

(5.4)

ake

(5.5)

ng

d to

(5.6)

84

Using the calculated from the wind-tunnel data, the wake blockage and change to the due

to the wake can be found.

5.3.3 Results

The calculated CDu is shown in figure 5.5 and the is shown is figure 5.6.

Figure 5.5 �– Plot of the angle of attack vs. the coefficient of drag

Figure 5.6 �– Plot of the angle of attack vs. wake blockage

0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

4 1 6 11 16

Coefficient

ofdrag,c

du


6.5 MPH

30 MPH

68 MPH

102 MPH

0.0002

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

4 1 6 11 16

Wakeblockage,

wb


6 MPG

30 MPH

68 MPH

102 MPH

85

5.3.4 Discussion

When comparing figures 5.5 and 5.6 to each other, it can be seen that the two plots are highly

coupled together. The coefficient of drag is the dominating factor in the wake blockage

correction. The correction for the coefficient of drag could not be completed due to the Clark Y-

14 not being graphed in figure 5.4 even though the thickness ratio is known for the Clark Y-14.

Being able to determine the correction factor for the coefficient of the drag is extremely

important and without it, the drag cannot be corrected.

5.4 Method of Images

5.4.1 Theory

Method of images has many applications in modern engineering from aerospace to electrical.

Method of images can be used in any application where the item of interest is located inside a

field. In electrical engineering, one example of its use is to determine a conductor�’s change in an

electromagnetic field whereas in aerospace, method of images can be used to determine the

downwash on a wing or airfoil in a wind-tunnel. A wing being flown in nature close to the

ground can have method of images applied to determine the downwash. Downwash is defined as

a small velocity component in the downward direction at the wing and is caused by the wing-tip

vortices downstream of the wing. The wing-tip vortices induce a small downward velocity

component in the neighborhood of the wing by the vortices �“dragging�” the surrounding air

around them and this motion induces a small downward velocity component on the wing.

(Anderson, 2007) The downwash then combines with the to produce a local relative wind that

the wing encounters. The downwash caused by these wing-tip vortices become very important

when the wing is located in a confined space such as a wind-tunnel. When the airflow is confined

by the walls of the wind-tunnel, downwash produces a higher induced velocity ( ) on the wing

which cre

velocity f

induced v

only care

angle of

geometri

wing enc

The indu

Figure 5

total drag

can be ap

(Anderso

wing mo

eates a mom

from the dow

velocity intr

e about the e

attack. The i

c angle of at

counters but

uced drag is d

5.7 - The eff

g on the win

pproximated

on, 2007) Be

re than if it w

ment on the w

wnwash acts

oduces the in

ffective ang

induced ang

ttack ( ). Th

adds to the d

defined as a

ffects of dow

g due to the

d by equating

ecause of the

was unconfin

wing. Figure

s upon a finit

nduced angl

le of attack (

le of attack a

he induced an

drag (D) the

component

wnwash on a

downwash o

g the L multi

e confined sp

ned, hence t

86

4.1 illustrat

te wing. The

le of attack (

( ), engin

adds to the e

ngle of attac

wing experi

of the

a finite wing2007)

of the airstre

iplied by the

pace of the w

the need for

es what occu

e moment cr

( ) compon

neers care gr

effective ang

ck reduces th

iences in the

g to produce

eam passing

e tangent of t

wind-tunnel,

a correction

urs when the

reated on the

nent to the w

reatly about

gle of attack

he local angl

e form of ind

e induced d

over it. The

the induced

the downwa

n of the induc

e induced

e wing by the

ing. While p

the induced

to equal the

le of attack t

duced drag (

drag (Ander

e induced dra

angle of atta

ash affects th

ced drag

e

pilots

d

the

).

rson,

ag

ack.

he

87

gathered from wind-tunnel data. An application of method of images is to correct for the inflated

induced drag on the wing due to the wind tunnel walls. To apply this method, the wing can be

replaced with a vortex system composed of a lifting line vortex and a pair of trailing vortices. A

solid body, like a wing, can be represented by a source-sink system where the body is located

and the wake can be represented by a source. (Pope, 1984) Using this vortex system can produce

accurate results to any degree necessary. The solid boundary of the wing is formed by the

production of a zero streamline matching the solid boundary. After the image system is

established for the wing, the system can be applied for a closed rectangular wind-tunnel. It

should be noted that the two-dimensional application of method of images only applies if the

downwash is needed along the lifting line and the three-dimensional application is necessary to

get induced upwash after the wing, the streamline curvature effect or the correction for the wing

with a lot of sweepback. (Pope, 1984)

To setup the image system, take the image and replicate the opposite sign of the image system as

demonstrated in figure 5.8 where one vortex A is bound by two walls 1 and 2. To correctly setup

Figure 5.8 - Single vortex arrangement for simulation with vertical boundaries

the images, second vortex is created that is assigned the opposite sign of A to wall 1 which is

vortex B. Vortex C is the same sign as B and created opposite side of wall 2. The higher the

order of accuracy needed, more images are needed in the system in order for the system to be

balanced

and C�’. V

vortex B

desired a

Figure 5

demonstr

d. With the ad

Vortex B�’ is

. The same c

accuracy. For

5.9 - Vortex

rates the vert

ddition of vo

added to the

concept is ap

r the case of

image syste

tical walls c

ortex B and C

e opposite si

pplied to vor

f a rectangula

em for the hsection

omponent an

88

C, there ima

de of vortex

rtex C and al

ar test sectio

horizontal sin (Pope, 198

nd figure 5.9

ages need to

x B and is ass

ll additional

on of a wind-

imulation o84)

9 demonstrat

be created w

signed the o

vortices nee

-tunnel, figu

of wing in a

tes the horiz

with vortex B

pposite sign

eded for the

ure 5.10

rectangular

zontal walls a

B�’

n of

r test

and

Figure

shows th

in a close

in figure

5.4.2 Ap

With the

vortex str

infinite v

velocity i

5.10 - Vorte

e image syst

ed rectangula

1.5.

proach

use of elem

rength ( ) at

vortex startin

is

ex image sys

tem become

ar test sectio

mentary vorte

t a distance (

ng at the lifti

stem for thesection

s a doubly in

on where the

ex theory and

(r) from each

ng line and t

89

e vertical simn (Pope, 198

nfinite system

e three-dimen

d the express

h bound vort

trailing to in

mulation of84)

m of vortice

nsional quan

sion for the i

tex. The exp

nfinity in the

f wing in a r

es. (Pope, 19

ntities are req

induced velo

pression appl

e aft direction

rectangular

984) For a wi

quired is sho

ocity due to

lies to a sem

n. The induc

test

ing

own

the

mi-

ced

and comb

between

produces

For each

velocity i

calculate

simulated

The wing

bined with th

the circulati

s;

h image of th

is calculated

d induced ve

d in the test

Figure

g in free fligh

he strength o

ion for a unif

he vortex wh

d. Since the p

elocity is sub

section.

5.11 �– Vorti

ht produces

of a vortex e

formly loade

here the vorte

positive dire

btracted from

ices image s

an induced v

90

equation whi

ed wing and

ex applies a

ction is cons

m the induce

setup to calc

velocity on i

ich is formed

lift is

downwash o

sidered the d

ed velocity c

culate the in

itself and tha

d from the re

on the wing,

down directi

calculated fo

nduced velo

at is found b

elationship

, the induced

on, the

or the wing

ocity

by

(

(5.7)

(5.8)

(5.9)

d

(5.10)

91

The coefficient of lift for the wing is found by using the axial and normal forces measured in the

tunnel by the sting balance, then applying equation 2.1 to get the lift. Once the lift is calculated

for the wing, the CL is found by

(5.11)

The correction to the angle of attack comes from the summing of equation 5.10 of all the images

but does not include the wing itself. When the sum of the change of the angle of attack is added

the induced angle of attack that the wing experiences in free flight, the total induced angle of

attack is found for in the tunnel.

(5.12)

Now the corrected needs to be introduced to determine the to calculate the corrected .

Since the cosine of the angle between the lift and lift component created in the wind-tunnel is

one, the

(5.13)

The induced drag coefficient can be written as

(5.14)

and the change in the induced drag caused by the boundary induced downwash becomes

(5.15)

This method will need to be modified to calculate the downwash on bigger models over the 80%

cross section length of the test section width.

5.4.3 Results

Using the method of images, figures 5.12 and 5.13 were plotted against the angle of attack for

the correction factor of and cdi, respectively.

92

Figure 5.12 �– Plot of vs. the u

Figure 5.13 �– Plot of cdi vs. the u

5.4.4 Discussion

The method of images is an accurate way of determining corrections utilizing the image

methodology. As seen from these plots, the run at 6.5 MPH, gives the most problematic data but

1.5

1.0

0.5

0.0

0.5

1.0

1.5

2.0

4 1 6 11 16

Chan

geinan

gleof

attack,

(degrees)


6.5 MPh

30 MPH

68 MPH

102 MPH

0.010

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

4 1 6 11 16

Chan

geincoefficient

ofdrag,c

di


6.5 MPh

30 MPH

68 MPH

102 MPH

93

other runs seem to align with each other except at high angles of attack. At high angles of attack,

the correction becomes larger and is expected based on the method used to develop the

correction equations.

5.5 Streamline Curvature Correction

5.5.1 Theory

The corrections for the streamline curvature for three-dimensional testing follows the same as for

protocol the two-dimensional case in that they are concerned with the variation of the boundary-

induced upwash along the chord. Once again the variation turns out to be essentially a linear

increase in angle so that the streamlines curvature effects may be treated as the loading on a a

circular arc airfoil. Similarly, the loading is treated as a flat-plate effect based on the flow angle

change between the quarter and half chord, and an elliptic load based on the flow angle change

between the half and three-quarters chord but for the three-dimensional case, the image system is

vastly different from the simple system for two dimensions.

The three-dimensional image system as in figure 1.5 where basically it consists of the real wing

with its bound vortex and its trailing vortices. The vertical boundary is simulated by the infinite

system of horseshoe vortices and the horizontal boundaries by the infinite lateral system. Linking

the two systems are the infinite diagonal system. The effect of the doubly infinite image system

at the lifting line of the real wing is the main boundary upwash effect. Mostly the area of interest

is in the change of the upwash along the chord and along the span as well.

5.5.2 Approach

The total additive correction for the angle of attack is

(5.16)

94

The additive lift correction is

(5.17)

where a is the wing lift curve slope which is plotted from the data collected from wind-tunnel

test on the Clark Y-14 wing.

The additive correction to the moment coefficient is

(5.18)

5.5.3 Results

The wing lift slope curves were created for each Reynolds number and is shown in figure 5.14 -

5.17.

Figure 5.14 �– Wing lift slope curves for 6.5 MPH

y = 0.0029x 0.0102

0.040

0.030

0.020

0.010

0.000

0.010

0.020

0.030

0.040

4 1 6 11 16

Lift,L

(lbs)


95

Figure 5.15 �– Wing lift slope curves for 30 MPH


y = 0.0229x + 0.2275

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

4 1 6 11 16

Lift,L

(lbs)


y = 0.1168x + 1.1553

0.000

0.500

1.000

1.500

2.000

2.500

3.000

3.500

4 1 6 11 16

Lift,L

(lbs)


96


Figure 5.18 �– 5.20 are derived from the corrections discussed in this section.

Figure 5.18 �– Plot of the change in the angle of attack vs. uncorrected angle of attack

y = 0.4029x + 2.5436

0.000

2.000

4.000

6.000

8.000

10.000

12.000

4 1 6 11 16

Lift,L

(lbs)


2.000

1.500

1.000

0.500

0.000

0.500

1.000

1.500

2.000

4 1 6 11 16

Chan

geinan

gleof

attack,

(degrees)


6.5 MPh

30 MPH

68 MPH

102 MPH

97

Figure 5.19 �– Plot of the change in coefficient of lift vs. uncorrected angle of attack

Figure 5.20 �– Plot of the change in moment coefficient vs. uncorrected angle of attack

0.008

0.006

0.004

0.002

0

0.002

0.004

0.006

0.008

4 1 6 11 16

Chan

geincoefficient

oflift,

C Lc


6.5 MPh

30 MPH

68 MPH

102 MPH

0.002

0.0015

0.001

0.0005

0

0.0005

0.001

0.0015

0.002

4 1 6 11 16

Chan

geincoefficient

ofmom

ent,

C mc


6.5 MPh

30 MPH

68 MPH

102 MPH

Chapte

6.1 Grid

Two grid

the Clark

construct

step struc

lengths a

er 6: Com

ds

ds were creat

kY-14 in free

ted by orthog

ctured grid i

around the ai

Figu

mputationa

ted to simula

e flight cond

gonality (Fig

s placed arou

irfoil.

ure 6.1 �– Or

al Fluid Dy

ate the fluid

ditions. The f

gure 6.1). Th

und the Clar

rthogonal g

98

ynamics of

flow inside

free flight gr

he airfoil is i

rk Y-14 Airf

rid around

f the Clar

the wind-tun

rid was creat

import from

foil. The grid

the Clark Y

rk Y-14 Ai

nnel and ano

ted in Pointw

SolidWorks

d was steppe

Y-14 Airfoil

irfoil

other to mod

wise and is

s where a on

ed out to 10 b

l

del

ne-

body

After the

All five d

being set

outlets. T

wall. The

The next

will be 3

properly.

not stepp

figure 6.3

e grid is form

down have th

t as the inlet.

The last boun

e grid is now

Figure

grid to be c

D due to an

. This grid al

ped out to 10

3 was steppe

med around th

he volume s

. All the rem

ndary condit

w ready to be

6.2 �– Free f

reated is for

bug in the so

lso be constr

0 body length

ed out 57 ste

he airfoil, th

etting set to

maining doma

tion to be set

e exported to

flight grid w

r the airfoil in

oftware that

ructed out of

hs. The step

eps. The orth

99

he main dom

fluid with th

ains will hav

t is the boun

o Fluent.

with 5 sub-do

nside the tun

will not allo

f an orthogo

out should b

hogonal grid

main is divide

he biggest do

ve their outsi

ndary around

omains for

nnel but inst

ow this grid

nal grid loca

be in a multi

is then divid

ed into 5 sma

omain outsid

ide boundary

d the airfoil n

the Clark Y

tead of the gr

type to be ex

ated around

iple of 8+1. T

ded up 6 sub

aller domain

de boundary

y set to pres

needs to be s

Y-14

rid being 2D

xported to F

the airfoil bu

The grid in

b-domains.

ns.

y

sure

set to

D, it

Fluent

ut

Fi

From the

section. A

condition

on the lef

as the air

6.2 Setu

The setup

of chord

they were

flow con

gure 6.3 �– G

e boundary o

All domains

ns are also se

ft. The uppe

rfoil. Once th

up

p for the grid

of 3.5 inche

e properly im

ditions are s

Grid modeli

of the orthog

in figure 6.3

etup as the v

r and lower

he setup is c

ds is perform

es. After the

mported into

set at inviscid

ing the flow

onal grid, a

3 are assigne

velocity inlet

boundaries a

omplete, the

med in Fluen

grid is scale

o Fluent. The

d with air se

100

w inside the w

new structur

ed the volum

t on the right

are set as wa

e grid is expo

nt where the

d, the bound

e residuals w

elected at the

wind-tunne

red out to th

me condition

t side of the

alls as their b

orted to Flue

grid was siz

dary conditio

were set for c

e medium.

l with the C

he boundarie

of fluid. Th

grid and a p

boundary co

ent.

zed to the cor

ons are check

convergence

Clark Y-14

s of the test

he boundary

pressure outl

onditions as w

rrect dimens

ked to ensur

e at 1e-07. Th

ine

well

sions

re

he

6.3 Resu

In figure

of attack

ults

s 6.4 �– 6.9, t

s of -4, 0, 4,

F

F

the static pre

8, 12, and 1

Figure 6.4 �–

Figure 6.5 �–

essure is plot

16 at a free-s

�– CFD Resu

�– CFD Resu

101

tted in the co

stream veloc

lts for the C

ults for the C

ontour map f

ity of 149.64

Clark Y-14 a

Clark Y-14

for the Clark

4 ft/sec..

at -4 aoa

at 0 aoa

k Y-14 at angle

F

F

Figure 6.6 �–

Figure 6.7 �–

�– CFD Resu

�– CFD Resu

102

ults for the C

ults for the C

Clark Y-14

Clark Y-14

at 4 aoa

at 8 aoa

In figure

lift over t

ft/sec.

F

F

s 6.10 �– 6.15

the airfoil at

Figure 6.8 �–

Figure 6.9 �–

5, the Cp ove

t angles of at

�– CFD Resul

�– CFD Resul

er the airfoil

ttack of -4, 0

103

lts for the C

lts for the C

is plotted an

0, 4, 8, 12 an

Clark Y-14 a

Clark Y-14 a

nd is used to

nd 16 and a f

at 12 aoa

at 16 aoa

o calculate th

flow velocity

he coefficien

y of 149.64

nt of

Fi

F

igure 6.10 �–

igure 6.11 �–

�–Plot of the C

�–Plot of the

104

Cp over the

Cp over the

Clark Y-14

e Clark Y-14

4 at -4 aoa

4 at 0 aoa

F

F

igure 6.12 �–

igure 6.13 �–

�–Plot of the

�–Plot of the

105

Cp over the

Cp over the

e Clark Y-14

e Clark Y-14

4 at 4 aoa

4 at 8 aoa

In figure

uncorrect

Fi

Fi

s 6.16 �– 6.18

ted, expecte

igure 6.14 �–P

igure 6.15 �–P

8, the coeffic

d and CFD r

Plot of the C

Plot of the C

cient of lift i

results.

106

Cp over the

Cp over the

is graphed fo

Clark Y-14

Clark Y-14

or -4, 0, 4, 8,

4 at 12 aoa

4 at 16 aoa

, 12 and 16 ffor corrected

d,

107

Figure 6.16 �– Plot of the Cl at a velocity of 44 ft/sec comparing uncorrected, corrected,

expected and CFD results


expected and CFD results

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

4 1 6 11 16

CorrectedCo

efficient

oflift,c l


Uncorrected

Corrected

Expected

CFD

0.0

0.2

0.4

0.6

0.8

1.0

1.2

4 1 6 11 16

CorrectedCo

efficient

oflift,c l


Uncorrected

Corrected

Expected

CFD

Figure 6

In figure

attack.

4

CorrectedCo

efficient

oflift,c l

6.18 �– Plot o

s , The strea

F

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

of the Cl at a

mlines are s

igure 6.19 �–

1Uncorrecte

a velocity of

expected

hown for on

�– Streamline

6d Angle of Att

108

f 149.64 ft/s

and CFD r

nly one veloc

es over the C

ack, u (degre

sec compari

esults

city of 149.6

Clark Y-14

11ees

ing uncorre

64 ft/sec at v

4 at -4 aoa

16

cted, correc

varies angles

Uncorrec

Correcte

Expected

CFD

cted,

of

cted

d

d

F

F

Figure 6.20 �–

Figure 6.21 �–

�– Streamlin

�– Streamlin

109

nes over the

nes over the

Clark Y-14

Clark Y-14

4 at 0 aoa

4 at 4 aoa

F

Fi

Figure 6.22 �–

igure 6.23 �–

�– Streamlin

�– Streamline

110

nes over the

es over the C

Clark Y-14

Clark Y-14

4 at 8 aoa

at 12 aoa

6.4 Disc

The CFD

149.642

static pre

the static

section 4

the graph

values. T

close to t

ft/sec, the

6.15.

Fi

cussion

D was succes

ft/sec at -4, 0

essure as the

c pressure sh

4.4 for use in

hs show how

The graphs sh

the corrected

e CFD result

igure 6.24 �–

ssful at plotti

0, 4, 8, 12 an

angle of atta

ifts over the

n comparing

w the correcti

how that cor

d results. For

ts are in App

�– Streamline

ing the cp ov

nd 16 degree

ack increase

airfoil as th

the data to c

ion factors c

rrected cl is c

r the CFD ca

pendix C but

111

es over the C

ver the Clark

es of angle o

es. It can be s

he airfoil stal

corrected and

compare with

close to the e

ases for the a

t mainly rep

Clark Y-14

k Y-14 for 9.

of attack. In f

seen that as

lls. The cp is

d expected r

h the CFD re

expected val

a velocity of

presents what

at 16 aoa

533, 44.000

figures 6.4 �–

the angle of

used to calc

results. In fig

esult and the

lues where th

f 9.533, 44.0

at is shown in

, 99.732 and

�– 6.9 shows t

f attack incre

culate the cl a

gures 6.16 �–

e expected

he CFD is ve

00 and 99.73

n figures 6.4

d

the

eases,

as in

6.18,

ery

3

4 �–

112

Chapter 7: Conclusion

As our civilization relies more heavily on aircrafts and rockets, the use of wind-tunnels has

increasing been integrated as an important aeronautical tool in their design. Even though wind-

tunnels are great scientific tools, they do have their flaws. Based on the specific wind-tunnel

design, one of the main negatives is that wind-tunnels cannot simulate free-flight conditions

without having to correct the data for wall effects and other flow phenomena.

Both two and three-dimensional flows need to have corrections applied that are unique to that

wind-tunnels design. For two dimensional flows, corrections that can be obtain are for the

with direct corrections available for . The

corrections are developed from the buoyancy, solid and wake blockages, and streamline

curvature corrections. For tree-dimensional flows, corrections can be obtain are ,

These corrections depend on the methods applied to the two-dimensional cases

along with the method of images.

The CFD can be a cheaper solution to wind-tunnels but as seen in the results throughout chapter

6, require an almost perfect grid. This can be very expensive due to grid building, setup and

supercomputer time to the point the cost match that of wind-tunnels. Wind Tunnel testing and the

corrections developed for that specific tunnel that are easily applied to any model, keep tunnels

operating and a competitive source of aeronautical information.

113

Works Cited

Abbott, I. (1959). Theory of Wing Sections. New York City: Dover Publications.

American Institute of Aeronautics and Astronautics (AIAA). (2004). NACA 0012 Airfoil

Aerodynamics Analysis. Reston: Hahn, Philip.

Anderson, J. D. (2007). Fundamentals of Aerodynamics , 4th Edition. New York City: McGraw-

Hill.

Kasravi, K. (2010). Tec452 body Structures I. Retrieved from

http://www.kasravi.com/cmu/tec452/aerodynamics/WindTunnel.html

Lilienthal, O. (2000). Birdflight as the Basis of Aviation. Hummelstown: Markowski

International Publishers

Monash University. (2004). Flying Wings: An Anthology: Horatio F. Phillips. Retrieved from

http://wwwctie.monash.edu.au/hargrave/phillis.html

National Aeronautics and Space Administration (NASA). (2005). Wind Tunnel History.

Retrieved from http://www.grc.nasa.gov/WWW/K-12/WindTunnel/History.html

National Aeronautics and Space Administration (NASA). (1950). Blockage Corrections for

Three-Dimensional �– Flow Closed �–Throat Wind (TR 643). Washington DC: U.S.

Government Printing Office.

National Aeronautics and Space Administration (NASA). (1944). Wall Interference in a Two-

Dimensional �– Flow Wind Tunnel with Considerations of the Effects of Compressibility

(TR 612). Washington DC: U.S. Government Printing Office.

Pankhurst, R. C. (1952). Wind Tunnel Technique. London: Pitman

Pope, A. (1984). Low-Speed Wind Tunnel Testing. New York City: John Wiley & Sons.

114

Society for Industrial and Applied Mathematics. (1991). Vortex Methods and Vortex Motion.

Philadelphia: Gustafson, K. E, Sethian, J. A.

115

Appendix A

/* This program determines the Pressure Gradient through the SJSU Wind Tunnel Test Section.*/ #define _CRT_SECURE_NO_DEPRECATE #include <stdio.h> #include <math.h> #define VISCOCITY 0.000000382f #define DENSITY 0.002325f #define PRESSURE 2.1162f #define VELOCITY_ZERO 0.0f #define AREA_ONE 1.0f double reynoldsNumber(double velocity, double cord_length) { return (DENSITY * velocity * cord_length) / VISCOCITY; } double criticalPoint(double velocity, double cord_length, double reynolds_number) { return ((reynolds_number * VISCOCITY) / (DENSITY * velocity)); } double laminarBoundaryDisplacement(double velocity, double cord_length) { return (1.72f * cord_length)/pow(reynoldsNumber(velocity,cord_length),0.5); } double turbulentBoundaryDisplacement(double velocity, double cord_length, double reynolds_number) { return (0.046f * cord_length)/pow(reynolds_number,0.2); } int main(void) { double reynolds_number = 0.0f; double velocity = 0.0f; double cord_length = 1.0f; double critical_point = 0.0f; double boundary_displacement=0.0; double effective_area = 0.0; double pressure_one = 0.0f; double velocity_two = 0.0f; double pressure_two = 0.0f; double ts_length = 0.0f;

116

double pressure_grad = 0.0f; double starting_velocity = 0.0; double ending_velocity = 0.0; double velocity_increment = 0.0; double velocity_mph = 0.0; int dummy; FILE *file; file = fopen("C:\\data.csv","w+"); printf("Enter the starting velocity (MPH) of the flow over flat plate > "); scanf_s("%lf", &starting_velocity); printf("Enter the ending velocity (MPH) of the flow over the flat plate > "); scanf_s("%lf", &ending_velocity); printf("Enter the velocity increment (MPH) > "); scanf_s("%lf", &velocity_increment); fprintf(file,"MPS,FPS,Reynolds Number,Cross-Sectional Test Section Area (ft),Pressure Gradient\n"); for (velocity_mph = starting_velocity;velocity_mph <= ending_velocity; velocity_mph+= velocity_increment) { velocity = velocity_mph * 1.46666666666667; reynolds_number = reynoldsNumber(velocity,cord_length); //printf("Reynolds Number -> %lf\n", reynolds_number); critical_point = criticalPoint(velocity,cord_length,500000); //printf("Critical Point (ft) -> %lf\n", critical_point); if (reynolds_number < 500000.0f) { //printf("Reynolds Number < 500000 - Laminar\n"); boundary_displacement = laminarBoundaryDisplacement(velocity,cord_length); effective_area = pow((cord_length - boundary_displacement),2.0); //printf("Laminar Boundary Displacement (ft) -> %lf\n",boundary_displacement); //printf("Effective Area (ft^2) -> %lf\n\n", effective_area); } else { double delta_x = 0.0; double turbulent_start_point = 0.0; double new_start_point = 0.0; double new_laminar_boundary_displacement = 0.0;

117

double turbulent_boundary_displacement = 0.0; //printf("Reynolds Number >= 500000 - Turbulent\n"); boundary_displacement = laminarBoundaryDisplacement(velocity,critical_point); delta_x = pow((boundary_displacement * pow(((DENSITY * velocity) / VISCOCITY),0.2) / 0.46),1.25); //printf("Delta X (ft) -> %lf\n",delta_x); turbulent_start_point = critical_point - delta_x; new_start_point = cord_length - turbulent_start_point; //printf("New Start Point Turbulent Boundary Distplacement (ft) -> %lf\n",new_start_point); turbulent_boundary_displacement = turbulentBoundaryDisplacement(velocity,new_start_point, reynolds_number); //printf("Turbulent Boundary Displacement (ft) -> %lf\n",turbulent_boundary_displacement); effective_area = pow(cord_length - turbulent_boundary_displacement,2.0); //printf("Effective Area (ft^2) -> %lf\n\n",effective_area); } pressure_one = PRESSURE - .5 * DENSITY * pow((velocity),2); //printf("Pressure at Test Section Entrance (lb/ft^2) -> %lf\n",pressure_one); velocity_two = (velocity * AREA_ONE) / effective_area; //printf("Test Section Exit Velocity (ft/sec) -> %lf\n",velocity_two); pressure_two = pressure_one - .5 * DENSITY * pow((velocity_two),2); //printf("Pressure at Test Section Exit (lb/ft^2) -> %lf\n",pressure_two); //printf("Enter Test Section Axial Length (ft) >"); //scanf_s("%lf", &ts_length); ts_length = 1.0; pressure_grad = (pressure_two - pressure_one) / ts_length; //printf("Pressure Gradient through the Test Section (lb/ft^3) -> %lf\n\n",pressure_grad); fprintf(file,"%lf,%lf,%lf,%lf,%lf\n",velocity_mph,velocity,reynolds_number,effective_area,pressure_grad); } printf("DONE.\n"); fclose(file);

118

scanf_s("%d",&dummy); return (0); }

1

Appendix B

2D Airfoil Data (Pressure)

qV_ref

Alpha P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9

P10

P11

P12

P13

P14

P15

P16

P17

P18

P19

count

[psf]

[mph]

[deg]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

1mbar =

2.088543

psf

1 0 2 0

1016.1

1016.4

1016.2

1016.1

1016.3

1015.9

1016.2

1016

1016.3

1016.3

1016.4

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1016

1mph=

1.466667

fps

2 0 3 0

1016.1

1016.4

1016.3

1016.1

1016.3

1015.8

1016.2

1016

1016.3

1016.3

1016.3

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1016

1sq.ft=

144

psin

3 0 4 0

1016.1

1016.4

1016.3

1016.1

1016.3

1015.9

1016.2

1016

1016.3

1016.3

1016.3

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1016

4 0 4 0

1016.1

1016.3

1016.2

1016.1

1016.3

1015.8

1016.2

1016

1016.3

1016.2

1016.4

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1016

5 0 3 0

1016.1

1016.4

1016.2

1016.1

1016.3

1015.8

1016.2

1016

1016.3

1016.3

1016.4

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1016

6 0.1 4 01016.

1016.

1016.

1016.

1016.

1015.

1016.

1016

1016.

1016.

1016.

1015.

1016.

1016.

1016.

1015.

1016.

1016.

1016

2

1 4 2 1 3 8 2 3 2 4 9 2 3 3 8 2 3

7 0 3 0

1016.1

1016.4

1016.2

1016.1

1016.3

1015.8

1016.2

1016

1016.3

1016.3

1016.4

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1016

8 0 2 0

1016.1

1016.4

1016.2

1016.1

1016.3

1015.8

1016.2

1016

1016.3

1016.3

1016.3

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1016

9 0 3 0

1016.1

1016.4

1016.3

1016.1

1016.3

1015.8

1016.2

1016

1016.3

1016.2

1016.3

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1016

10 0 4 0

1016.1

1016.4

1016.2

1016.1

1016.3

1015.8

1016.2

1016

1016.3

1016.3

1016.3

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1015.9

11 0 4 0

1016.1

1016.4

1016.2

1016.1

1016.3

1015.8

1016.2

1016

1016.3

1016.3

1016.3

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1015.9

12 0.1 5 0

1016.1

1016.4

1016.3

1016.1

1016.3

1015.8

1016.2

1016

1016.3

1016.2

1016.3

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1016

13 0.1 5 0

1016.1

1016.4

1016.3

1016.1

1016.3

1015.8

1016.2

1016

1016.3

1016.2

1016.4

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1016

14 0 2 0

1016.1

1016.3

1016.3

1016.1

1016.3

1015.8

1016.2

1016

1016.3

1016.2

1016.3

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1015.9

15 0 2 0

1016.1

1016.4

1016.3

1016.1

1016.3

1015.8

1016.2

1016

1016.3

1016.2

1016.3

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1016

16 0 2 0

1016.1

1016.4

1016.3

1016.1

1016.3

1015.8

1016.2

1016

1016.3

1016.2

1016.3

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1015.9

17 0 3 01016

1016.4

1016.2

1016.1

1016.3

1015.8

1016.2

1016

1016.3

1016.2

1016.3

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1015.9

3

18 0 3 01016

1016.3

1016.2

1016.1

1016.2

1015.8

1016.2

1016

1016.3

1016.2

1016.3

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1015.9

19 0 4 0

1016.1

1016.4

1016.2

1016.1

1016.3

1015.8

1016.2

1016

1016.3

1016.2

1016.3

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1015.9

20 0 1 0

1016.1

1016.4

1016.2

1016.1

1016.3

1015.8

1016.2

1016

1016.3

1016.2

1016.3

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1015.9

0.015

3.15 0

1016.09

1016.385

1016.24

1016.1

1016.295

1015.81

1016.2

1016

1016.3

1016.24

1016.33

1015.9

1016.2

1016.3

1016.3

1015.8

1016.2

1016.3

1015.96

Avg

2122.148

2122.764

2122.461

2122.169

2122.576

2121.563

2122.378

2121.96

2122.587

2122.461

2122.649

2121.751

2122.378

2122.587

2122.587

2121.542

2122.378

2122.587

2121.877 psf

4.620001

FPS

Airfoil

Station 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

% ofChor

d 0.8 0.70.6 0.5 0.4 0.3 0.2 0.1

0.075 0

0.075 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Distance 2.8

2.45

2.1

1.75 1.4

1.05 0.7

0.35

0.262 0

0.262

0.35 0.7

1.05 1.4

1.75 2.1

2.45 2.8

4

from LE

5 5

qV_ref

Alpha P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9

P10

P11

P12

P13

P14

P15

P16

P17

P18

P19

count

[psf]

[mph]

[deg]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

1mbar =

2.088543

psf

1 0.1 5 01016

1016.3

1016.2

1016.1

1016.2

1015.8

1016.2

1015.9

1016.3

1016.2

1016.2

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.2

1015.9

1mph=

1.466667

fps

2 0.1 5 01016

1016.3

1016.3

1016.1

1016.2

1015.8

1016.2

1016

1016.3

1016.3

1016.2

1015.9

1016.1

1016.2

1016.2

1015.7

1016.1

1016.2

1015.9

1sq.ft=

144

psin

3 0.1 7 01016

1016.3

1016.3

1016.1

1016.2

1015.8

1016.2

1016

1016.3

1016.3

1016.3

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.2

1015.9

4 0.1 6 01016

1016.3

1016.2

1016

1016.2

1015.8

1016.2

1016

1016.3

1016.3

1016.2

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.2

1015.9

5 0.1 7 01016

1016.4

1016.2

1016

1016.2

1015.8

1016.2

1016

1016.3

1016.2

1016.3

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.2

1015.9

6 0.1 5 01016

1016.3

1016.2

1016

1016.2

1015.8

1016.2

1016

1016.3

1016.2

1016.3

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.2

1015.9

7 0.2 8 01016

1016.3

1016.2

1016

1016.2

1015.8

1016.2

1015.9

1016.3

1016.2

1016.2

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.2

1015.9

5

8 0.1 7 0

1016.1

1016.3

1016.2

1016

1016.2

1015.8

1016.2

1016

1016.3

1016.2

1016.3

1015.9

1016.1

1016.2

1016.2

1015.7

1016.1

1016.2

1015.9

9 0.1 7 01016

1016.3

1016.2

1016

1016.2

1015.7

1016.2

1015.9

1016.3

1016.2

1016.3

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.2

1015.9

10 0.1 5 01016

1016.3

1016.2

1016

1016.2

1015.8

1016.2

1016

1016.3

1016.2

1016.3

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.2

1015.9

11 0.1 6 01016

1016.3

1016.2

1016

1016.2

1015.8

1016.2

1016

1016.3

1016.3

1016.2

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.2

1015.9

12 0.1 6 0

1016.1

1016.3

1016.2

1016

1016.2

1015.8

1016.2

1015.9

1016.3

1016.3

1016.3

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.2

1015.9

13 0.1 6 01016

1016.3

1016.2

1016

1016.2

1015.8

1016.1

1015.9

1016.3

1016.3

1016.3

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.2

1015.9

14 0.2 8 01016

1016.3

1016.2

1016

1016.2

1015.8

1016.2

1016

1016.3

1016.3

1016.3

1015.9

1016.1

1016.2

1016.2

1015.7

1016.1

1016.2

1015.9

15 0.1 7 01016

1016.3

1016.2

1016

1016.2

1015.8

1016.2

1016

1016.3

1016.3

1016.2

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.2

1015.9

16 0.1 7 0

1016.1

1016.3

1016.2

1016

1016.2

1015.8

1016.2

1015.9

1016.3

1016.3

1016.3

1015.8

1016.1

1016.3

1016.2

1015.7

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1016.2

1015.9

17 0.1 7 01016

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1016

1016.2

1015.8

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1015.9

1016.3

1016.3

1016.2

1015.8

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1016.2

1016.2

1015.7

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1015.9

18 0.1 7 01016

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1016

1016.2

1015.8

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1015.9

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1016.2

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1015.8

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1016.2

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1016.1

1016.2

1015.9

19 0.1 7 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

6

16 16.3

16.2

16 16.2

15.8

16.2

15.9

16.3

16.3

16.3

15.8

16.1

16.3

16.2

15.7

16.1

16.2

15.9

20 0.1 7 01016

1016.3

1016.2

1016

1016.2

1015.8

1016.2

1015.9

1016.3

1016.3

1016.3

1015.8

1016.1

1016.2

1016.2

1015.7

1016.2

1016.2

1015.9

0.11 6.5 0

1016.015

1016.305

1016.21

1016.015

1016.2

1015.795

1016.185

1015.95

1016.3

1016.26

1016.26

1015.815

1016.1

1016.21

1016.2

1015.7

1016.105

1016.2

1015.9

Avg

2121.991

2122.597

2122.399

2121.991

2122.378

2121.532

2122.346

2121.856

2122.587

2122.503

2122.503

2121.574

2122.169

2122.399

2122.378

2121.334

2122.179

2122.378

2121.751 psf

9.533336

FPS

0.42401

0.51894

0.430397

0.61387

0.80374

0.715199

0.715199

0.050662 1

1.379735

0.32907

0.61387

0.89868

0.70881

0.89868

0.89868

0.80374

0.89868

0.13921 Cp

21 2.4 31 0

1014.7

1014.9

1014.8

1014.5

1014.6

1014.2

1014.6

1014.7

1015.4

1015.8

1014.3

1014

1014.3

1015

1015

1014.5

1014.9

1015.1

1014.8

22 2.3 30 0

1014.7

1014.9

1014.8

1014.5

1014.7

1014.2

1014.6

1014.7

1015.5

1015.8

1014.4

1014.1

1014.3

1015.1

1015

1014.5

1015

1015.1

1014.8

23 2.2 30 0

1014.7

1014.9

1014.8

1014.5

1014.7

1014.2

1014.6

1014.7

1015.5

1015.8

1014.4

1014

1014.3

1015.1

1015

1014.5

1015

1015.1

1014.8

24 2.4 30 0

1014.7

1014.9

1014.8

1014.5

1014.7

1014.2

1014.6

1014.7

1015.5

1015.8

1014.4

1014

1014.3

1015

1015

1014.5

1015

1015.1

1014.8

7

25 2.3 30 0

1014.7

1014.9

1014.8

1014.5

1014.7

1014.2

1014.6

1014.7

1015.5

1015.8

1014.4

1014.1

1014.3

1015.1

1015.1

1014.5

1015

1015.1

1014.8

26 2.2 30 0

1014.6

1014.9

1014.8

1014.5

1014.7

1014.2

1014.6

1014.7

1015.5

1015.8

1014.4

1014.1

1014.3

1015

1015

1014.5

1015

1015.1

1014.8

27 2.3 30 0

1014.6

1014.9

1014.8

1014.5

1014.7

1014.2

1014.6

1014.7

1015.5

1015.8

1014.3

1014.1

1014.3

1015.1

1015.1

1014.5

1015

1015.1

1014.8

28 2.3 30 0

1014.7

1015

1014.8

1014.5

1014.7

1014.2

1014.6

1014.7

1015.5

1015.8

1014.3

1014.1

1014.3

1015.1

1015

1014.5

1015

1015.1

1014.8

29 2.3 30 0

1014.7

1014.9

1014.8

1014.5

1014.7

1014.2

1014.6

1014.7

1015.5

1015.8

1014.4

1014.1

1014.3

1015.1

1015.1

1014.5

1015

1015.1

1014.8

30 2.3 30 0

1014.7

1014.9

1014.8

1014.5

1014.7

1014.2

1014.6

1014.7

1015.5

1015.8

1014.4

1014.1

1014.3

1015

1015

1014.5

1015

1015.1

1014.8

31 2.3 30 0

1014.6

1014.9

1014.8

1014.5

1014.7

1014.2

1014.6

1014.7

1015.5

1015.8

1014.4

1014.1

1014.3

1015

1015

1014.5

1014.9

1015.1

1014.8

32 2.3 30 0

1014.6

1014.9

1014.8

1014.5

1014.7

1014.2

1014.6

1014.7

1015.5

1015.8

1014.4

1014.1

1014.3

1015

1015

1014.5

1015

1015.1

1014.8

33 2.3 30 0

1014.7

1014.9

1014.8

1014.5

1014.7

1014.2

1014.6

1014.7

1015.5

1015.8

1014.4

1014.1

1014.3

1015.1

1015

1014.5

1015

1015.1

1014.8

34 2.3 30 0

1014.7

1014.9

1014.8

1014.5

1014.7

1014.2

1014.6

1014.7

1015.4

1015.8

1014.4

1014.1

1014.3

1015.1

1015

1014.5

1014.9

1015.1

1014.8

35 2.4 30 0

1014.6

1014.9

1014.8

1014.5

1014.7

1014.2

1014.6

1014.7

1015.5

1015.8

1014.3

1014

1014.3

1015

1015

1014.5

1015

1015.1

1014.8

36 2.4 30 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

8

14.7

14.9

14.8

14.5

14.7

14.2

14.6

14.7

15.5

15.8

14.4

14 14.3

15.1

15 14.5

15 15.1

14.8

37 2.3 30 0

1014.7

1014.9

1014.8

1014.5

1014.7

1014.2

1014.6

1014.7

1015.5

1015.8

1014.4

1014

1014.3

1015.1

1015

1014.5

1014.9

1015.1

1014.8

38 2.3 30 0

1014.6

1014.9

1014.8

1014.5

1014.6

1014.2

1014.5

1014.7

1015.5

1015.8

1014.3

1014

1014.3

1015

1015

1014.5

1015

1015.1

1014.8

39 2.4 31 0

1014.6

1014.9

1014.8

1014.5

1014.7

1014.2

1014.6

1014.7

1015.5

1015.8

1014.3

1014

1014.3

1015.1

1015

1014.5

1015

1015.1

1014.8

40 2.4 30 0

1014.7

1014.9

1014.8

1014.5

1014.6

1014.2

1014.6

1014.6

1015.5

1015.8

1014.3

1014

1014.2

1015.1

1015

1014.5

1014.9

1015.1

1014.8

2.32

30.1 0

1014.665

1014.905

1014.8

1014.5

1014.685

1014.2

1014.595

1014.695

1015.49

1015.8

1014.365

1014.055

1014.295

1015.06

1015.015

1014.5

1014.975

1015.1

1014.8

Avg

2119.172

2119.673

2119.454

2118.827

2119.214

2118.201

2119.026

2119.235

2120.895

2121.542

2118.545

2117.898

2118.399

2119.997

2119.903

2118.827

2119.819

2120.08

2119.454 psf

44.14668

FPS

0.28283

0.33235

0.29634

0.44037

0.44938

0.44938

0.44488

0.17481

0.27081

0.603897

0.76896

0.66093

0.71495

0.11629

0.1568

0.1703

0.10279

0.08028

0.04427 Cp

41 9.5 61 0

1010.3

1010.2

1009.9

1009.3

1009.3

1008.8

1009.1

1010.3

1012.8

1014.6

1008.2

1008.4

1011

1011

1011.2

1010.9

1011.4

1011.7

1011.5

9

42 9.5 61 0

1010.3

1010.2

1009.8

1009.3

1009.3

1008.8

1009.1

1010.4

1012.9

1014.6

1008.2

1008.5

1011.1

1011.1

1011.2

1010.9

1011.5

1011.7

1011.5

43 9.3 60 0

1010.3

1010.2

1009.9

1009.3

1009.3

1008.8

1009.1

1010.4

1012.9

1014.6

1008.2

1008.5

1011.1

1011

1011.3

1010.9

1011.4

1011.7

1011.5

44 9.4 61 0

1010.3

1010.2

1009.9

1009.3

1009.3

1008.8

1009.1

1010.4

1012.8

1014.6

1008.2

1008.5

1011.1

1011.1

1011.2

1010.9

1011.4

1011.7

1011.6

45 9.5 61 0

1010.3

1010.2

1009.9

1009.4

1009.3

1008.8

1009.1

1010.4

1012.9

1014.6

1008.2

1008.5

1011.1

1011.1

1011.3

1010.9

1011.5

1011.7

1011.5

46 9.4 61 0

1010.3

1010.2

1009.9

1009.4

1009.3

1008.8

1009.2

1010.4

1012.8

1014.6

1008.2

1008.5

1011.1

1011.1

1011.3

1010.9

1011.4

1011.7

1011.5

47 9.5 61 0

1010.3

1010.2

1009.9

1009.3

1009.3

1008.8

1009.1

1010.3

1012.9

1014.6

1008.2

1008.4

1011.1

1011

1011.2

1010.9

1011.4

1011.7

1011.5

48 9.3 60 0

1010.3

1010.2

1009.9

1009.4

1009.3

1008.8

1009.1

1010.4

1012.9

1014.6

1008.2

1008.5

1011.1

1011.1

1011.2

1010.9

1011.4

1011.7

1011.6

49 9.4 61 0

1010.3

1010.2

1009.9

1009.4

1009.3

1008.8

1009.1

1010.4

1012.9

1014.6

1008.2

1008.5

1011.1

1011

1011.2

1010.9

1011.4

1011.7

1011.5

50 9.4 61 0

1010.3

1010.2

1009.8

1009.3

1009.3

1008.8

1009.1

1010.3

1012.9

1014.6

1008.1

1008.4

1011.1

1011

1011.2

1010.8

1011.4

1011.7

1011.5

51 9.6 61 0

1010.2

1010.2

1009.8

1009.3

1009.3

1008.8

1009.1

1010.3

1012.8

1014.6

1008.2

1008.4

1011.1

1011

1011.2

1010.9

1011.4

1011.7

1011.5

52 9.4 61 0

1010.3

1010.2

1009.8

1009.3

1009.3

1008.8

1009.1

1010.3

1012.8

1014.6

1008.2

1008.4

1011.1

1011

1011.2

1010.8

1011.4

1011.7

1011.5

53 9.5 61 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

10

10.3

10.2

09.8

09.3

09.2

08.8

09.1

10.3

12.8

14.6

08.2

08.4

11.1

11 11.2

10.8

11.4

11.7

11.5

54 9.5 61 0

1010.2

1010.2

1009.8

1009.3

1009.3

1008.8

1009.1

1010.3

1012.8

1014.6

1008.1

1008.4

1011.1

1011

1011.2

1010.8

1011.4

1011.7

1011.5

55 9.4 61 0

1010.3

1010.2

1009.8

1009.3

1009.3

1008.7

1009.1

1010.3

1012.8

1014.6

1008.2

1008.4

1011

1011

1011.2

1010.9

1011.4

1011.7

1011.5

56 9.6 61 0

1010.3

1010.2

1009.8

1009.3

1009.3

1008.8

1009.1

1010.3

1012.8

1014.6

1008.1

1008.5

1011

1011

1011.2

1010.8

1011.4

1011.7

1011.5

57 9.4 60 0

1010.2

1010.2

1009.8

1009.3

1009.2

1008.8

1009.1

1010.3

1012.8

1014.6

1008.1

1008.4

1011

1011

1011.2

1010.9

1011.5

1011.7

1011.5

58 9.4 61 0

1010.3

1010.2

1009.8

1009.3

1009.3

1008.8

1009.1

1010.3

1012.8

1014.6

1008.2

1008.5

1011.1

1011

1011.2

1010.8

1011.4

1011.7

1011.5

59 9.4 61 0

1010.3

1010.2

1009.9

1009.3

1009.3

1008.8

1009.1

1010.3

1012.8

1014.7

1008.2

1008.5

1011.1

1011.1

1011.2

1010.9

1011.5

1011.7

1011.5

60 9.4 61 0

1010.3

1010.2

1009.9

1009.4

1009.3

1008.8

1009.1

1010.4

1012.9

1014.6

1008.2

1008.5

1011.1

1011.1

1011.2

1010.9

1011.5

1011.7

1011.5

9.44

60.85 0

1010.285

1010.2

1009.85

1009.325

1009.29

1008.795

1009.105

1010.34

1012.84

1014.605

1008.18

1008.455

1011.08

1011.035

1011.215

1010.87

1011.425

1011.7

1011.51

Avg

2110.024

2109.847

2109.116

2108.019

2107.946

2106.912

2107.56

2110.139

2115.36

2119.047

2105.628

2106.202

2111.684

2111.59

2111.966

2111.246

2112.405

2112.979

2112.583 psf

89.2466

FPS

11

9

0.28432

0.36839

0.41375

0.49893

0.54981

0.55203

0.56973

0.25224

0.234496

0.638266

0.80314

0.64716

0.13277

0.16485

0.12503

0.09073

0.05644

0.01772

0.015464 Cp

6127.7

104 0

1001.5

998.5

997.7

996.4

995.9

995.3

995.5

999.6

1006.5

1011.3

991.9

993.5

1000.1

1000.9

1001.6

1001.6

1002.5

1003

1003.2

6227.3

103 0

1001.5

998.5

997.6

996.4

995.9

995.3

995.5

999.6

1006.5

1011.3

991.9

993.5

1000

1000.9

1001.6

1001.6

1002.5

1003

1003.2

6326.9

103 0

1001.6

998.5

997.7

996.5

996

995.3

995.6

999.7

1006.6

1011.3

992

993.6

1000.1

1000.9

1001.6

1001.7

1002.6

1003.1

1003.2

6426.6

102 0

1001.6

998.6

997.8

996.5

996

995.4

995.7

999.7

1006.6

1011.3

992

993.6

1000.1

1001

1001.6

1001.7

1002.5

1003

1003.2

6526.7

102 0

1001.5

998.5

997.7

996.4

995.9

995.3

995.5

999.6

1006.5

1011.3

992

993.6

1000.1

1000.9

1001.6

1001.6

1002.5

1003

1003.2

6626.9

103 0

1001.5

998.5

997.7

996.4

995.9

995.3

995.6

999.6

1006.5

1011.3

991.9

993.4

1000

1000.9

1001.6

1001.6

1002.5

1003

1003.2

6726.8

102 0

1001.5

998.5

997.7

996.4

995.9

995.3

995.6

999.7

1006.6

1011.3

991.9

993.5

1000.1

1001

1001.6

1001.7

1002.5

1003

1003.2

6826.2

101 0

1001.6

998.6

997.8

996.5

996

995.4

995.7

999.7

1006.6

1011.2

992

993.6

1000.1

1001

1001.7

1001.7

1002.6

1003

1003.2

6926.9

103 0

1001.6

998.6

997.8

996.6

996

995.4

995.7

999.8

1006.6

1011.3

992

993.6

1000.1

1001

1001.7

1001.7

1002.6

1003.1

1003.2

70 26. 10 0 10 99 99 99 99 99 99 99 10 10 99 99 10 10 10 10 10 10 10

12

4 2 01.6

8.6 7.8 6.5 6 5.4 5.6 9.7 06.6

11.3

2 3.5 00.1

00.9

01.7

01.7

02.5

03 03.2

7126.5

102 0

1001.6

998.5

997.8

996.5

996

995.4

995.6

999.7

1006.6

1011.3

992

993.6

1000.1

1001

1001.6

1001.6

1002.5

1003

1003.2

7226.8

102 0

1001.6

998.5

997.8

996.5

996

995.4

995.7

999.8

1006.6

1011.3

992

993.6

1000.1

1001

1001.7

1001.7

1002.6

1003.1

1003.3

7326.6

102 0

1001.7

998.7

997.8

996.6

996.1

995.5

995.8

999.8

1006.6

1011.3

992.2

993.7

1000.2

1001

1001.7

1001.8

1002.6

1003.1

1003.3

7426.3

101 0

1001.6

998.6

997.8

996.5

996

995.5

995.7

999.8

1006.6

1011.3

992.1

993.7

1000.2

1001

1001.7

1001.7

1002.5

1003

1003.2

7527.2

103 0

1001.6

998.5

997.8

996.5

995.9

995.3

995.6

999.7

1006.6

1011.3

992

993.6

1000.1

1000.9

1001.6

1001.7

1002.5

1003.1

1003.2

7626.5

102 0

1001.6

998.6

997.7

996.5

995.9

995.4

995.6

999.7

1006.6

1011.3

992.1

993.7

1000.1

1001

1001.7

1001.7

1002.6

1003.1

1003.3

7726.8

102 0

1001.6

998.6

997.8

996.6

996.1

995.5

995.7

999.8

1006.6

1011.3

992.1

993.7

1000.2

1001

1001.7

1001.7

1002.6

1003.1

1003.3

7826.9

103 0

1001.6

998.6

997.9

996.6

996.1

995.5

995.8

999.8

1006.7

1011.4

992.3

993.8

1000.2

1001.1

1001.8

1001.8

1002.7

1003.2

1003.4

79 27103 0

1001.7

998.7

997.9

996.6

996.1

995.5

995.7

999.8

1006.6

1011.3

992.1

993.7

1000.2

1001

1001.8

1001.7

1002.6

1003.1

1003.3

8026.2

101 0

1001.6

998.5

997.7

996.5

995.9

995.3

995.6

999.7

1006.6

1011.3

991.9

993.5

1000.1

1000.9

1001.6

1001.6

1002.5

1003

1003.2

26.76

102.3 0

1001.

998.5

997.7

996.5

995.9

995.3

995.6

999.7

1006.

1011.

992.0

993.6

1000.

1000.

1001.

1001.

1002.

1003.

1003.

Avg

13

585

6 65 8 85 4 15 585

3 2 115

965

66 68 55 05 235

2091.854

2085.536

2083.876

2081.234

2080.147

2078.905

2079.437

2087.948

2102.296

2112.144

2071.877

2075.177

2088.784

2090.559

2092.01

2092.052

2093.869

2094.913

2095.3 psf

150.04

FPS

0.13207

0.39119

0.44192

0.52973

0.58553

0.59411

0.60465

0.271

0.241771

0.614447

0.89733

0.74045

0.25539

0.19685

0.14261

0.10203

0.06534

0.03413

0.006849 Cp

qV_ref

Alpha P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9

P10

P11

P12

P13

P14

P15

P16

P17

P18

P19

count

[psf]

[mph]

[deg]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

1mbar =

2.088543

psf

1 0.1 7 01016

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.9

1016.1

1016.2

1016.2

1015.8

1016

1016.2

1016.1

1015.6

1016.1

1016.2

1015.9

1mph=

1.466667

fps

2 0.1 6 01016

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.9

1016.1

1016.2

1016.2

1015.7

1016

1016.2

1016.2

1015.6

1016.1

1016.2

1015.9

1sq.ft=

144

psin

3 0.1 7 01016

1016.3

1016.1

1016

1016.1

1015.7

1016.1

1015.9

1016.2

1016.2

1016.2

1015.8

1016

1016.2

1016.2

1015.7

1016

1016.2

1015.9

4 0 4 01016

1016.

1016.

1016

1016.

1015.

1016.

1015.

1016.

1016.

1016.

1015.

1016

1016.

1016.

1015.

1016.

1016.

1015.

14

3 1 1 7 1 9 1 2 2 7 2 2 7 1 2 9

5 0.1 6 01016

1016.3

1016.2

1016

1016.1

1015.7

1016.1

1015.9

1016.2

1016.2

1016.2

1015.7

1016

1016.2

1016.2

1015.7

1016.1

1016.2

1015.9

6 0.1 6 01016

1016.3

1016.2

1016

1016.1

1015.7

1016.1

1015.9

1016.2

1016.2

1016.2

1015.8

1016

1016.2

1016.2

1015.7

1016.1

1016.2

1015.9

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2121.96

2122.534

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2121.929

2122.242

2121.334

2122.169

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2121.26

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8.873335

FPS

0.97862

1.41831

1.08854

1.52824

2.51755

1.41831

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1.63816

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1.85801

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2118.827

2119.287

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44.14

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18

668

0.42829

0.49567

0.44177

0.51812

0.50465

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41 12 69 0

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100.0267

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994.3

993.3

991.8

990.5

992.7

997.9

1015.8

1000.5

1000.9

1002.7

1003.3

1003.6

1003.2

1003.8

1004

1003.9

7326.9

102 0

1000.7

998.8

995.2

994.1

992.9

991.4

990.1

992.3

997.6

1015.8

1000.3

1000.7

1002.5

1003.2

1003.5

1003.1

1003.7

1003.9

1003.9

7426.5

102 0

1000.5

998.8

995.1

994

992.9

991.4

990.2

992.3

997.6

1015.8

1000.3

1000.8

1002.6

1003.2

1003.5

1003.2

1003.7

1004

1004

7526.5

102 0

1000.7

998.9

995.3

994.2

993.1

991.5

990.3

992.4

997.7

1015.8

1000.4

1000.9

1002.6

1003.3

1003.5

1003.2

1003.8

1004

1003.9

7626.8

102 0

1000.6

998.8

995.2

994.1

993

991.5

990.2

992.4

997.7

1015.8

1000.5

1000.9

1002.6

1003.3

1003.5

1003.3

1003.8

1004.1

1004

77 27103 0

1000.7

999

995.4

994.3

993.2

991.7

990.4

992.5

997.8

1015.8

1000.5

1000.9

1002.7

1003.3

1003.5

1003.2

1003.8

1004

1003.9

78 27. 10 0 10 99 99 99 99 99 99 99 99 10 10 10 10 10 10 10 10 10 10

22

4 4 00.5

8.7 5.1 4 2.9 1.3 0 2.2 7.5 15.8

00.2

00.7

02.5

03.1

03.4

03 03.6

03.8

03.7

7926.5

102 0

1000.5

998.8

995.1

994

993

991.4

990.2

992.4

997.7

1015.8

1000.3

1000.8

1002.5

1003.3

1003.4

1003.2

1003.8

1004

1004

80 27103 0

1000.5

998.7

995.1

993.9

992.8

991.3

990

992.2

997.5

1015.8

1000.2

1000.7

1002.5

1003.1

1003.4

1003.1

1003.6

1003.9

1003.8

26.77

102.35 0

1000.605

998.83

995.19

994.075

992.985

991.445

990.18

992.355

997.65

1015.795

1000.34

1000.8

1002.565

1003.235

1003.47

1003.17

1003.73

1003.97

1003.905

Avg

2089.807

2086.1

2078.498

2076.169

2073.892

2070.676

2068.034

2072.577

2083.635

2121.532

2089.254

2090.214

2093.901

2095.3

2095.791

2095.164

2096.334

2096.835

2096.699 psf

150.1134

FPS

0.20811

0.36961

0.64228

0.71835

0.8186

0.90091

1.03003

0.84474

0.45504

0.965282

0.24751

0.17807

0.06378

0.01931

0.00097

0.014632

0.027115

0.038037

0.059492 Cp

qV_ref

Alpha P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9

P10

P11

P12

P13

P14

P15

P16

P17

P18

P19

count

[psf]

[mph]

[deg]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

1mbar =

2.088543

psf

1 0.1 6 01015.

1016.

1016.

1015.

1016.

1015.

1016.

1015.

1016.

1016.

1016.

1015.

1016

1016.

1016.

1015.

1016

1016.

1015.

1m

1.466

fp

23

9 2 1 9 1 7 1 8 1 2 2 8 2 1 6 1 8 ph=

667

s

2 0.1 6 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016

1015.8

1016.1

1016.2

1016.2

1015.8

1016

1016.2

1016.2

1015.7

1016

1016.2

1015.8

1sq.ft=

144

psin

3 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016

1015.8

1016.2

1016.2

1016.2

1015.7

1016

1016.2

1016.1

1015.6

1016

1016.1

1015.8

4 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016

1015.8

1016.1

1016.2

1016.2

1015.8

1016

1016.2

1016.1

1015.7

1016

1016.1

1015.8

5 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016

1015.8

1016.1

1016.2

1016.2

1015.8

1016

1016.2

1016.1

1015.6

1016

1016.1

1015.8

6 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016

1015.8

1016.1

1016.2

1016.2

1015.8

1016

1016.2

1016.1

1015.6

1016

1016.1

1015.8

7 0.1 6 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016

1015.8

1016.1

1016.2

1016.2

1015.8

1016

1016.2

1016.2

1015.6

1016

1016.1

1015.8

8 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016

1015.8

1016.1

1016.2

1016.2

1015.8

1016

1016.2

1016.2

1015.6

1016

1016.1

1015.8

9 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016

1015.8

1016.1

1016.2

1016.2

1015.8

1016

1016.2

1016.2

1015.6

1016

1016.1

1015.8

10 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.2

1015.8

1016

1016.2

1016.2

1015.7

1016

1016.1

1015.8

11 0.1 6 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.2

1015.8

1016

1016.2

1016.2

1015.7

1016

1016.1

1015.8

12 0.2 8 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

24

15.9

16.2

16.1

15.9

16.1

15.7

16.1

15.8

16.1

16.2

16.2

15.8

16 16.2

16.1

15.6

16 16.1

15.8

13 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.2

1015.8

1016

1016.2

1016.1

1015.6

1016

1016.1

1015.8

14 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.2

1015.8

1016

1016.2

1016.1

1015.6

1016

1016.1

1015.8

15 0.1 6 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.2

1015.7

1016

1016.2

1016.1

1015.6

1016

1016.1

1015.8

16 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.2

1015.8

1016.1

1016.2

1016.1

1015.6

1016

1016.1

1015.8

17 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.2

1015.8

1016

1016.2

1016.2

1015.6

1016

1016.1

1015.8

18 0.1 6 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.2

1015.7

1016

1016.2

1016.2

1015.6

1016

1016.1

1015.8

19 0.1 6 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016

1015.8

1016.1

1016.2

1016.2

1015.7

1016

1016.2

1016.1

1015.6

1016

1016.1

1015.8

20 0.2 8 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016

1015.8

1016.1

1016.2

1016.2

1015.7

1016

1016.2

1016.1

1015.6

1016

1016.1

1015.8

0.11

6.75 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.05

1015.8

1016.105

1016.2

1016.2

1015.775

1016.005

1016.2

1016.14

1015.62

1016

1016.105

1015.8

Avg

2121.751

2122.378

2122.169

2121.751

2122.169

2121.334

2122.065

2121.542

2122.179

2122.378

2122.378

2121.49

2121.971

2122.378

2122.253

2121.166

2121.96

2122.179

2121.542 psf

25

9.900002

FPS

2.60748

2.51255

1.65815

2.79735

2.70242

1.08854

1.84801

2.79735

2.70242

0.24053

1.46828

1.37334

2.70242

0.89868

2.03788

2.41762

2.79735

2.70242

2.03788 Cp

21 2.4 31 0

1014.7

1014.7

1014

1013.7

1013.9

1013.4

1013.6

1013.2

1013.7

1016

1015.4

1014.9

1015.1

1015.2

1015.2

1014.7

1015.1

1015.1

1014.8

22 2.4 31 0

1014.7

1014.7

1014

1013.7

1013.9

1013.4

1013.6

1013.2

1013.7

1016

1015.4

1014.9

1015.2

1015.2

1015.2

1014.7

1015.1

1015.2

1014.8

23 2.3 30 0

1014.7

1014.7

1014

1013.8

1013.9

1013.5

1013.6

1013.2

1013.7

1016

1015.4

1014.9

1015.2

1015.3

1015.2

1014.7

1015.1

1015.2

1014.8

24 2.4 31 0

1014.7

1014.7

1014

1013.7

1013.9

1013.4

1013.6

1013.2

1013.7

1016

1015.4

1014.9

1015.1

1015.3

1015.2

1014.7

1015.1

1015.2

1014.9

25 2.5 31 0

1014.7

1014.7

1014

1013.7

1013.9

1013.4

1013.5

1013.2

1013.7

1016

1015.4

1014.9

1015.1

1015.3

1015.2

1014.7

1015.1

1015.2

1014.8

26 2.4 30 0

1014.7

1014.7

1014

1013.8

1013.9

1013.4

1013.6

1013.2

1013.7

1016

1015.4

1014.9

1015.1

1015.2

1015.2

1014.7

1015.1

1015.2

1014.8

27 2.5 31 0

1014.7

1014.7

1014

1013.7

1013.9

1013.5

1013.5

1013.2

1013.7

1016

1015.4

1014.9

1015.2

1015.3

1015.2

1014.7

1015.1

1015.2

1014.8

28 2.5 31 0

1014.7

1014.7

1014

1013.8

1013.9

1013.5

1013.5

1013.2

1013.7

1016

1015.4

1014.9

1015.2

1015.3

1015.2

1014.7

1015.1

1015.2

1014.8

29 2.5 31 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

26

14.7

14.7

14 13.7

13.9

13.5

13.5

13.2

13.7

16 15.4

14.9

15.2

15.3

15.2

14.7

15.1

15.2

14.8

30 2.4 31 0

1014.7

1014.7

1014

1013.8

1013.9

1013.4

1013.5

1013.2

1013.7

1015.9

1015.4

1014.9

1015.1

1015.2

1015.2

1014.7

1015.1

1015.2

1014.9

31 2.6 32 0

1014.7

1014.7

1014

1013.7

1013.9

1013.4

1013.5

1013.2

1013.6

1016

1015.4

1014.9

1015.1

1015.2

1015.2

1014.7

1015.1

1015.2

1014.8

32 2.5 31 0

1014.7

1014.7

1014

1013.7

1013.9

1013.4

1013.5

1013.2

1013.7

1016

1015.4

1014.9

1015.1

1015.2

1015.2

1014.7

1015.1

1015.2

1014.8

33 2.4 31 0

1014.7

1014.7

1014

1013.7

1013.9

1013.4

1013.5

1013.2

1013.6

1016

1015.4

1014.9

1015.1

1015.2

1015.2

1014.7

1015.1

1015.1

1014.8

34 2.5 31 0

1014.7

1014.7

1014

1013.7

1013.9

1013.4

1013.5

1013.2

1013.6

1016

1015.4

1014.9

1015.1

1015.2

1015.2

1014.7

1015.1

1015.2

1014.8

35 2.4 31 0

1014.7

1014.7

1014

1013.7

1013.9

1013.4

1013.5

1013.2

1013.7

1016

1015.4

1014.9

1015.1

1015.2

1015.2

1014.7

1015.1

1015.2

1014.8

36 2.5 31 0

1014.7

1014.8

1014

1013.7

1013.9

1013.4

1013.5

1013.2

1013.7

1016

1015.4

1014.9

1015.1

1015.2

1015.2

1014.7

1015.1

1015.2

1014.8

37 2.4 31 0

1014.7

1014.7

1014

1013.7

1013.9

1013.4

1013.5

1013.2

1013.6

1016

1015.4

1014.9

1015.1

1015.2

1015.2

1014.7

1015.1

1015.1

1014.8

38 2.5 31 0

1014.7

1014.7

1014

1013.7

1013.9

1013.4

1013.5

1013.2

1013.6

1016

1015.4

1014.9

1015.1

1015.3

1015.2

1014.7

1015.1

1015.1

1014.8

39 2.5 32 0

1014.7

1014.7

1014

1013.7

1013.9

1013.4

1013.5

1013.2

1013.6

1016

1015.5

1014.9

1015.1

1015.3

1015.2

1014.7

1015.1

1015.2

1014.9

40 2.4 30 01014.

1014.

1014

1013.

1013.

1013.

1013.

1013.

1013.

1016

1015.

1014.

1015.

1015.

1015.

1014.

1015.

1015.

1014.

27

7 7 8 9 4 6 2 7 4 9 2 3 2 7 1 2 8

2.45

30.95 0

1014.7

1014.705

1014

1013.725

1013.9

1013.42

1013.53

1013.2

1013.67

1015.995

1015.405

1014.9

1015.13

1015.245

1015.2

1014.7

1015.1

1015.18

1014.815

Avg

2119.245

2119.255

2117.783

2117.209

2117.574

2116.572

2116.801

2116.112

2117.094

2121.95

2120.717

2119.663

2120.143

2120.383

2120.289

2119.245

2120.08

2120.248

2119.485 psf

45.39334

FPS

0.18493

0.43214

0.90953

1.02461

1.04166

1.0374

1.27609

1.38691

1.24199

0.791146

0.211468

0.147533

0.087861

0.100648

0.062287

0.062287

0.062287

0.045237

0.023926 Cp

4111.8 68 0

1009.1

1008.3

1007.3

1005.3

1004.7

1003.5

1002.5

1002

1003

1014.8

1012.4

1011.4

1011.6

1011.6

1011.4

1010.8

1011.2

1011.2

1010.9

4212.1 69 0

1009.1

1008.3

1007.3

1005.3

1004.6

1003.5

1002.5

1002

1003

1014.8

1012.4

1011.4

1011.6

1011.6

1011.4

1010.9

1011.2

1011.2

1010.9

4311.8 68 0

1009.1

1008.3

1007.3

1005.3

1004.7

1003.5

1002.6

1002.1

1003.1

1014.8

1012.4

1011.4

1011.6

1011.6

1011.4

1010.9

1011.2

1011.2

1010.9

4412.1 69 0

1009.1

1008.3

1007.3

1005.3

1004.6

1003.5

1002.5

1002

1003

1014.8

1012.4

1011.4

1011.5

1011.6

1011.4

1010.9

1011.2

1011.2

1010.9

4511.8 68 0

1009.1

1008.3

1007.3

1005.3

1004.6

1003.5

1002.5

1002

1003

1014.8

1012.4

1011.4

1011.5

1011.6

1011.4

1010.9

1011.2

1011.2

1010.9

46 12. 69 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

28

3 09.1

08.2

07.2

05.3

04.6

03.5

02.5

02 03 14.8

12.4

11.4

11.5

11.5

11.4

10.9

11.2

11.2

10.8

4711.8 68 0

1009

1008.2

1007.2

1005.2

1004.5

1003.4

1002.4

1001.9

1003

1014.8

1012.4

1011.4

1011.5

1011.6

1011.4

1010.9

1011.2

1011.2

1010.9

4811.9 68 0

1009.1

1008.3

1007.3

1005.3

1004.7

1003.5

1002.6

1002.1

1003.1

1014.8

1012.4

1011.4

1011.5

1011.6

1011.4

1010.9

1011.2

1011.2

1010.9

4912.1 69 0

1009.1

1008.3

1007.3

1005.3

1004.6

1003.5

1002.5

1002

1003

1014.8

1012.4

1011.4

1011.5

1011.6

1011.4

1010.9

1011.2

1011.2

1010.9

5012.2 69 0

1009

1008.2

1007.2

1005.2

1004.6

1003.4

1002.4

1001.9

1003

1014.8

1012.4

1011.4

1011.5

1011.5

1011.4

1010.8

1011.1

1011.2

1010.9

5111.9 68 0

1009

1008.2

1007.2

1005.2

1004.4

1003.3

1002.3

1001.8

1002.8

1014.8

1012.4

1011.3

1011.5

1011.5

1011.4

1010.7

1011.1

1011.1

1010.7

5212.5 70 0

1008.8

1008

1007

1005

1004.2

1003

1002

1001.5

1002.5

1014.7

1012.2

1011.2

1011.4

1011.4

1011.2

1010.6

1011

1011

1010.6

5312.5 70 0

1008.7

1007.8

1006.8

1004.8

1004

1002.9

1001.8

1001.3

1002.3

1014.7

1012.2

1011.2

1011.3

1011.4

1011.2

1010.6

1011

1011

1010.6

5412.5 70 0

1008.7

1007.8

1006.8

1004.8

1004

1002.8

1001.8

1001.3

1002.3

1014.7

1012.2

1011.2

1011.3

1011.3

1011.2

1010.6

1010.9

1011

1010.6

5512.7 70 0

1008.7

1007.8

1006.8

1004.8

1004

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1001.8

1001.3

1002.3

1014.7

1012.2

1011.1

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1011.3

1011.2

1010.6

1010.9

1010.9

1010.6

56 13 71 0

1008.7

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1006.7

1004.7

1004

1002.7

1001.7

1001.2

1002.2

1014.7

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5712.6 70 0

1008.

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29

7 8 7 7 9 7 7 2 2 7 2 1 2 3 1 6 9 9 6

5812.7 70 0

1008.6

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5912.9 71 0

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1004.7

1003.9

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1014.7

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1011.3

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1010.6

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6012.8 71 0

1008.6

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1006.7

1004.6

1003.9

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1011.3

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1010.9

1010.5

12.3

69.3 0

1008.895

1008.06

1007.04

1005.035

1004.32

1003.15

1002.145

1001.645

1002.66

1014.755

1012.31

1011.28

1011.415

1011.46

1011.29

1010.74

1011.065

1011.075

1010.74

Avg

2107.121

2105.377

2103.247

2099.059

2097.566

2095.122

2093.023

2091.979

2094.099

2119.36

2114.253

2112.102

2112.384

2112.478

2112.123

2110.974

2111.653

2111.674

2110.974 psf

101.64

FPS

0.22171

0.41359

0.56216

0.87884

1.03336

1.14967

1.38654

1.43748

1.31608

0.747847

0.317403

0.215523

0.187506

0.178167

0.149301

0.140811

0.128076

0.112794

0.113643 Cp

62 27103 0

1000.2

997.7

995.1

992.8

989.5

987.3

984.6

983.8

985.7

1013

1007.5

1005.8

1005.8

1005.6

1005.3

1004.6

1004.9

1004.8

1004.4

6326.8

102 0

1000.1

997.6

994.9

992.7

989.4

987.1

984.4

983.6

985.6

1013

1007.4

1005.7

1005.7

1005.4

1005.2

1004.5

1004.8

1004.7

1004.3

6427.2

103 0

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989

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984

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985.2

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30

9 3 6 6 4 1 5 7 7 3

6527.1

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985.3

1012.9

1007.3

1005.6

1005.6

1005.4

1005.1

1004.5

1004.7

1004.7

1004.3

6627.6

104 0

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989

986.7

984

983.2

985.2

1012.9

1007.3

1005.6

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1005.1

1004.4

1004.7

1004.6

1004.2

6727.5

104 0

999.8

997.4

994.6

992.3

988.9

986.7

983.8

983.1

985.1

1012.9

1007.3

1005.6

1005.6

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1004.5

1004.7

1004.7

1004.3

6827.3

103 0

999.9

997.5

994.7

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989.1

986.9

984.1

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985.3

1012.9

1007.4

1005.6

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1005.4

1005.2

1004.5

1004.8

1004.7

1004.3

6927.3

103 0

999.9

997.5

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989.2

986.9

984.2

983.4

985.4

1013

1007.4

1005.7

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1005.2

1004.6

1004.8

1004.8

1004.4

7027.1

103 0

1000

997.6

994.9

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989.3

987.1

984.3

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1013

1007.4

1005.7

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1005.5

1005.2

1004.5

1004.8

1004.8

1004.3

7127.3

103 0

999.9

997.5

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989.1

986.8

984

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985.1

1012.9

1007.3

1005.6

1005.5

1005.3

1005.1

1004.4

1004.6

1004.6

1004.2

7227.9

104 0

999.7

997.2

994.5

992.2

988.8

986.5

983.7

982.9

984.9

1012.9

1007.2

1005.5

1005.5

1005.2

1005

1004.3

1004.5

1004.5

1004.1

7328.1

105 0

999.6

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994.3

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988.6

986.3

983.5

982.7

984.8

1012.9

1007.2

1005.5

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1005.3

1005

1004.4

1004.6

1004.6

1004.2

7427.6

104 0

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997.3

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989

986.7

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983.3

985.4

1013

1007.4

1005.7

1005.6

1005.4

1005.1

1004.6

1004.8

1004.8

1004.4

7526.6

102 0

1000.1

997.6

995

992.7

989.4

987.2

984.4

983.6

985.6

1012.9

1007.4

1005.7

1005.6

1005.4

1005.2

1004.5

1004.8

1004.7

1004.3

31

7627.3

103 0

999.9

997.4

994.7

992.4

989.1

986.8

984.1

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985.3

1012.9

1007.3

1005.7

1005.6

1005.4

1005.1

1004.5

1004.7

1004.7

1004.3

7727.1

103 0

999.8

997.3

994.6

992.4

989

986.7

983.9

983.2

985.2

1012.9

1007.3

1005.6

1005.6

1005.4

1005.1

1004.4

1004.7

1004.7

1004.3

7827.2

103 0

999.9

997.4

994.6

992.4

989.1

986.8

984

983.2

985.2

1012.9

1007.3

1005.6

1005.6

1005.4

1005.1

1004.5

1004.7

1004.7

1004.2

7927.1

103 0

999.9

997.4

994.6

992.4

989.1

986.8

984

983.2

985.2

1012.9

1007.3

1005.7

1005.6

1005.4

1005.1

1004.4

1004.7

1004.6

1004.2

80 27103 0

999.8

997.3

994.6

992.3

989

986.7

983.9

983.2

985.2

1012.9

1007.3

1005.7

1005.6

1005.4

1005.1

1004.5

1004.7

1004.7

1004.3

27.26842

103.2105 0

999.8895

997.4158

994.6895

992.4368

989.0842

986.8158

984.0474

983.2789

985.2737

1012.926

1007.332

1005.642

1005.595

1005.395

1005.126

1004.479

1004.721

1004.689

1004.279

Avg

2088.313

2083.146

2077.452

2072.747

2065.745

2061.008

2055.226

2053.621

2057.787

2115.541

2103.856

2100.327

2100.228

2099.811

2099.25

2097.898

2098.404

2098.338

2097.48 psf

151.3755

FPS

0.24083

0.45289

0.6506

0.81241

1.08413

1.22073

1.46263

1.50617

1.37637

0.746198

0.310793

0.214327

0.187721

0.164744

0.144185

0.132898

0.120804

0.110726

0.105325 Cp

qV_ref

Alph P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9

P10

P11

P12

P13

P14

P15

P16

P17

P18

P19

32

a

count

[psf]

[mph]

[deg]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

1mbar =

2.088543

psf

1 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.1

1016.2

1015.8

1016

1016.2

1016.2

1015.6

1016

1016.1

1015.8

1mph=

1.466667

fps

2 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.1

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1016

1016.2

1016.2

1015.6

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1016.1

1015.8

1sq.ft=

144

psin

3 0.1 7 0

1015.9

1016.2

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4 0.1 6 0

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5 0.1 6 0

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6 0.1 7 0

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8 0.1 7 0

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33

10 0.1 7 0

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12 0.1 7 0

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13 0.1 7 0

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14 0.1 6 0

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15 0.1 6 0

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16 0.1 6 0

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17 0.1 7 0

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18 0.1 6 0

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19 0.1 5 0

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20 0.1 7 0

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1016.1

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0.1 6.5 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Av

34

15.895

16.2

16.1

15.89

16.1

15.7

16.03

15.795

16.095

16.18

16.2

15.735

16.005

16.18

16.145

15.6

16 16.1

15.8

g

2121.741

2122.378

2122.169

2121.73

2122.169

2121.334

2122.023

2121.532

2122.159

2122.336

2122.378

2121.407

2121.971

2122.336

2122.263

2121.125

2121.96

2122.169

2121.542 psf

9.533336

FPS

3.07266

2.86381

1.92396

3.38594

3.07266

1.2974

2.55052

3.28151

3.28151

0.25313

1.71511

2.4461

3.07266

1.50625

2.23724

3.17709

3.17709

3.17709

2.34167 Cp

21 2.4 31 0

1014.3

1014.6

1014.5

1014.3

1014.5

1014.1

1014.4

1014

1014.2

1016

1015.3

1014.8

1015.1

1015.2

1015.1

1014.6

1014.9

1014.9

1014.6

22 2.4 30 0

1014.3

1014.6

1014.4

1014.3

1014.4

1014.1

1014.5

1014

1014.2

1016

1015.3

1014.8

1015.1

1015.2

1015.1

1014.5

1014.9

1014.9

1014.6

23 2.5 31 0

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1014.6

1014.4

1014.3

1014.5

1014.1

1014.5

1014

1014.2

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1015.3

1014.8

1015.1

1015.2

1015.1

1014.5

1014.9

1014.9

1014.6

24 2.3 30 0

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1014.4

1014.3

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25 2.4 31 0

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1014.6

1014.5

1014.3

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1014.2

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1015.4

1014.8

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1015.2

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1014.9

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26 2.5 31 0

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1014.3

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1014.8

1015.1

1015.2

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1014.5

1014.9

1014.9

1014.6

35

27 2.4 31 0

1014.3

1014.6

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1014.3

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1015.3

1014.8

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28 2.5 31 0

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1014.9

1014.9

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29 2.5 31 0

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1014.6

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1015.4

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1014.9

1014.9

1014.6

30 2.5 31 0

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1014.6

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1015.1

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1014.9

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31 2.4 31 0

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1014.6

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1015.4

1014.8

1015.1

1015.2

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1014.5

1014.9

1014.9

1014.6

32 2.5 31 0

1014.3

1014.6

1014.4

1014.3

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1014.9

1015.1

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1014.6

1014.9

1015

1014.6

33 2.6 32 0

1014.3

1014.6

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1014.6

1014.9

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34 2.4 31 0

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35 2.3 30 0

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1014.6

1014.9

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1014.6

36 2.4 31 0

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1014.6

1014.5

1014.3

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1016.1

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1014.8

1015.1

1015.2

1015.1

1014.6

1014.9

1015

1014.6

37 2.5 31 0

1014.3

1014.6

1014.5

1014.3

1014.5

1014.1

1014.5

1014

1014.2

1016.1

1015.4

1014.8

1015.1

1015.2

1015.1

1014.6

1014.9

1015

1014.6

38 2.4 31 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

36

14.4

14.6

14.5

14.3

14.5

14.1

14.5

14 14.2

16 15.4

14.8

15.1

15.2

15.1

14.6

14.9

14.9

14.6

39 2.4 31 0

1014.3

1014.6

1014.5

1014.3

1014.5

1014.1

1014.5

1014

1014.2

1016

1015.4

1014.9

1015.1

1015.1

1015.1

1014.6

1014.9

1014.9

1014.6

40 2.5 31 0

1014.3

1014.6

1014.5

1014.3

1014.5

1014.1

1014.5

1014

1014.2

1016

1015.4

1014.9

1015.1

1015.2

1015.1

1014.6

1014.9

1015

1014.6

2.44

30.9 0

1014.305

1014.595

1014.465

1014.3

1014.48

1014.1

1014.47

1014

1014.2

1016.025

1015.37

1014.82

1015.095

1015.18

1015.1

1014.555

1014.9

1014.935

1014.6

Avg

2118.42

2119.026

2118.754

2118.41

2118.786

2117.992

2118.765

2117.783

2118.201

2122.012

2120.644

2119.496

2120.07

2120.248

2120.08

2118.942

2119.663

2119.736

2119.036 psf

45.32001

FPS

0.52789

0.53217

0.51933

0.54073

0.55357

0.46369

0.48081

0.71192

0.79752

0.815969

0.178278

0.075563

0.054164

0.041324

0.02715

0.06567

0.11275

0.16839

0.16411 Cp

4112.1 69 0

1009.2

1008.2

1006.7

1005.4

1004.8

1001

1000.4

998.4

997.3

1008.7

1014.5

1013.1

1012.7

1012.5

1012.2

1011.5

1011.7

1011.6

1011.1

4211.9 68 0

1009.2

1008.2

1006.7

1005.4

1004.8

1001

1000.4

998.3

997.3

1008.7

1014.5

1013.1

1012.7

1012.5

1012.2

1011.5

1011.7

1011.6

1011.1

4312.1 69 0

1009.1

1008.1

1006.6

1005.3

1004.7

1001

1000.3

998.3

997.2

1008.7

1014.5

1013.1

1012.7

1012.4

1012.2

1011.5

1011.7

1011.6

1011.1

37

44 12 69 0

1009.1

1008.1

1006.7

1005.3

1004.7

1000.9

1000.3

998.3

997.3

1008.7

1014.5

1013.1

1012.7

1012.4

1012.2

1011.5

1011.7

1011.6

1011.1

4511.8 68 0

1009.2

1008.1

1006.7

1005.4

1004.7

1000.9

1000.3

998.2

997.2

1008.7

1014.5

1013.1

1012.7

1012.5

1012.2

1011.4

1011.7

1011.5

1011

4611.9 68 0

1009.1

1008.2

1006.7

1005.4

1004.8

1001

1000.4

998.3

997.2

1008.7

1014.5

1013.1

1012.7

1012.5

1012.2

1011.5

1011.7

1011.6

1011.1

4712.1 69 0

1009.1

1008.2

1006.7

1005.4

1004.8

1001

1000.4

998.4

997.3

1008.7

1014.5

1013.1

1012.7

1012.5

1012.2

1011.5

1011.7

1011.6

1011.1

4811.4 67 0

1009.2

1008.2

1006.7

1005.5

1004.8

1001

1000.4

998.4

997.3

1008.7

1014.5

1013.1

1012.7

1012.4

1012.2

1011.5

1011.7

1011.6

1011.1

4911.5 67 0

1009.2

1008.2

1006.7

1005.4

1004.7

1001

1000.4

998.3

997.3

1008.7

1014.5

1013.1

1012.7

1012.5

1012.2

1011.5

1011.7

1011.6

1011.1

5012.2 69 0

1009.2

1008.2

1006.8

1005.4

1004.8

1001

1000.4

998.4

997.4

1008.7

1014.5

1013.1

1012.7

1012.5

1012.2

1011.5

1011.7

1011.6

1011.1

51 12 69 0

1009.2

1008.2

1006.8

1005.5

1004.8

1001.1

1000.5

998.4

997.4

1008.8

1014.5

1013.1

1012.7

1012.5

1012.2

1011.5

1011.7

1011.6

1011.1

5212.3 69 0

1009.1

1008.1

1006.7

1005.4

1004.7

1000.9

1000.3

998.2

997.1

1008.6

1014.5

1013

1012.7

1012.4

1012.1

1011.4

1011.7

1011.5

1011

5312.2 69 0

1009.1

1008.1

1006.6

1005.2

1004.6

1000.8

1000.1

998

997

1008.6

1014.5

1013.1

1012.7

1012.4

1012.1

1011.4

1011.6

1011.5

1011

54 12 68 01009

1008

1006.6

1005.2

1004.5

1000.7

1000

998

996.9

1008.6

1014.5

1013.1

1012.7

1012.4

1012.1

1011.4

1011.6

1011.5

1011

55 12. 69 0 10 10 10 10 10 10 10 99 99 10 10 10 10 10 10 10 10 10 10

38

1 09 08 06.5

05.2

04.5

00.7

00 7.9 6.9 08.5

14.5

13.1

12.7

12.4

12.1

11.4

11.6

11.5

11

5612.2 69 0

1009

1008

1006.5

1005.1

1004.5

1000.7

1000

997.9

996.9

1008.6

1014.5

1013.1

1012.7

1012.4

1012.1

1011.4

1011.6

1011.5

1011

5711.8 68 0

1009.1

1008

1006.5

1005.2

1004.5

1000.7

1000.1

998

997

1008.6

1014.5

1013.1

1012.7

1012.4

1012.1

1011.4

1011.6

1011.5

1011

5811.9 68 0

1009.1

1008

1006.6

1005.2

1004.6

1000.7

1000.1

998

997

1008.6

1014.5

1013.1

1012.7

1012.4

1012.1

1011.4

1011.7

1011.5

1011

5912.1 69 0

1009.1

1008.1

1006.7

1005.3

1004.7

1000.9

1000.3

998.3

997.3

1008.7

1014.5

1013.1

1012.7

1012.5

1012.2

1011.5

1011.7

1011.7

1011.2

6011.7 68 0

1009.3

1008.3

1006.9

1005.7

1005

1001.3

1000.7

998.7

997.7

1008.8

1014.5

1013.1

1012.8

1012.5

1012.3

1011.5

1011.8

1011.6

1011.1

11.965

68.45 0

1009.13

1008.125

1006.67

1005.345

1004.7

1000.915

1000.29

998.235

997.2

1008.67

1014.5

1013.095

1012.705

1012.45

1012.17

1011.46

1011.68

1011.565

1011.065

Avg

2107.612

2105.513

2102.474

2099.707

2098.36

2090.454

2089.149

2084.857

2082.696

2106.651

2118.827

2115.893

2115.078

2114.546

2113.961

2112.478

2112.938

2112.697

2111.653 psf

100.3934

FPS

0.2149

0.44182

0.67049

0.87733

1.02396

1.59999

1.77716

2.10096

2.33399

0.32138

0.680565

0.510375

0.389932

0.327966

0.27909

0.242434

0.211014

0.173485

0.145556 Cp

39

6126.9

103 0

1000.5

997.6

994.3

991.2

988.8

982.2

979.3

975.3

972.5

999

1012.4

1009.7

1008.5

1007.7

1007.1

1006.1

1006.1

1005.7

1005

6227.2

103 0

1000.6

997.7

994.4

991.4

988.9

982.2

979.3

975.2

972.5

999.1

1012.4

1009.7

1008.5

1007.7

1007

1006

1006.1

1005.7

1004.9

6327.3

103 0

1000.4

997.5

994.2

991.1

988.6

981.9

978.9

974.8

972

998.9

1012.4

1009.7

1008.4

1007.7

1007

1006.1

1006

1005.7

1005

6426.8

102 0

1000.5

997.6

994.4

991.3

988.8

982.1

979.2

975.1

972.4

999

1012.4

1009.7

1008.4

1007.7

1007

1006.1

1006

1005.7

1005

6526.7

102 0

1000.5

997.7

994.4

991.3

988.8

982.2

979.2

975.2

972.5

999

1012.4

1009.7

1008.4

1007.7

1007

1006.1

1006.1

1005.7

1005

6626.6

102 0

1000.5

997.6

994.3

991.2

988.7

982.1

979.2

975.1

972.3

998.9

1012.3

1009.7

1008.4

1007.6

1007

1006

1006

1005.6

1004.9

6727.4

104 0

1000.4

997.5

994.2

991.1

988.6

981.9

978.9

974.8

972.1

998.8

1012.3

1009.7

1008.4

1007.6

1007

1006

1006

1005.7

1004.9

6827.5

104 0

1000.4

997.6

994.3

991.2

988.7

982

978.9

974.8

972

998.8

1012.3

1009.6

1008.4

1007.6

1006.9

1005.9

1005.9

1005.6

1004.9

6927.4

103 0

1000.4

997.5

994.2

991.1

988.6

982

979

974.9

972.1

998.8

1012.3

1009.6

1008.3

1007.6

1006.9

1005.9

1005.9

1005.6

1004.9

70 27103 0

1000.3

997.5

994.2

991.1

988.5

981.9

978.9

974.8

972.1

998.8

1012.3

1009.6

1008.3

1007.6

1006.9

1005.9

1005.9

1005.6

1004.9

7127.1

103 0

1000.4

997.5

994.2

991.1

988.6

982

978.9

974.9

972.1

998.8

1012.3

1009.6

1008.3

1007.6

1006.9

1006

1006

1005.7

1005

72 26. 10 0 10 99 99 99 98 98 97 97 97 99 10 10 10 10 10 10 10 10 10

40

1 1 00.5

7.6 4.4 1.3 8.8 2.3 9.3 5.2 2.5 8.9 12.3

09.7

08.4

07.7

07 06.1

06 05.7

05

7326.7

102 0

1000.5

997.8

994.4

991.4

988.9

982.3

979.4

975.3

972.6

998.9

1012.3

1009.7

1008.4

1007.6

1007

1006

1006

1005.6

1004.9

7426.3

101 0

1000.4

997.6

994.3

991.2

988.8

982.2

979.2

975.1

972.4

998.8

1012.3

1009.7

1008.4

1007.6

1007

1006

1006

1005.6

1004.9

7526.4

102 0

1000.5

997.6

994.4

991.3

988.8

982.2

979.2

975.1

972.4

998.9

1012.3

1009.6

1008.4

1007.6

1007

1006

1006

1005.6

1004.9

7627.5

104 0

1000.4

997.6

994.3

991.2

988.7

982.1

979.1

975

972.1

998.8

1012.3

1009.6

1008.3

1007.6

1006.9

1005.9

1005.9

1005.5

1004.9

7727.1

103 0

1000.4

997.5

994.2

991

988.5

981.9

978.8

974.6

971.8

998.6

1012.2

1009.5

1008.3

1007.5

1006.8

1005.8

1005.8

1005.3

1004.6

7827.6

104 0

1000.1

997.1

993.7

990.6

988

981.4

978.1

973.9

971.1

998.4

1012.2

1009.4

1008.2

1007.4

1006.7

1005.7

1005.6

1005.3

1004.6

79 28105 0

999.9

996.9

993.5

990.3

987.7

981.1

977.7

973.6

970.9

998.3

1012.2

1009.4

1008.1

1007.3

1006.6

1005.6

1005.6

1005.2

1004.5

8027.1

103 0

1000

997

993.6

990.5

988

981.3

978.1

974

971.1

998.4

1012.2

1009.5

1008.1

1007.4

1006.6

1005.7

1005.7

1005.3

1004.6

27.035

102.85 0

1000.38

997.5

994.195

991.095

988.59

981.965

978.93

974.835

972.075

998.795

1012.305

1009.62

1008.345

1007.59

1006.915

1005.945

1005.93

1005.57

1004.865

Avg

2089.337

2083.322

2076.419

2069.945

2064.713

2050.877

2044.538

2035.985

2030.221

2086.027

2114.243

2108.635

2105.972

2104.395

2102.986

2100.96

2100.928

2100.177

2098.704 psf

41

150.8467

FPS

0.21074

0.45543

0.69896

0.92709

1.13517

1.60837

1.87233

2.17251

2.40833

0.34445

0.689801

0.516013

0.394631

0.328738

0.276717

0.240495

0.208511

0.17306

0.14493 Cp

qV_ref

Alpha P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9

P10

P11

P12

P13

P14

P15

P16

P17

P18

P19

count

[psf]

[mph]

[deg]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

1mbar =

2.088543

psf

1 0.1 6 01016

1016.2

1016.1

1015.9

1016.1

1015.7

1016

1015.8

1016.1

1016.2

1016.3

1015.8

1016

1016.2

1016.2

1015.7

1016.1

1016.1

1015.8

1mph=

1.466667

fps

2 0.1 6 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.2

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.1

1015.8

1sq.ft=

144

psin

3 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.3

1015.8

1016

1016.2

1016.2

1015.7

1016.1

1016.1

1015.8

4 0.1 6 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.3

1015.8

1016

1016.2

1016.2

1015.7

1016.1

1016.1

1015.8

5 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.3

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.1

1015.8

6 0.1 7 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

42

15.9

16.2

16.1

15.8

16.1

15.7

16 15.8

16.1

16.2

16.3

15.8

16.1

16.2

16.2

15.7

16.1

16.1

15.8

7 0.2 8 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.3

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.1

1015.8

8 0.1 6 01016

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.3

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.1

1015.8

9 0.1 7 01016

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.3

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.1

1015.8

10 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.3

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.1

1015.8

11 0.1 6 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016

1016.2

1016.3

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.1

1015.8

12 0.1 6 01016

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.3

1015.8

1016

1016.2

1016.2

1015.7

1016.1

1016.1

1015.8

13 0.1 6 01016

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.3

1015.8

1016.1

1016.2

1016.2

1015.7

1016.1

1016.1

1015.8

14 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.3

1015.8

1016

1016.2

1016.2

1015.7

1016.1

1016.1

1015.8

15 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.3

1015.8

1016

1016.2

1016.2

1015.7

1016.1

1016.1

1015.8

16 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.3

1015.8

1016

1016.2

1016.2

1015.7

1016.1

1016.1

1015.8

17 0.1 7 01015.

1016.

1016.

1015.

1016.

1015.

1016.

1015.

1016.

1016.

1016.

1015.

1016.

1016.

1016.

1015.

1016.

1016.

1015.

43

9 2 1 9 1 7 1 8 1 2 3 8 1 2 2 7 1 1 8

18 0.1 6 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.3

1015.8

1016.1

1016.2

1016.2

1015.7

1016

1016.1

1015.8

19 0.1 6 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.3

1015.8

1016

1016.2

1016.1

1015.7

1016.1

1016.1

1015.8

20 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.2

1016.3

1015.8

1016

1016.2

1016.1

1015.7

1016.1

1016.1

1015.8

0.105 6.6 0

1015.925

1016.2

1016.1

1015.895

1016.1

1015.7

1016.09

1015.8

1016.095

1016.2

1016.295

1015.8

1016.055

1016.2

1016.19

1015.7

1016.095

1016.1

1015.8

Avg

2121.803

2122.378

2122.169

2121.741

2122.169

2121.334

2122.148

2121.542

2122.159

2122.378

2122.576

2121.542

2122.075

2122.378

2122.357

2121.334

2122.159

2122.169

2121.542 psf

9.680002

FPS

2.282

2.67981

1.78472

3.07763

2.87872

1.188

1.188

2.97818

3.07763

0.204364

0.303819

0.98909

1.88418

0.98909

1.188

0.98909

1.08854

2.97818

2.18254 Cp

21 2.4 30 0

1014.2

1014.5

1014.4

1014.2

1014.4

1014

1014.4

1014.1

1014.1

1015.8

1015.7

1015

1015.2

1015.3

1015.2

1014.6

1015

1015

1014.5

22 2.2 30 0

1014.3

1014.6

1014.4

1014.2

1014.4

1014

1014.4

1014.1

1014.1

1015.8

1015.7

1015

1015.2

1015.3

1015.2

1014.6

1015

1015

1014.6

23 2.2 29 0 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

44

14.2

14.6

14.4

14.2

14.4

14 14.4

14.1

14.1

15.7

15.7

15 15.2

15.3

15.2

14.6

15 15 14.6

24 2.3 30 0

1014.3

1014.6

1014.4

1014.2

1014.4

1014

1014.4

1014.1

1014.1

1015.8

1015.7

1015

1015.2

1015.3

1015.2

1014.6

1015

1014.9

1014.6

25 2.3 30 0

1014.2

1014.5

1014.4

1014.2

1014.4

1014

1014.4

1014.1

1014.1

1015.7

1015.7

1015

1015.2

1015.3

1015.2

1014.7

1015

1015

1014.6

26 2.4 31 0

1014.3

1014.6

1014.4

1014.2

1014.4

1014

1014.4

1014.1

1014.1

1015.8

1015.6

1015

1015.2

1015.3

1015.1

1014.6

1015

1015

1014.6

27 2.5 31 0

1014.3

1014.6

1014.4

1014.2

1014.4

1014

1014.5

1014.1

1014.1

1015.8

1015.6

1015

1015.2

1015.3

1015.2

1014.6

1015

1015

1014.6

28 2.3 30 0

1014.2

1014.6

1014.4

1014.2

1014.4

1014

1014.4

1014.1

1014.1

1015.8

1015.7

1015

1015.2

1015.3

1015.2

1014.7

1015

1015

1014.6

29 2.4 30 0

1014.2

1014.5

1014.4

1014.2

1014.4

1014

1014.4

1014.1

1014.1

1015.8

1015.7

1015

1015.2

1015.3

1015.2

1014.6

1015

1015

1014.6

30 2.3 30 0

1014.3

1014.6

1014.4

1014.2

1014.4

1014

1014.4

1014.1

1014.1

1015.8

1015.6

1015

1015.2

1015.3

1015.2

1014.6

1015

1015

1014.6

31 2.3 30 0

1014.2

1014.5

1014.4

1014.2

1014.4

1014

1014.4

1014.1

1014

1015.8

1015.6

1015

1015.2

1015.3

1015.2

1014.6

1015

1015

1014.6

32 2.4 31 0

1014.2

1014.5

1014.4

1014.2

1014.4

1014

1014.4

1014.1

1014.1

1015.8

1015.6

1015

1015.2

1015.3

1015.2

1014.6

1015

1015

1014.6

33 2.4 31 0

1014.3

1014.5

1014.4

1014.2

1014.4

1014

1014.4

1014.1

1014.1

1015.8

1015.7

1015

1015.2

1015.3

1015.2

1014.6

1015

1015

1014.6

34 2.3 30 01014.

1014.

1014.

1014.

1014.

1014

1014.

1014.

1014.

1015.

1015.

1015

1015.

1015.

1015.

1014.

1015

1015

1014.

45

2 5 4 2 4 5 1 1 8 6 2 3 2 6 6

35 2.4 31 0

1014.2

1014.5

1014.4

1014.2

1014.4

1014

1014.5

1014.1

1014.1

1015.8

1015.7

1015.1

1015.2

1015.3

1015.2

1014.6

1015

1015

1014.6

36 2.4 30 0

1014.2

1014.5

1014.4

1014.2

1014.4

1014

1014.4

1014.1

1014.1

1015.8

1015.7

1015

1015.2

1015.3

1015.2

1014.6

1015

1015

1014.6

37 2.4 30 0

1014.2

1014.6

1014.4

1014.2

1014.4

1014

1014.4

1014.1

1014.1

1015.8

1015.7

1015

1015.2

1015.3

1015.1

1014.6

1015

1015

1014.6

38 2.4 30 0

1014.3

1014.6

1014.5

1014.2

1014.4

1014

1014.4

1014.1

1014.1

1015.8

1015.7

1015

1015.2

1015.3

1015.2

1014.6

1015

1015

1014.6

39 2.3 30 0

1014.3

1014.5

1014.4

1014.2

1014.4

1014

1014.4

1014.1

1014.1

1015.8

1015.7

1015

1015.2

1015.3

1015.2

1014.6

1015

1015

1014.6

40 2.3 30 0

1014.2

1014.5

1014.4

1014.2

1014.4

1014

1014.4

1014.1

1014.1

1015.8

1015.7

1015

1015.2

1015.3

1015.2

1014.6

1015

1015

1014.6

2.345

30.2 0

1014.24

1014.545

1014.405

1014.2

1014.4

1014

1014.415

1014.1

1014.095

1015.79

1015.67

1015.005

1015.2

1015.3

1015.19

1014.61

1015

1014.995

1014.595

Avg

2118.284

2118.921

2118.629

2118.201

2118.618

2117.783

2118.65

2117.992

2117.981

2121.522

2121.271

2119.882

2120.289

2120.498

2120.268

2119.057

2119.872

2119.861

2119.026 psf

44.29334

FPS

0.647

0.638

0.634

0.692

0.687

0.612

0.589

0.692

0.963

0.59921

0.41218

0.20288

0.10936

0.10936

0.01139

0.059

0.068

0.162

0.215 Cp

46

68 77 32 21 76 05 79 21 85 3 3 3 3 86 76 28 72

4112.1 69 0

1006.1

1006.4

1006.4

1006.3

1006.6

1006.3

1006.4

1005.7

1004.8

1012.2

1013.9

1012.5

1012.2

1011.9

1011.4

1010.7

1010.7

1010.3

1009.5

4212.3 69 0

1006.2

1006.4

1006.5

1006.5

1006.8

1006.4

1006.5

1005.9

1005

1012.4

1013.8

1012.5

1012.1

1011.8

1011.5

1010.6

1010.7

1010.3

1009.5

4311.8 68 0

1006.3

1006.6

1006.6

1006.6

1006.8

1006.5

1006.6

1006

1005

1012.4

1013.8

1012.5

1012.1

1011.9

1011.4

1010.6

1010.7

1010.4

1009.5

44 12 69 0

1006.3

1006.6

1006.5

1006.5

1006.8

1006.4

1006.5

1006

1005

1012.5

1013.8

1012.5

1012.1

1011.8

1011.4

1010.6

1010.7

1010.3

1009.5

4511.9 68 0

1006.2

1006.4

1006.3

1006.3

1006.7

1006.3

1006.4

1005.8

1004.8

1012.3

1013.8

1012.5

1012.2

1011.8

1011.4

1010.6

1010.7

1010.3

1009.5

4612.2 69 0

1006.3

1006.6

1006.6

1006.5

1006.7

1006.4

1006.4

1005.8

1004.9

1012.2

1013.8

1012.5

1012.1

1011.8

1011.4

1010.6

1010.7

1010.3

1009.5

4711.7 68 0

1006.1

1006.4

1006.4

1006.4

1006.7

1006.4

1006.5

1006.2

1005

1013.1

1013.5

1012.3

1012.1

1011.7

1011.4

1010.6

1010.6

1010.5

1009.7

4811.7 68 0

1005.8

1006

1006

1006.1

1006.6

1006.1

1006.3

1005.7

1004.7

1011.7

1014

1012.6

1012.2

1011.9

1011.5

1010.6

1010.7

1010.3

1009.5

4912.3 69 0

1005.9

1006.2

1006.2

1006.1

1006.4

1006

1006.2

1005.6

1004.7

1011.8

1013.8

1012.5

1012.1

1011.7

1011.4

1010.4

1010.5

1010.1

1009.3

5012.4 70 0

1005.7

1005.9

1005.8

1005.8

1006.1

1005.9

1006

1005.3

1004.5

1011.7

1013.8

1012.4

1012

1011.7

1011.3

1010.4

1010.4

1010

1009.2

5112.6 70 0

1005.

1005.

1005.

1005.

1006.

1005.

1006

1005.

1004.

1011.

1013.

1012.

1012

1011.

1011.

1010.

1010.

1010

1009.

47

6 9 9 9 3 9 4 5 7 8 4 7 3 4 4 2

5213.1 71 0

1005.5

1005.7

1005.6

1005.7

1006.1

1005.9

1006

1005.4

1004.7

1011.8

1013.8

1012.4

1012

1011.6

1011.2

1010.3

1010.4

1009.9

1009.1

5313.3 72 0

1005.3

1005.7

1005.7

1005.8

1006.1

1005.8

1006

1005.3

1004.5

1011.8

1013.7

1012.3

1011.9

1011.6

1011.1

1010.3

1010.3

1009.9

1009

5413.2 72 0

1005.3

1005.6

1005.6

1005.5

1005.8

1005.5

1005.6

1005.2

1004.4

1011.6

1013.7

1012.3

1011.9

1011.5

1011.1

1010.2

1010.3

1009.8

1009

5513.2 72 0

1005.1

1005.3

1005.4

1005.4

1005.7

1005.4

1005.5

1004.9

1004.2

1011.5

1013.7

1012.3

1011.9

1011.5

1011.1

1010.2

1010.2

1009.8

1009

5613.3 72 0

1005.1

1005.3

1005.3

1005.3

1005.7

1005.4

1005.5

1004.8

1003.9

1011.5

1013.7

1012.3

1011.8

1011.5

1011

1010.2

1010.2

1009.8

1009

5713.2 72 0

1005.2

1005.5

1005.6

1005.6

1006

1005.6

1005.7

1004.9

1003.9

1011.4

1013.7

1012.3

1011.8

1011.4

1011

1010.2

1010.2

1009.8

1008.9

5813.7 73 0

1005.2

1005.4

1005.3

1004.8

1004.7

1004.6

1004.9

1004.5

1003.9

1011.6

1013.8

1012.3

1011.8

1011.5

1011

1010.2

1010.2

1009.7

1008.9

5913.4 72 0

1005.2

1005.4

1005.1

1004.7

1004.8

1004.4

1005.1

1004.4

1003.7

1011.5

1013.8

1012.3

1011.8

1011.5

1011

1010.1

1010.2

1009.8

1008.9

6013.2 72 0

1005

1005.2

1005.3

1005.3

1005.8

1005.4

1005.5

1004.9

1004

1011.6

1013.7

1012.2

1011.8

1011.4

1011

1010.1

1010.2

1009.8

1008.9

12.63

70.25 0

1005.67

1005.925

1005.905

1005.855

1006.16

1005.83

1005.98

1005.385

1004.505

1011.915

1013.77

1012.395

1011.995

1011.66

1011.245

1010.395

1010.45

1010.055

1009.23

Avg

2100.

2100.

2100.

2100.

2101.

2100.

2101.

2099.

2097.

2113.

2117.

2114.

2113.

2112.

2112.

2110.

2110.

2109.

2107. psf

48

385

918

876

772

409

72 033

79 952

428

303

431

596

896

029

254

369

544

821

103.0334

FPS

0.72309

0.7297

0.70903

0.69415

0.67596

0.65033

0.69002

0.75534

0.95046

0.284802

0.576669

0.4204

0.304646

0.232712

0.164087

0.106209

0.049159

0.0327

0.1129 Cp

6127.4

103 0

1000.2

1000

996.6

992.1

987.7

982.7

975.1

967.2

960.2

979.5

1014.6

1011.8

1009.9

1008.8

1007.8

1006.6

1006.3

1005.7

1004.5

6227.5

104 0

1000.2

1000.2

997

992.3

987.8

982.8

975.4

967.4

960.3

979.3

1014.5

1011.8

1009.9

1008.8

1007.8

1006.6

1006.3

1005.6

1004.5

6326.5

102 0

1000.4

1000.3

997

992.4

987.9

983

975.5

967.8

960.8

979.8

1014.6

1011.8

1010

1008.8

1007.8

1006.6

1006.3

1005.7

1004.5

6427.5

104 0

1000.3

1000.2

997

992.4

987.9

983

975.4

967.6

960.6

979.9

1014.6

1011.8

1009.9

1008.8

1007.8

1006.6

1006.4

1005.7

1004.6

6526.4

102 0

1000.3

1000.3

997.1

992.5

988.1

983.2

975.8

968

960.9

979.3

1014.6

1011.8

1010

1008.9

1007.9

1006.6

1006.4

1005.7

1004.6

6627.4

103 0

1000.3

1000.2

996.9

992.3

987.9

982.8

975.4

967.4

960.4

979.4

1014.6

1011.8

1010

1008.8

1007.8

1006.6

1006.3

1005.6

1004.5

6726.6

102 0

1000.3

1000.2

997

992.4

987.9

982.8

975.3

967.3

960.1

979.2

1014.6

1011.8

1009.9

1008.7

1007.8

1006.5

1006.3

1005.6

1004.5

6828.4

105 0

1000.

1000.

996.8

992.2

987.7

982.7

975.3

967.4

960.4

979.4

1014.

1011.

1009.

1008.

1007.

1006.

1006.

1005.

1004.

49

2 1 6 8 9 9 8 7 4 8 6

6926.2

101 0

1000.7

1000.4

997.2

992.7

988.3

983.5

976.1

968.5

961.5

979.9

1014.6

1011.9

1010.1

1008.9

1007.9

1006.8

1006.5

1005.8

1004.6

7026.6

102 0

1000.5

1000.4

997.2

992.7

988.2

983.2

975.8

968

961

979.7

1014.6

1011.9

1010.1

1008.9

1007.9

1006.7

1006.5

1005.8

1004.7

7127.2

103 0

1000.4

1000.4

997.3

992.7

988.3

983.3

975.9

967.9

960.9

979.6

1014.6

1011.9

1010

1008.9

1007.9

1006.7

1006.4

1005.7

1004.6

7226.1

101 0

1000.3

1000.3

997.3

992.7

988.2

983.2

975.8

968

961

979.5

1014.6

1011.9

1010

1008.9

1007.9

1006.7

1006.5

1005.8

1004.7

7326.6

102 0

1000.6

1000.5

997.4

992.8

988.4

983.5

976.1

968.4

961.5

980.2

1014.6

1011.8

1010

1008.9

1007.9

1006.7

1006.4

1005.8

1004.6

7427.1

103 0

1000.3

1000.3

997.2

992.6

988.1

983.1

975.6

967.7

960.7

979.6

1014.6

1011.9

1010

1008.9

1007.9

1006.7

1006.4

1005.8

1004.6

7527.5

104 0

1000.4

1000.4

997.3

992.7

988.2

983.2

975.8

967.7

960.5

979.2

1014.6

1011.9

1010

1008.9

1007.9

1006.6

1006.4

1005.7

1004.6

7626.2

101 0

1000.3

1000.4

997.6

992.7

988

983.1

975.6

967.8

960.8

979.6

1014.6

1011.8

1010

1008.8

1007.9

1006.6

1006.4

1005.7

1004.5

7726.9

103 0

1000.2

1000.2

997.1

992.4

987.9

982.9

975.4

967.6

960.7

979.6

1014.6

1011.8

1010

1008.8

1007.8

1006.6

1006.3

1005.7

1004.6

7826.9

103 0

1000.3

1000.2

997

992.4

988

983.1

975.7

968.2

961.4

980.2

1014.6

1011.8

1010

1008.9

1007.9

1006.8

1006.5

1005.9

1004.8

7926.5

102 0

1000.5

1000.4

997.4

992.8

988.3

983.4

975.9

968.1

961.1

979.7

1014.6

1011.9

1010

1008.9

1007.9

1006.7

1006.5

1005.8

1004.7

50

8027.4

103 0

1000.8

999.9

996.3

992.3

988.2

983.4

976.1

968.4

961.4

979.7

1014.6

1011.9

1010.1

1009

1008

1006.8

1006.5

1005.9

1004.8

26.945

102.65 0

1000.375

1000.265

997.085

992.505

988.05

983.095

975.65

967.82

960.81

979.615

1014.595

1011.84

1009.99

1008.86

1007.865

1006.66

1006.4

1005.74

1004.605

Avg

2089.327

2089.097

2082.455

2072.89

2063.585

2053.237

2037.687

2021.334

2006.693

2045.968

2119.026

2113.272

2109.408

2107.048

2104.97

2102.453

2101.91

2100.532

2098.161 psf

150.5534

FPS

0.21809

0.24948

0.48473

0.82888

1.18931

1.53578

2.14309

2.7345

3.30111

1.83885

0.865518

0.685304

0.518654

0.423316

0.346192

0.291546

0.240389

0.18148

0.119859 Cp

qV_ref

Alpha P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9

P10

P11

P12

P13

P14

P15

P16

P17

P18

P19

count

[psf]

[mph]

[deg]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

[mbar]

1mbar =

2.088543

psf

1 0.1 6 0

1015.9

1016.2

1016.1

1015.8

1016.1

1015.6

1016

1015.8

1016

1016.1

1016.2

1015.8

1016

1016.1

1016.1

1015.6

1016

1016.1

1015.8

1mph=

1.466667

fps

2 0.1 6 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.6

1016

1015.8

1016

1016.1

1016.2

1015.8

1016

1016.1

1016.1

1015.6

1016

1016.1

1015.8

1sq.ft

144

psi

51

= n

3 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.6

1016

1015.8

1016

1016.1

1016.2

1015.8

1016

1016.1

1016.1

1015.6

1016

1016.1

1015.8

4 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.6

1016

1015.8

1016

1016.1

1016.2

1015.8

1016

1016.1

1016.1

1015.6

1016

1016.1

1015.8

5 0.1 6 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.6

1016

1015.8

1016

1016.1

1016.2

1015.8

1016

1016.2

1016.1

1015.6

1016

1016.1

1015.8

6 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.6

1016

1015.7

1016

1016.1

1016.2

1015.8

1016

1016.2

1016.1

1015.6

1016.1

1016.2

1015.8

7 0.1 7 0

1015.9

1016.2

1016

1015.9

1016.1

1015.6

1016

1015.8

1016

1016.1

1016.2

1015.8

1016

1016.2

1016.1

1015.6

1016

1016.1

1015.8

8 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.6

1016

1015.8

1016.1

1016.1

1016.2

1015.8

1016

1016.2

1016.1

1015.6

1016.1

1016.1

1015.8

9 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.6

1016

1015.8

1016

1016.1

1016.2

1015.8

1016

1016.2

1016.1

1015.6

1016

1016.2

1015.8

10 0.2 8 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016

1016.1

1016.2

1015.8

1016

1016.2

1016.2

1015.6

1016

1016.2

1015.8

11 0.1 7 0

1015.9

1016.1

1016.1

1015.8

1016.1

1015.6

1016

1015.8

1016.1

1016.1

1016.2

1015.8

1016

1016.2

1016.2

1015.6

1016

1016.2

1015.8

12 0.1 7 0

1015.9

1016.2

1016.1

1015.8

1016

1015.6

1016

1015.8

1016

1016.1

1016.2

1015.8

1016

1016.2

1016.2

1015.6

1016

1016.2

1015.8

13 0.1 7 0

1015.9

1016.2

1016.1

1015.8

1016

1015.6

1016

1015.8

1016

1016.1

1016.2

1015.8

1016

1016.2

1016.2

1015.6

1016

1016.1

1015.8

52

14 0.1 7 0

1015.9

1016.2

1016

1015.9

1016.1

1015.7

1016

1015.8

1016.1

1016.1

1016.2

1015.8

1016

1016.2

1016.1

1015.6

1016.1

1016.1

1015.8

15 0.1 6 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.6

1016

1015.8

1016

1016.1

1016.2

1015.8

1016

1016.2

1016.1

1015.6

1016

1016.1

1015.8

16 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.6

1016.1

1015.8

1016

1016.1

1016.2

1015.8

1016

1016.2

1016.1

1015.6

1016

1016.1

1015.8

17 0.1 7 0

1015.9

1016.1

1016.1

1015.9

1016.1

1015.6

1016

1015.8

1016.1

1016.1

1016.2

1015.8

1016

1016.2

1016.1

1015.6

1016

1016.1

1015.8

18 0.1 8 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016

1015.8

1016.1

1016.1

1016.2

1015.8

1016

1016.2

1016.1

1015.6

1016

1016.1

1015.8

19 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016.1

1015.8

1016.1

1016.1

1016.2

1015.8

1016

1016.2

1016.2

1015.6

1016

1016.1

1015.8

20 0.1 7 0

1015.9

1016.2

1016.1

1015.9

1016.1

1015.7

1016

1015.8

1016

1016.1

1016.2

1015.8

1016

1016.2

1016.2

1015.6

1016.1

1016.1

1015.8

0.105 6.9 0

1015.9

1016.19

1016.09

1015.88

1016.09

1015.625

1016.015

1015.795

1016.03

1016.1

1016.2

1015.8

1016

1016.18

1016.13

1015.6

1016.02

1016.125

1015.8

Avg

2121.751

2122.357

2122.148

2121.709

2122.148

2121.177

2121.991

2121.532

2122.023

2122.169

2122.378

2121.542

2121.96

2122.336

2122.232

2121.125

2122.002

2122.221

2121.542 psf

10.12

FPS

2.779

2.878

1.983

3.376

3.077

2.679

2.679

3.077

4.370

1.784

1.585

0.989

2.978

1.386

2.381

2.978

2.580

2.480

2.182 Cp

53

27 72 63 63 81 81 63 54 72 82 09 18 91 45 18 36 91 54

21 2.3 30 0

1014.1

1014.4

1014.3

1014

1014.2

1013.9

1014.2

1014

1014.1

1015.2

1015.9

1015.2

1015.3

1015.3

1015.3

1014.7

1015

1015

1014.5

22 2.4 31 0

1014.1

1014.4

1014.3

1014.1

1014.3

1013.9

1014.3

1014

1014.1

1015.3

1015.8

1015.2

1015.3

1015.4

1015.2

1014.6

1015

1015

1014.6

23 2.5 31 0

1014.1

1014.3

1014.2

1014

1014.2

1013.8

1014.2

1014

1014.1

1015.2

1015.8

1015.2

1015.3

1015.3

1015.2

1014.7

1015

1015

1014.5

24 2.3 30 0

1014.1

1014.4

1014.2

1014

1014.2

1013.9

1014.2

1014

1014.1

1015.2

1015.9

1015.2

1015.3

1015.4

1015.2

1014.7

1015

1014.9

1014.6

25 2.3 30 0

1014.1

1014.4

1014.2

1014

1014.2

1013.9

1014.2

1014

1014.1

1015.2

1015.9

1015.2

1015.3

1015.4

1015.2

1014.7

1015

1015

1014.6

26 2.4 31 0

1014.1

1014.3

1014.2

1014

1014.2

1013.9

1014.2

1014

1014.1

1015.2

1015.9

1015.2

1015.3

1015.4

1015.2

1014.7

1015

1015

1014.6

27 2.2 30 0

1014.1

1014.3

1014.2

1014

1014.2

1013.9

1014.2

1014

1014.1

1015.2

1015.9

1015.2

1015.3

1015.4

1015.2

1014.6

1015

1015

1014.5

28 2.4 31 0

1014.1

1014.4

1014.2

1014

1014.3

1013.9

1014.2

1014

1014.1

1015.2

1015.8

1015.2

1015.3

1015.4

1015.2

1014.6

1015

1015

1014.5

29 2.5 31 0

1014.1

1014.3

1014.2

1014

1014.2

1013.8

1014.2

1013.9

1014

1015.2

1015.9

1015.3

1015.3

1015.4

1015.2

1014.6

1015

1014.9

1014.6

30 2.3 30 01014

1014.3

1014.1

1013.9

1014.1

1013.8

1014.1

1013.9

1014

1015.2

1015.9

1015.2

1015.3

1015.4

1015.2

1014.6

1015

1014.9

1014.5

31 2.4 31 01014

1014.

1014.

1014

1014.

1013.

1014.

1014

1014.

1015.

1015.

1015.

1015.

1015.

1015.

1014.

1015

1015

1014.

54

3 2 2 8 2 1 2 9 3 3 4 2 7 6

32 2.5 32 0

1014.1

1014.3

1014.2

1014

1014.2

1013.9

1014.2

1014

1014

1015.2

1015.9

1015.3

1015.3

1015.4

1015.2

1014.7

1015

1015

1014.6

33 2.4 30 0

1014.1

1014.3

1014.2

1014

1014.2

1013.9

1014.2

1014

1014.1

1015.3

1015.9

1015.2

1015.3

1015.4

1015.2

1014.6

1015

1015

1014.6

34 2.4 31 0

1014.1

1014.4

1014.2

1014

1014.2

1013.8

1014.2

1014

1014

1015.2

1015.9

1015.3

1015.3

1015.4

1015.2

1014.6

1015

1015

1014.5

35 2.4 31 0

1014.1

1014.3

1014.2

1014

1014.2

1013.8

1014.2

1014

1014.1

1015.3

1015.9

1015.2

1015.3

1015.3

1015.2

1014.6

1015

1015

1014.6

36 2.4 31 0

1014.1

1014.3

1014.2

1014

1014.2

1013.9

1014.2

1014

1014.1

1015.2

1015.9

1015.3

1015.3

1015.4

1015.2

1014.6

1015

1015

1014.6

37 2.3 30 0

1014.1

1014.3

1014.2

1014

1014.2

1013.9

1014.2

1014

1014.1

1015.3

1015.8

1015.2

1015.3

1015.3

1015.2

1014.6

1015

1015

1014.6

38 2.4 31 0

1014.1

1014.3

1014.2

1014

1014.2

1013.8

1014.2

1013.9

1014

1015.2

1015.9

1015.2

1015.3

1015.4

1015.3

1014.7

1015

1015

1014.5

39 2.6 32 0

1014.1

1014.3

1014.2

1014

1014.2

1013.8

1014.1

1013.9

1014

1015.2

1015.9

1015.2

1015.4

1015.4

1015.3

1014.7

1015

1015

1014.6

40 2.3 30 0

1014.1

1014.3

1014.2

1014

1014.3

1013.9

1014.2

1014.1

1014.1

1015.3

1015.8

1015.2

1015.3

1015.4

1015.3

1014.6

1015

1015

1014.5

2.385

30.7 0

1014.09

1014.33

1014.205

1014

1014.21

1013.86

1014.195

1013.985

1014.07

1015.225

1015.875

1015.225

1015.305

1015.38

1015.22

1014.645

1015

1014.985

1014.56

Avg

2117.

2118.

2118.

2117.

2118.

2117.

2118.

2117.

2117.

2120.

2121.

2120.

2120.

2120.

2120.

2119.

2119.

2119.

2118. psf

55

971

472

211

783

222

491

19 752

929

341

699

341

509

665

331

13 872

84 953

45.02668

FPS

0.7514

0.79956

0.78205

0.83897

0.82583

0.70761

0.75578

0.76453

0.95281

0.111165

0.601557

0.408903

0.216249

0.194356

0.054244

0.01143

0.05084

0.15154

0.22598 Cp

4111.6 67 0

1006.4

1006.7

1006.7

1006.5

1006.7

1006.2

1006.5

1006.2

1006.2

1011.6

1014.2

1012.8

1012.3

1012

1011.4

1010.6

1010.5

1010.1

1009.3

4211.7 68 0

1006.5

1006.9

1006.8

1006.6

1006.8

1006.4

1006.6

1006.3

1006.4

1011.5

1014.2

1012.8

1012.3

1011.9

1011.4

1010.6

1010.5

1010.1

1009.3

4311.7 68 0

1006.5

1006.8

1006.7

1006.5

1006.7

1006.3

1006.5

1006.2

1006.3

1011.6

1014.2

1012.8

1012.3

1011.9

1011.4

1010.5

1010.5

1010.1

1009.2

4411.5 67 0

1006.4

1006.7

1006.6

1006.4

1006.5

1006.1

1006.3

1006.1

1006.1

1011.4

1014.2

1012.8

1012.3

1011.9

1011.4

1010.5

1010.5

1010.1

1009.2

4511.7 68 0

1006.5

1006.8

1006.7

1006.6

1006.8

1006.3

1006.6

1006.3

1006.3

1011.6

1014.2

1012.8

1012.3

1011.9

1011.4

1010.6

1010.5

1010.1

1009.3

4611.6 67 0

1006.6

1006.9

1006.8

1006.6

1006.9

1006.4

1006.7

1006.4

1006.4

1011.7

1014.2

1012.8

1012.3

1012

1011.4

1010.6

1010.6

1010.2

1009.3

4711.8 68 0

1006.8

1007

1006.9

1006.7

1006.9

1006.4

1006.7

1006.4

1006.4

1011.7

1014.1

1012.7

1012.3

1011.9

1011.4

1010.5

1010.5

1010.1

1009.2

4811.8 68 0

1006.

1006.

1006.

1006.

1006.

1006.

1006.

1006.

1006.

1011.

1014.

1012.

1012.

1011.

1011.

1010.

1010.

1010.

1009.

56

5 8 7 6 8 4 6 4 4 7 2 7 3 9 4 5 5 1 2

4911.8 68 0

1006.6

1006.8

1006.7

1006.5

1006.7

1006.2

1006.5

1006.3

1006.3

1011.6

1014.2

1012.7

1012.3

1011.9

1011.4

1010.5

1010.5

1010.1

1009.2

5011.6 67 0

1006.5

1006.8

1006.7

1006.5

1006.7

1006.2

1006.4

1006.1

1006.2

1011.5

1014.2

1012.8

1012.3

1011.9

1011.4

1010.6

1010.5

1010.1

1009.2

5111.8 68 0

1006.5

1006.8

1006.7

1006.6

1006.8

1006.3

1006.6

1006.2

1006.3

1011.6

1014.2

1012.7

1012.3

1011.9

1011.4

1010.5

1010.5

1010

1009.2

5211.7 68 0

1006.6

1006.8

1006.7

1006.6

1006.8

1006.3

1006.6

1006.3

1006.3

1011.7

1014.1

1012.7

1012.2

1011.9

1011.4

1010.5

1010.5

1010.1

1009.2

5311.6 67 0

1006.2

1006.6

1006.5

1006.4

1006.6

1006.2

1006.4

1006.1

1006.2

1011.5

1014.2

1012.8

1012.3

1011.9

1011.4

1010.5

1010.5

1010.1

1009.2

5412.1 69 0

1006.4

1006.7

1006.6

1006.4

1006.7

1006.2

1006.4

1006.1

1006.1

1011.2

1014.2

1012.8

1012.3

1011.9

1011.4

1010.5

1010.5

1010.1

1009.2

5511.8 68 0

1006.2

1006.6

1006.5

1006.3

1006.5

1006.1

1006.4

1006.1

1006.1

1011.6

1014.2

1012.8

1012.3

1011.9

1011.4

1010.5

1010.4

1010

1009.2

5611.7 68 0

1006.5

1006.8

1006.6

1006.5

1006.8

1006.3

1006.5

1006.2

1006.2

1011.6

1014.2

1012.7

1012.3

1011.9

1011.4

1010.5

1010.5

1010.1

1009.2

5711.5 67 0

1006.6

1006.9

1006.8

1006.5

1006.6

1006.1

1006.3

1006

1006.1

1011.4

1014.2

1012.8

1012.3

1011.9

1011.4

1010.5

1010.5

1010

1009.2

5811.8 68 0

1006.4

1006.7

1006.7

1006.5

1006.7

1006.2

1006.5

1006.2

1006.3

1011.7

1014.1

1012.7

1012.2

1011.8

1011.3

1010.5

1010.4

1010

1009.1

5912.2 69 0

1006.4

1006.6

1006.6

1006.3

1006.5

1006

1006.3

1006

1006.1

1011.5

1014.2

1012.7

1012.2

1011.8

1011.3

1010.5

1010.4

1010

1009.1

57

6012.1 69 0

1006.5

1006.8

1006.6

1006.5

1006.7

1006.2

1006.5

1006.1

1006.2

1011.5

1014.2

1012.7

1012.2

1011.8

1011.3

1010.5

1010.4

1010

1009.1

11.755

67.85 0

1006.48

1006.775

1006.68

1006.505

1006.71

1006.24

1006.495

1006.2

1006.245

1011.56

1014.185

1012.755

1012.28

1011.895

1011.385

1010.525

1010.485

1010.075

1009.205

Avg

2102.077

2102.693

2102.495

2102.129

2102.558

2101.576

2102.109

2101.492

2101.586

2112.687

2118.169

2115.183

2114.191

2113.387

2112.321

2110.525

2110.442

2109.585

2107.768 psf

99.51336

FPS

0.70744

0.70744

0.69855

0.70477

0.70299

0.70033

0.72431

0.74119

0.7865

0.168491

0.618892

0.441219

0.303523

0.217351

0.126738

0.062776

0.0154

0.10601

0.20018 Cp

6127.6

104 0

993.9

994.2

993.9

993.7

993.8

993.2

993.1

992.3

992.3

1005.6

1011.5

1008.8

1007.2

1006.2

1005

1003.6

1003

1002

1000.3

6227.4

103 0

993.7

994.1

994

994

994.3

993.7

993.7

992.7

992.7

1005.1

1011.5

1008.8

1007.3

1006.2

1005

1003.7

1003.1

1002

1000.4

6326.3

101 0

993.8

994.1

994.1

994

994.3

993.8

993.7

992.9

992.7

1005.4

1011.5

1008.8

1007.3

1006.2

1005

1003.7

1003.1

1002

1000.3

6427.5

104 0

993.9

994.3

994.2

994.2

994.4

993.9

993.8

992.8

992.5

1005.2

1011.4

1008.6

1007.2

1006.1

1005

1003.6

1003

1001.9

1000.3

6527.8

104 0

993.4

993.8

993.8

993.8

994.2

993.7

993.6

992.7

992.6

1005.

1011.

1008.

1007.

1006

1005

1003.

1002.

1001.

1000.

58

1 5 7 2 5 9 8 2

6627.9

104 0

993.7

993.9

993.8

993.8

994

993.4

993.2

992.1

991.8

1004.9

1011.4

1008.6

1007.2

1005.9

1004.8

1003.4

1002.8

1001.7

1000.1

6728.1

105 0

993.4

993.7

993.7

993.7

994

993.7

993.6

992.7

992.4

1005.4

1011.4

1008.6

1007.1

1006

1004.8

1003.4

1002.8

1001.7

1000.1

68 27103 0

993.7

994

993.9

993.8

994.1

993.6

993.5

992.7

992.4

1005.4

1011.3

1008.6

1007.1

1006

1004.8

1003.5

1002.9

1001.8

1000.2

6927.2

103 0

994.1

994.3

994.2

994.1

994.4

994

993.8

992.9

992.5

1005.3

1011.4

1008.6

1007.2

1006

1004.9

1003.5

1002.9

1001.8

1000.2

7027.1

103 0

993.7

994

993.9

993.9

994.1

993.6

993.5

992.5

992

1004.6

1011.5

1008.8

1007.2

1006.1

1004.9

1003.6

1003

1001.9

1000.2

7127.2

103 0

993.6

994

994

993.9

994.3

993.7

993.6

992.6

992.1

1005.2

1011.4

1008.6

1007.1

1006

1004.9

1003.5

1002.9

1001.8

1000.2

7227.4

104 0

993.4

993.7

993.8

993.7

993.9

993.6

993.4

992.5

992.2

1005.2

1011.4

1008.7

1007.2

1006.1

1004.9

1003.6

1002.9

1002

1000.3

7326.5

102 0

993.7

994.1

994.1

994

994.4

994.1

993.9

993

992.7

1005.4

1011.5

1008.8

1007.3

1006.2

1005

1003.7

1003.1

1002.1

1000.5

7426.9

103 0

994.1

994.4

994.3

994.3

994.5

994

993.9

992.9

992.6

1005.3

1011.5

1008.7

1007.3

1006.2

1005.1

1003.7

1003.1

1001.9

1000.3

7526.9

103 0

993.7

994.1

994.1

994.1

994.3

994

993.9

993

992.7

1005.6

1011.5

1008.8

1007.3

1006.2

1005.1

1003.7

1003.1

1002.1

1000.5

7626.6

102 0

994.2

994.5

994.5

994.4

994.8

994.3

994.2

993.1

993

1005.5

1011.5

1008.9

1007.4

1006.3

1005.1

1003.8

1003.2

1002.2

1000.5

59

7727.4

103 0

994.2

994.5

994.4

994.2

994.4

993.9

993.8

992.6

992.4

1004.9

1011.6

1008.9

1007.4

1006.3

1005.2

1003.8

1003.2

1002.2

1000.6

7826.7

102 0

994.1

994.4

994.4

994.3

994.5

994

993.9

993

992.7

1005.2

1011.5

1008.9

1007.4

1006.3

1005.2

1003.8

1003.2

1002.1

1000.5

7927.1

103 0

993.9

994.3

994.2

994

994.2

993.7

993.6

992.8

992.8

1005.5

1011.5

1008.7

1007.3

1006.1

1005.1

1003.6

1003

1002

1000.3

8027.2

103 0

993.9

994.3

994.2

994.1

994.3

993.9

993.8

992.9

992.7

1005.5

1011.3

1008.6

1007.2

1006.1

1004.9

1003.6

1003

1001.9

1000.3

27.19

103.1 0

993.805

994.135

994.075

994

994.26

993.79

993.675

992.735

992.49

1005.265

1011.455

1008.725

1007.245

1006.125

1004.985

1003.615

1003.01

1001.945

1000.315

Avg

2075.605

2076.294

2076.169

2076.012

2076.555

2075.574

2075.333

2073.37

2072.858

2099.54

2112.468

2106.766

2103.675

2101.336

2098.955

2096.094

2094.83

2092.606

2089.201 psf

151.2134

FPS

0.71178

0.70909

0.70256

0.69757

0.69257

0.69142

0.73021

0.78705

0.82892

0.156978

0.625537

0.448867

0.31214

0.218428

0.130862

0.064035

0.01316

0.10265

0.20174 Cp

2D Airfoil Calculations

% of ChordUpper Surface Lower Surface

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19

60

MPH 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

0.075 0

0.075 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

AOA=

4

60.42401

0.51894

0.43039

70.61387

0.80374

0.71519

9

0.71519

9

0.05066

2 1

1.37973

50.32907

0.61387

0.89868

0.70881

0.89868

0.89868

0.80374

0.89868

0.13921

300.28283

0.33235

0.29634

0.44037

0.44938

0.44938

0.44488

0.17481

0.27081

0.60389

70.76896

0.66093

0.71495

0.11629

0.1568

0.1703

0.10279

0.08028

0.04427

680.28432

0.36839

0.41375

0.49893

0.54981

0.55203

0.56973

0.25224

0.23449

6

0.63826

60.80314

0.64716

0.13277

0.16485

0.12503

0.09073

0.05644

0.01772

0.01546

4

102

0.13207

0.39119

0.44192

0.52973

0.58553

0.59411

0.60465

0.271

0.24177

1

0.61444

70.89733

0.74045

0.25539

0.19685

0.14261

0.10203

0.06534

0.03413

0.00684

9

AOA=0

60.97862

1.41831

1.08854

1.52824

2.51755

1.41831

1.19847

1.63816

1.96793

0.12061

31.85801

1.63816

2.95724

1.19847

1.41831

1.96793

1.30839

1.30839

0.31908

300.42829

0.49567

0.44177

0.51812

0.50465

0.61245

0.76066

0.60795

0.23516

0.88771

30.46423

0.34745

0.25762

0.16779

0.1633

0.1633

0.1633

0.14982

0.10042

680.16304

0.44368

0.61172

0.6821

0.77359

0.86069

0.98385

0.8079

0.43312

0.95777

20.23254

0.16216

0.05747

0.01524

0.00147

6

0.01555

2

0.02698

9

0.03930

5

0.06129

9

102

0.20811

0.36961

0.64228

0.71835

0.8186

0.90091

1.03003

0.84474

0.45504

0.96528

20.24751

0.17807

0.06378

0.01931

0.00097

0.01463

2

0.02711

5

0.03803

7

0.05949

2

AOA=4 6

2.60748

2.51255

1.65815

2.79735

2.70242

1.08854

1.84801

2.79735

2.70242

0.24053

1.46828

1.37334

2.70242

0.89868

2.03788

2.41762

2.79735

2.70242

2.03788

300.18493

0.43214

0.90953

1.02461

1.04166

1.0374

1.27609

1.38691

1.24199

0.79114

6

0.21146

8

0.14753

3

0.08786

1

0.10064

8

0.06228

7

0.06228

7

0.06228

7

0.04523

7

0.02392

668 0.74 0.31 0.21 0.18 0.17 0.14 0.14 0.12 0.11 0.11

61

0.22171

0.41359

0.56216

0.87884

1.03336

1.14967

1.38654

1.43748

1.31608

7847

7403

5523

7506

8167

9301

0811

8076

2794

3643

102

0.24083

0.45289

0.6506

0.81241

1.08413

1.22073

1.46263

1.50617

1.37637

0.74619

8

0.31079

3

0.21432

7

0.18772

1

0.16474

4

0.14418

5

0.13289

8

0.12080

4

0.11072

6

0.10532

5

AOA=8

63.07266

2.86381

1.92396

3.38594

3.07266

1.2974

2.55052

3.28151

3.28151

0.25313

1.71511

2.4461

3.07266

1.50625

2.23724

3.17709

3.17709

3.17709

2.34167

300.52789

0.53217

0.51933

0.54073

0.55357

0.46369

0.48081

0.71192

0.79752

0.81596

9

0.17827

8

0.07556

3

0.05416

4

0.04132

40.02715

0.06567

0.11275

0.16839

0.16411

680.2149

0.44182

0.67049

0.87733

1.02396

1.59999

1.77716

2.10096

2.33399

0.32138

0.68056

5

0.51037

5

0.38993

2

0.32796

60.27909

0.24243

4

0.21101

4

0.17348

5

0.14555

6

102

0.21074

0.45543

0.69896

0.92709

1.13517

1.60837

1.87233

2.17251

2.40833

0.34445

0.68980

1

0.51601

3

0.39463

1

0.32873

8

0.27671

7

0.24049

5

0.20851

10.17306

0.14493

AOA=12

62.28

22.67981

1.78472

3.07763

2.87872

1.188

1.188

2.97818

3.07763

0.20436

4

0.30381

90.98909

1.88418

0.98909

1.188

0.98909

1.08854

2.97818

2.18254

300.64768

0.63877

0.63432

0.69221

0.68776

0.61205

0.58979

0.69221

0.96385

0.59921

30.41218

0.20288

0.10936

3

0.10936

3

0.01139

30.05986

0.06876

0.16228

0.21572

680.72309

0.7297

0.70903

0.69415

0.67596

0.65033

0.69002

0.75534

0.95046

0.28480

2

0.57666

90.4204

0.30464

6

0.23271

2

0.16408

7

0.10620

9

0.04915

90.0327

0.1129

102

0.21809

0.24948

0.48473

0.82888

1.18931

1.53578

2.14309

2.7345

3.30111

1.83885

0.86551

8

0.68530

4

0.51865

4

0.42331

6

0.34619

2

0.29154

6

0.24038

90.18148

0.11985

9

AOA=16

62.77927

2.87872

1.98363

3.376

3.07763

2.67981

2.67981

3.07763

4.37054

1.78472

1.58582

0.98909

2.97818

1.38691

2.38145

2.97818

2.58036

2.48091

2.18254

30 0.75 0.79 0.78 0.83 0.82 0.70 0.75 0.76 0.950.11116

0.60155

0.40890

0.21624

0.19435

0.05424 0.01 0.05 0.15 0.22

62

14 956 205 897 583 761 578 453 281 5 7 3 9 6 4 143 084 154 598

680.70744

0.70744

0.69855

0.70477

0.70299

0.70033

0.72431

0.74119

0.7865

0.16849

1

0.61889

2

0.44121

9

0.30352

3

0.21735

1

0.12673

8

0.06277

60.0154

0.10601

0.20018

102

0.71178

0.70909

0.70256

0.69757

0.69257

0.69142

0.73021

0.78705

0.82892

0.15697

8

0.62553

7

0.44886

70.31214

0.21842

8

0.13086

2

0.06403

50.01316

0.10265

0.20174

For V = 6MPH


Airfoil

Station P1 P2 P3 P4 P5 P6 P7 P8 P9

P10

P11

P12

P13

P14

P15

P16

P17

P18

P19

% ofChor

d 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.10.075 0

0.075 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Distance

fromLE(in) 2.8

2.45 2.1

1.75 1.4

1.05 0.7

0.35

0.2625 0

0.2625

0.35 0.7

1.05 1.4

1.75 2.1

2.45 2.8

Angleof

Attack

(deg)

4

0.42401

0.51894

0.430397

0.61387

0.80374

0.715199

0.715199

0.050662 1

1.379735

0.32907

0.61387

0.89868

0.70881

0.89868

0.89868

0.80374

0.89868

0.13921

C p

0

0.97862

1.41831

1.08854

1.52824

2.51755

1.41831

1.19847

1.63816

1.96793

0.120613

1.85801

1.63816

2.95724

1.19847

1.41831

1.96793

1.30839

1.30839

0.31908

4 0.2

63

2.60748

2.51255

1.65815

2.79735

2.70242

1.08854

1.84801

2.79735

2.70242

4053

1.46828

1.37334

2.70242

0.89868

2.03788

2.41762

2.79735

2.70242

2.03788

8

3.07266

2.86381

1.92396

3.38594

3.07266

1.2974

2.55052

3.28151

3.28151

0.25313

1.71511

2.4461

3.07266

1.50625

2.23724

3.17709

3.17709

3.17709

2.34167

122.282

2.67981

1.78472

3.07763

2.87872

1.188

1.188

2.97818

3.07763

0.204364

0.303819

0.98909

1.88418

0.98909

1.188

0.98909

1.08854

2.97818

2.18254

16

2.77927

2.87872

1.98363

3.376

3.07763

2.67981

2.67981

3.07763

4.37054

1.78472

1.58582

0.98909

2.97818

1.38691

2.38145

2.97818

2.58036

2.48091

2.18254

2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8109

Cl

uppe

r

1011

1112

1213

1314

1415

1516

1617

1718

1819

Cl

lower

Cl

total

Angleof

Attack

(deg) 4

0.047147

0.004427

0.009174

0.070881

0.004427

0.07152

0.03829

0.01313

0.08924

0.07613

0.0394

0.01179

0.07563

0.08037

0.08037

0.08987

0.08512

0.08512

0.05189

0.52077

0.5969

0.44464

0

0.119847

0.125343

0.130839

0.202289

0.196793

0.130839

0.141831

0.045076

0.069274

1.162132

0.06515

0.0437

0.22977

0.20779

0.13084

0.16931

0.16382

0.13084

0.08137

1.22259

0.06046

2.38472

4

0.256002

0.208535

0.222775

0.274988

0.189548

0.146828

0.232268

0.068747

0.092321

1.692012

0.04604

0.03552

0.20379

0.18005

0.14683

0.22277

0.26075

0.27499

0.23701

1.60776

0.084254

3.29977

8

0.29682

0.23938

0.26549

0.32293

0.21850

0.19239

0.29160

0.08203

0.13254

2.04172

0.073

0.052

0.275

0.228

0.187

0.270

0.317

0.317

0.275

1.999

0.04177

4.041

64

3 8 5 3 6 2 8 9 4 81 02 94 95 17 72 71 71 94 95 1 68

12

0.248091

0.223227

0.243118

0.297818

0.203336

0.1188

0.208309

0.075698

0.107748

1.726143

0.019057

0.00857

0.14366

0.14366

0.10885

0.10885

0.10388

0.20334

0.25804

1.0598

0.666345

2.78594

16

0.2829

0.243118

0.267981

0.322681

0.287872

0.267981

0.287872

0.093102

0.230822

2.284331

0.1264

0.03219

0.19836

0.21825

0.18842

0.26798

0.27793

0.25306

0.23317

1.79576

0.48857

4.08009

For V =30 MPH


Airfoil


P10

P11

P12

P13

P14

P15

P16

P17

P18

P19

% ofChor

d 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.10.075 0

0.075 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Distance

fromLE(in) 2.8

2.45 2.1

1.75 1.4

1.05 0.7

0.35

0.2625 0

0.2625

0.35 0.7

1.05 1.4

1.75 2.1

2.45 2.8

Angleof

Attack

(deg)

4

0.28283

0.33235

0.29634

0.44037

0.44938

0.44938

0.44488

0.17481

0.27081

0.603897

0.76896

0.66093

0.71495

0.11629

0.1568

0.1703

0.10279

0.08028

0.04427

C p

0

0.42829

0.49567

0.44177

0.51812

0.50465

0.61245

0.76066

0.60795

0.23516

0.887713

0.46423

0.34745

0.25762

0.16779

0.1633

0.1633

0.1633

0.14982

0.10042

65

4

0.18493

0.43214

0.90953

1.02461

1.04166

1.0374

1.27609

1.38691

1.24199

0.791146

0.211468

0.147533

0.087861

0.100648

0.062287

0.062287

0.062287

0.045237

0.023926

8

0.52789

0.53217

0.51933

0.54073

0.55357

0.46369

0.48081

0.71192

0.79752

0.815969

0.178278

0.075563

0.054164

0.041324

0.02715

0.06567

0.11275

0.16839

0.16411

12

0.64768

0.63877

0.63432

0.69221

0.68776

0.61205

0.58979

0.69221

0.96385

0.599213

0.41218

0.20288

0.109363

0.109363

0.011393

0.05986

0.06876

0.16228

0.21572

16

0.7514

0.79956

0.78205

0.83897

0.82583

0.70761

0.75578

0.76453

0.95281

0.111165

0.601557

0.408903

0.216249

0.194356

0.054244

0.01143

0.05084

0.15154

0.22598

2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8109

Cl

uppe

r

1011

1112

1213

1314

1415

1516

1617

1718

1819

Cl

lower

Cl

total

Angleof

Attack

(deg) 4

0.030759

0.031434

0.036836

0.044488

0.044938

0.044713

0.030984

0.0012

0.0328

0.230149

0.00619

0.01787

0.06879

0.04156

0.01365

0.01636

0.01365

0.00915

0.00623

0.19346

0.036685

0.42361

0

0.046198

0.046872

0.047995

0.051139

0.055855

0.068655

0.068431

0.010539

0.02447

0.371212

0.015881

0.01015

0.03025

0.02127

0.01655

0.01633

0.01633

0.01566

0.01251

0.12317

0.248043

0.49438

4

0.030854

0.067083

0.096707

0.103313

0.103953

0.115674

0.13315

0.032861

0.016907

0.700501

0.037598

0.004488

0.01177

0.009425

0.008147

0.006229

0.006229

0.005376

0.003458

0.092719

0.79322

0.60778

80.053

0.052

0.053

0.054

0.050

0.047

0.059

0.018 0.0

0.389

0.037

0.003

0.006

0.004

0.000 0.0 0.0 0.0 0.0

0.008

0.397 0.3

66

003

575

003

715

863

225

637

868

0069

197

284

173

486

774

709

0464

0892

1406

1662

183

38 8101

12

0.064322

0.063655

0.066326

0.068998

0.06499

0.060092

0.0641

0.020701

0.013674

0.486859

0.037927

0.007688

0.015612

0.010936

0.006038

0.00242

0.00643

0.01155

0.0189

0.038895

0.525754

0.44796

16

0.077548

0.079081

0.081051

0.08324

0.076672

0.07317

0.076016

0.021467

0.031562

0.599806

0.026727

0.012631

0.031258

0.02053

0.01243

0.002141

0.00311

0.01012

0.01888

0.073607

0.673413

0.5262

For V =68 MPH


Airfoil


P10

P11

P12

P13

P14

P15

P16

P17

P18

P19

% ofChor

d 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.10.075 0

0.075 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Distance

fromLE(in) 2.8

2.45 2.1

1.75 1.4

1.05 0.7

0.35

0.2625 0

0.2625

0.35 0.7

1.05 1.4

1.75 2.1

2.45 2.8

Angleof

Attack

(deg)

4

0.28432

0.36839

0.41375

0.49893

0.54981

0.55203

0.56973

0.25224

0.234496

0.638266

0.80314

0.64716

0.13277

0.16485

0.12503

0.09073

0.05644

0.01772

0.015464 C p

00.163

0.443

0.611

0.682

0.773

0.860

0.983

0.807

0.433

0.95777

0.232

0.162

0.057

0.015

0.00147

0.01555

0.02698

0.03930

0.06129

67

04 68 72 1 59 69 85 9 12 2 54 16 47 24 6 2 9 5 9

4

0.22171

0.41359

0.56216

0.87884

1.03336

1.14967

1.38654

1.43748

1.31608

0.747847

0.317403

0.215523

0.187506

0.178167

0.149301

0.140811

0.128076

0.112794

0.113643

8

0.2149

0.44182

0.67049

0.87733

1.02396

1.59999

1.77716

2.10096

2.33399

0.32138

0.680565

0.510375

0.389932

0.327966

0.27909

0.242434

0.211014

0.173485

0.145556

12

0.72309

0.7297

0.70903

0.69415

0.67596

0.65033

0.69002

0.75534

0.95046

0.284802

0.576669

0.4204

0.304646

0.232712

0.164087

0.106209

0.049159

0.0327

0.1129

16

0.70744

0.70744

0.69855

0.70477

0.70299

0.70033

0.72431

0.74119

0.7865

0.168491

0.618892

0.441219

0.303523

0.217351

0.126738

0.062776

0.0154

0.10601

0.20018

2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8109

Cl

uppe

r

1011

1112

1213

1314

1415

1516

1617

1718

1819

Cl

lower

Cl

total

Angleof

Attack

(deg) 4

0.032636

0.039107

0.045634

0.052437

0.055092

0.056088

0.041098

0.000222

0.03273

0.289585

0.00618

0.01813

0.039

0.01488

0.01449

0.01079

0.00736

0.00371

0.00011

0.11465

0.174935

0.40424

0

0.030336

0.05277

0.064691

0.072784

0.081714

0.092227

0.089588

0.015513

0.01967

0.479948

0.027196

0.00493

0.01098

0.00364

0.00069

0.000851

0.002127

0.003315

0.00503

0.018281

0.498228

0.46167

4

0.031765

0.048787

0.07205

0.09561

0.109151

0.126811

0.141201

0.034419

0.021309

0.681104

0.039947

0.006662

0.020151

0.018284

0.016373

0.014506

0.013444

0.012043

0.011322

0.152732

0.833836

0.52837

8 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.0 0.0 0.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.2 1.1

68

32836

55615

77391

95065

31197

68857

93906

55437

99576

0988

1347

14887

45015

35895

30353

26076

22672

19225

15952

23545

33425

0.68634

12

0.07264

0.071937

0.070159

0.068506

0.066315

0.067017

0.072268

0.021323

0.024962

0.535126

0.032305

0.012463

0.036252

0.026868

0.01984

0.013515

0.007768

0.000823

0.00728

0.142555

0.677681

0.39257

16

0.070744

0.070299

0.070166

0.070388

0.070166

0.071232

0.073275

0.019096

0.023175

0.538542

0.029527

0.013251

0.037237

0.026044

0.017204

0.009476

0.002369

0.00607

0.01531

0.113728

0.65227

0.42481

For V =102MPH


Airfoil


P10

P11

P12

P13

P14

P15

P16

P17

P18

P19

% ofChor

d 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.10.075 0

0.075 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Distance

fromLE(in) 2.8

2.45 2.1

1.75 1.4

1.05 0.7

0.35

0.2625 0

0.2625

0.35 0.7

1.05 1.4

1.75 2.1

2.45 2.8

(deg)

4

0.13207

0.39119

0.44192

0.52973

0.58553

0.59411

0.60465

0.271

0.241771

0.614447

0.89733

0.74045

0.25539

0.19685

0.14261

0.10203

0.06534

0.03413

0.006849

C p

0 0.9 0.0 0.0 0.0 0.0

69

0.20811

0.36961

0.64228

0.71835

0.8186

0.90091

1.03003

0.84474

0.45504

65282

0.24751

0.17807

0.06378

0.01931

0.00097

14632

27115

38037

59492

4

0.24083

0.45289

0.6506

0.81241

1.08413

1.22073

1.46263

1.50617

1.37637

0.746198

0.310793

0.214327

0.187721

0.164744

0.144185

0.132898

0.120804

0.110726

0.105325

8

0.21074

0.45543

0.69896

0.92709

1.13517

1.60837

1.87233

2.17251

2.40833

0.34445

0.689801

0.516013

0.394631

0.328738

0.276717

0.240495

0.208511

0.17306

0.14493

12

0.21809

0.24948

0.48473

0.82888

1.18931

1.53578

2.14309

2.7345

3.30111

1.83885

0.865518

0.685304

0.518654

0.423316

0.346192

0.291546

0.240389

0.18148

0.119859

16

0.71178

0.70909

0.70256

0.69757

0.69257

0.69142

0.73021

0.78705

0.82892

0.156978

0.625537

0.448867

0.31214

0.218428

0.130862

0.064035

0.01316

0.10265

0.20174

2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8109

Cl

uppe

r

1011

1112

1213

1314

1415

1516

1617

1718

1819

Cl

lower

Cl

total

Angleof

Attack

(deg)

4

0.026163

0.041656

0.048582

0.055763

0.058982

0.059938

0.043782

0.000365

0.03211

0.303124

0.01061

0.02047

0.04979

0.02261

0.01697

0.01223

0.00837

0.00497

0.00136

0.1474

0.155729

0.45052

0

0.028886

0.050594

0.068031

0.076847

0.085976

0.096547

0.093738

0.016247

0.01913

0.497733

0.026916

0.00532

0.01209

0.00415

0.00101

0.000683

0.002087

0.003258

0.004876

0.015241

0.512974

0.48249

4

0.03468

0.05517

0.07315

0.09482

0.11524

0.13416

0.14844

0.03603

0.02363

0.71535

0.03963

0.00656

0.02010

0.01762

0.01544

0.01385

0.01268

0.01157

0.01080

0.14829

0.86364

0.567

70

6 4 7 3 8 2 1 2 7 4 2 3 6 4 5 7 3 2 4 06

8

0.033308

0.05772

0.081303

0.103113

0.137177

0.174035

0.202242

0.05726

0.103229

0.949386

0.012951

0.015073

0.045532

0.036168

0.030273

0.025861

0.02245

0.019079

0.0159

0.223286

1.172672

0.7261

12

0.023379

0.036711

0.065681

0.100909

0.136255

0.183943

0.243879

0.075445

0.192748

1.05895

0.0365

0.019385

0.060198

0.047099

0.038475

0.031887

0.026597

0.021093

0.015067

0.223301

1.282251

0.83565

16

0.071043

0.070582

0.070006

0.069507

0.0692

0.071082

0.075863

0.0202

0.025198

0.54268

0.029344

0.01343

0.03805

0.026528

0.017465

0.009745

0.002544

0.00579

0.01522

0.116096

0.658776

0.42658

V = 6 MPH Dynamic Pressure

Cl q c (ft) L' (lbf) 6 MPH 30 MPH 68 MPH 102 MPH

Angleof

Attack

(deg)

4 0.597 0.104 0.292 0.01813

Angleof

Attack

(deg)

4 0.11 2.32 9.44 26.760 0.060 0.104 0.292 0.00184 0 0.10 2.33 11.87 26.774 0.084 0.104 0.292 0.00256 4 0.11 2.45 12.30 27.278 0.042 0.104 0.292 0.001269 8 0.10 2.44 11.97 27.04

12 0.666 0.104 0.292 0.020245 12 0.11 2.35 12.63 26.9516 0.489 0.104 0.292 0.014844 16 0.11 2.39 11.76 27.19

0.10 2.38 11.66 26.99 AvgV = 30 MPH

Angleof

Attack

(deg)

4 0.037 2.378 0.292 0.025438 1 inch = 0.083333 ft0 0.248 2.378 0.292 0.1720024 0.793 2.378 0.292 0.5500498 0.397 2.378 0.292 0.275558

12 0.526 2.378 0.292 0.36457816 0.673 2.378 0.292 0.46697

71

V = 68 MPHAn

gleof

Attack

(deg)

4 0.175 11.660 0.292 0.5949240 0.498 11.660 0.292 1.6943924 0.834 11.660 0.292 2.8357388 1.133 11.660 0.292 3.854591

12 0.678 11.660 0.292 2.3046816 0.652 11.660 0.292 2.218262

V = 102 MPH

Angleof

Attack

(deg)

4 0.156 26.995 0.292 1.2261240 0.513 26.995 0.292 4.038884 0.864 26.995 0.292 6.7998678 1.173 26.995 0.292 9.232991

12 1.282 26.995 0.292 10.0957616 0.659 26.995 0.292 5.186853

Appendix C

3D Wing Data

q V_ref Alpha NF/SF AF/AF2 PM/YM Mc/4[psf] [mph] [deg] [lbf] [lbf] [in lbf] [in lbf]

0.1 6 4 0.03 0.01 0.01 0.0520.1 5 4 0.02 0 0.02 0.021

72

0.1 5 4 0.04 0.02 0.01 0.0730.1 7 4 0.05 0.01 0.01 0.1140.1 5 4 0 0 0.01 0.0100.1 6 4 0.05 0.02 0.01 0.0940.1 6 4 0.03 0 0.01 0.0520.1 6 4 0.02 0.01 0.02 0.0210.1 6 4 0.02 0 0.02 0.0210.1 5 4 0.03 0 0.05 0.0120.1 6 4 0 0 0.04 0.0100.1 6 4 0.05 0 0.01 0.0940.1 5 4 0.04 0 0.01 0.0730.1 6 4 0.03 0 0.03 0.0320.1 6 4 0.02 0 0 0.0410.1 6 4 0.03 0 0.02 0.0820.1 5 4 0.03 0.01 0.03 0.0320.1 6 4 0.03 0.01 0.02 0.0420.1 5 4 0.04 0.01 0.03 0.0530.1 6 4 0.03 0 0 0.0620.1 5.7 4 0.0295 0.003 0.015 0.047639 Avg.

2.3 30 4 0.13 0.02 0.07 0.1992.4 31 4 0.08 0.02 0.06 0.1062.3 30 4 0 0.01 0.08 0.0802.3 30 4 0.02 0.02 0.01 0.0512.5 31 4 0.12 0.03 0.08 0.1692.3 30 4 0.08 0.04 0.06 0.1062.4 31 4 0.04 0.05 0.01 0.0932.4 31 4 0.04 0.04 0.02 0.0632.5 31 4 0.11 0.03 0.05 0.1782.4 31 4 0.07 0.03 0.02 0.1252.5 31 4 0.14 0.03 0.06 0.230

73

2.4 31 4 0.11 0.02 0.04 0.1882.5 31 4 0.12 0.02 0.06 0.1892.3 30 4 0.1 0.02 0.05 0.1572.5 31 4 0.05 0.03 0.03 0.1342.5 31 4 0.05 0.03 0.02 0.1242.5 31 4 0.08 0.03 0.07 0.0962.5 31 4 0.14 0.03 0.08 0.2102.4 30 4 0.11 0.02 0.03 0.1982.4 31 4 0.04 0.02 0.01 0.093

2.415 30.7 4 0.0815 0.027 0.0295 0.13941 Avg.

12.1 69 4 0.39 0.14 0.05 0.75812.2 69 4 0.46 0.17 0.17 0.78312.1 69 4 0.35 0.13 0.02 0.08012.1 69 4 0.39 0.14 0.04 0.76811.9 68 4 0.22 0.16 0.12 0.57612.1 69 4 0.51 0.15 0.16 0.89711.9 68 4 0.41 0.1 0.01 0.84012.1 69 4 0.33 0.14 0.05 0.73412 69 4 0.47 0.12 0.12 0.85412 69 4 0.4 0.13 0.03 0.799

12.1 69 4 0.43 0.16 0.11 0.78112.3 69 4 0.42 0.17 0.11 0.76011.9 68 4 0.39 0.09 0.05 0.75812.2 69 4 0.49 0.08 0.13 0.88612 69 4 0.51 0.13 0.15 0.907

11.9 68 4 0.5 0.12 0.17 0.86612.1 69 4 0.43 0.11 0.1 0.79111.9 68 4 0.35 0.15 0.03 0.69512.2 69 4 0.44 0.13 0.1 0.81211.9 68 4 0.36 0.11 0.06 0.686

74

12.05 68.7 4 0.4125 0.1315 0.072 0.75164 Avg.

26.9 103 4 1 0.14 0.13 1.94326.8 102 4 0.91 0.46 0.22 1.66627.5 104 4 1.04 0.08 0.28 0.08026.9 103 4 0.85 0.54 0.23 1.53226.8 102 4 1.06 0.13 0.29 1.90726.7 102 4 1.02 0.14 0.19 1.92426.3 101 4 1.05 0.21 0.32 1.85627.3 103 4 1.05 0.25 0.32 1.85626.2 101 4 0.97 0.27 0.26 1.75026.3 101 4 0.95 0.39 0.22 1.74927.2 103 4 0.95 0.51 0.3 1.66926.1 101 4 1.02 0.25 0.26 1.85426.7 102 4 0.99 0.25 0.31 1.74226.5 102 4 1.04 0.31 0.27 1.88526.9 103 4 0.93 0.28 0.34 1.58726.3 101 4 1.02 0.28 0.32 1.79426.3 101 4 1.03 0.21 0.33 1.80526.9 103 4 0.99 0.29 0.33 1.72226.9 103 4 0.97 0.42 0.21 1.80027.3 103 4 0.95 0.37 0.2 1.769

26.74 102.2 4 0.9895 0.289 0.2665 1.69447 Avg.q V_ref Alpha NF/SF AF/AF2 PM/YM Mc/4[psf] [mph] [deg] [lbf] [lbf] [in lbf] [in lbf]

0.1 6 0 0 0.03 0.01 0.0100.1 5 0 0.01 0 0.01 0.0110.1 6 0 0.01 0.01 0.02 0.0800.1 7 0 0.01 0.01 0.02 0.0410.1 6 0 0.02 0.01 0.01 0.0310.1 6 0 0 0.01 0.01 0.010

75

0.1 6 0 0.03 0.01 0 0.0620.1 6 0 0.03 0.01 0.01 0.0520.1 7 0 0.02 0.01 0.01 0.0310.1 7 0 0.01 0.01 0.02 0.0010.1 6 0 0 0.01 0.03 0.0300.1 7 0 0.02 0.02 0 0.0410.1 6 0 0 0.01 0 0.0000.1 7 0 0.02 0 0.01 0.0510.1 6 0 0.01 0.01 0.02 0.0410.1 7 0 0.01 0.01 0.01 0.0110.1 6 0 0.01 0.02 0.03 0.0510.1 7 0 0.01 0 0 0.0210.1 6 0 0.01 0.01 0.01 0.0110.1 6 0 0 0 0.03 0.0300.1 6.3 0 0.0065 0.007 0.006 0.015435 Avg.

2.4 31 0 0.23 0.04 0.3 0.1772.3 30 0 0.2 0.02 0.22 0.1952.3 30 0 0.19 0.02 0.18 0.0802.3 30 0 0.24 0.01 0.28 0.2172.3 30 0 0.23 0.04 0.26 0.2172.3 30 0 0.23 0.03 0.26 0.2172.4 30 0 0.2 0.04 0.21 0.2052.3 30 0 0.2 0.05 0.2 0.2152.3 30 0 0.22 0.04 0.24 0.2162.4 30 0 0.25 0.03 0.28 0.2382.3 30 0 0.27 0.01 0.29 0.2702.4 31 0 0.21 0.03 0.2 0.2352.3 30 0 0.19 0.03 0.2 0.1942.4 31 0 0.23 0.04 0.24 0.2372.4 31 0 0.28 0.04 0.28 0.300

76

2.3 30 0 0.27 0.02 0.25 0.3102.3 30 0 0.22 0.01 0.22 0.2362.4 30 0 0.24 0.03 0.26 0.2372.5 31 0 0.27 0.05 0.26 0.3002.3 30 0 0.22 0.01 0.19 0.266

2.345 30.25 0 0.2295 0.0295 0.241 0.22795 Avg.

11.8 68 0 1.14 0.16 1.28 1.08312 69 0 1.11 0.13 1.31 0.990

12.1 69 0 1.22 0.11 1.24 0.08012.1 69 0 1.16 0.14 1.32 1.08411.8 68 0 1.12 0.12 1.23 1.09112.2 69 0 1.15 0.12 1.2 1.18312 69 0 1.14 0.13 1.27 1.093

11.9 68 0 1.16 0.12 1.18 1.22412.1 69 0 1.15 0.14 1.28 1.10312.1 69 0 1.15 0.13 1.24 1.14312.2 69 0 1.11 0.14 1.29 1.01012 69 0 1.15 0.17 1.3 1.083

11.9 68 0 1.18 0.13 1.28 1.16611.7 68 0 1.15 0.11 1.32 1.06311.9 68 0 1.16 0.12 1.3 1.10411.9 68 0 1.16 0.17 1.27 1.13412.1 69 0 1.13 0.15 1.37 0.97211.9 68 0 1.14 0.16 1.32 1.04311.9 68 0 1.15 0.1 1.27 1.11312.2 69 0 1.15 0.12 1.32 1.063

11.99 68.55 0 1.149 0.1335 1.2795 1.04138 Avg.

27.2 103 0.1 2.72 0.35 3.21 2.42727.1 103 0.1 2.98 0.23 3.36 2.816

77

26.9 103 0.1 2.58 0.39 2.98 0.08026.6 102 0.1 2.47 0.42 3.03 2.08927.1 103 0.1 2.52 0.43 3.05 2.17326.9 103 0.1 2.69 0.26 3.18 2.39527.1 103 0.1 2.91 0.35 3.45 2.58126.5 102 0.1 2.68 0.29 3.2 2.35427.6 104 0.1 2.6 0.43 3.09 2.29927.4 103 0.1 2.62 0.48 3.21 2.22027.3 103 0.1 3.02 0.3 3.31 2.94927.5 104 0.1 2.79 0.32 3.36 2.42226.5 102 0.1 2.53 0.42 2.99 2.25326.1 101 0.1 2.48 0.37 3.01 2.13026.9 103 0.1 2.65 0.3 2.98 2.51227.1 103 0.1 2.7 0.32 3.24 2.35626.9 103 0.1 2.95 0.21 3.47 2.64427.6 104 0.1 3 0.21 3.41 2.80827.1 103 0.1 2.63 0.39 3.07 2.38126.5 102 0.1 2.54 0.42 3.12 2.144

26.995 102.85 0.1 2.703 0.3445 3.186 2.30162 Avg.q V_ref Alpha NF/SF AF/AF2 PM/YM Mc/4

[psf] [mph] [deg] [lbf] [lbf] [in lbf] [in lbf]0.2 8 3.9 0 0.01 0.02 0.0200.1 6 4 0.01 0.01 0.02 0.0410.1 7 3.9 0.01 0 0.01 0.0800.1 7 3.9 0 0.01 0.03 0.0300.1 6 4 0.01 0.02 0.02 0.0410.1 5 4 0.01 0.01 0.03 0.0090.1 6 3.9 0.01 0.01 0.01 0.0310.1 5 3.9 0.03 0 0 0.0620.1 7 4 0.01 0.02 0.01 0.0110.1 7 3.9 0.01 0.01 0 0.021

78

0.1 6 3.9 0 0.01 0.01 0.0100.1 6 4 0 0.01 0.01 0.0100.1 6 4 0.02 0 0.01 0.0310.1 6 4 0.02 0.01 0 0.0410.1 7 3.9 0.02 0 0.01 0.0310.1 7 4 0 0.01 0.02 0.0200.1 6 3.9 0.01 0 0.02 0.0010.1 8 4 0.01 0 0.02 0.0010.2 8 3.9 0.01 0 0.04 0.0190.1 7 4 0.01 0.02 0.03 0.009

0.11 6.55 3.95 0.005 0 0.009 0.013826 Avg.

2.3 30 4 0.34 0.01 0.43 0.2752.3 30 4 0.27 0 0.45 0.1102.4 31 4 0.42 0.01 0.53 0.0802.4 30 4 0.36 0.01 0.41 0.3362.4 30 4 0.36 0.02 0.46 0.2862.4 31 3.9 0.45 0.05 0.54 0.3932.3 30 4 0.39 0.02 0.48 0.3282.4 31 4 0.37 0.03 0.47 0.2972.3 30 4 0.32 0.03 0.46 0.2032.4 30 4 0.37 0 0.48 0.2872.3 30 4 0.3 0.04 0.43 0.1922.4 31 4 0.39 0.04 0.45 0.3582.4 31 4 0.36 0.04 0.46 0.2862.3 30 4 0.35 0.03 0.46 0.2652.4 31 4 0.38 0.01 0.48 0.3082.4 31 3.9 0.29 0.03 0.42 0.1812.5 31 4 0.35 0.04 0.5 0.2252.3 30 4 0.37 0.01 0.47 0.2972.4 31 4 0.41 0 0.5 0.350

79

2.5 32 4 0.39 0.03 0.55 0.2582.375 30.55 3.99 0.362 0.0205 0.4715 0.26572 Avg.

11.7 68 4 1.95 0 2.17 1.87111.8 68 4 1.78 0.05 2.62 1.06911.7 68 4 1.68 0.03 2.59 0.08011.8 68 4 1.79 0.08 2.49 1.22011.8 68 4 1.87 0.03 2.22 1.65611.7 68 4 1.94 0.24 1.89 2.13111.9 68 4 1.77 0.13 2.35 1.31811.5 67 4 1.78 0.02 2.22 1.46911.8 68 4 1.72 0.09 2.79 0.77511.7 68 4 1.89 0.05 2.34 1.57711.6 67 4 1.79 0.05 2.62 1.09011.8 68 4 1.76 0.22 2.58 1.06812.1 69 4 1.96 0.17 2.19 1.87212.1 69 4 1.88 0.11 2.38 1.51612 69 4 1.87 0.12 2.38 1.496

11.7 68 4 1.8 0.23 2.1 1.63111.9 68 4 1.73 0.08 2.7 0.88512 68 4 1.81 0.25 2.22 1.531

11.8 68 4 1.87 0.18 2.16 1.71611.8 68 4 1.85 0.05 2.42 1.414

11.81 68.05 4 1.8245 0.107 2.3715 1.36919 Avg.

27 103 4 4.41 0.05 5.83 3.31026.2 101 4 4.33 0.06 5.41 3.56426.7 102 4 3.96 0.19 5.69 0.08026.7 102 4 4.37 0.19 4.61 4.44726.6 102 4 3.94 0.1 6.24 1.92626.8 102 4 4.02 0.27 6.15 2.181

80

26.7 102 4 4.23 0.56 4.98 3.78726.8 102 4 4.27 0.05 5.41 3.44026.7 102 4 4.38 0.27 6.28 2.79826.5 102 4 3.99 0.06 6.44 1.82926 101 4 4.16 0.26 4.43 4.19226 101 4 4.29 0.16 6.12 2.771

25.8 100 4 4.1 0.07 5.96 2.53726.2 101 4 3.97 0.42 5.24 2.98826 101 4 4.18 0.12 6.01 2.653

26.6 102 4 4.14 0.22 5.08 3.50026.2 101 4 4.25 0.23 5.54 3.26826.6 102 4 4.28 0.24 5.54 3.33026.6 102 4.1 4.02 0.1 5.93 2.40126.3 101 4 4.55 0.41 4.98 4.450


[psf] [mph] [deg] [lbf] [lbf] [in lbf] [in lbf]0.1 6 8 0.05 0.01 0.01 0.0940.1 6 8 0.03 0.01 0.02 0.0820.1 7 8 0.04 0.02 0.06 0.0800.1 6 8 0.03 0.02 0.04 0.1020.2 8 8 0.04 0 0.01 0.0930.1 7 8 0.03 0.01 0 0.0620.2 8 8 0.04 0.02 0.01 0.0730.1 7 8 0.04 0 0.03 0.0530.1 7 8 0.03 0.02 0.02 0.0820.1 7 8 0.02 0.02 0.01 0.0310.1 7 8 0.02 0.01 0 0.0410.1 6 8 0.03 0.01 0 0.0620.1 7 8 0 0 0 0.0000.1 7 8 0.03 0.02 0.01 0.072

81

0.1 6 8 0.01 0.01 0.03 0.0510.1 6 8 0.04 0.01 0.01 0.0730.1 7 8 0.01 0.01 0 0.0210.2 8 8 0.04 0.02 0.01 0.0730.1 7 8 0.05 0.01 0.01 0.0940.2 8 8 0.04 0.03 0.02 0.063

0.12 6.9 8 0.031 0.011 0.004 0.0651 Avg.

2.4 31 8 0.47 0.02 0.57 0.4042.5 32 8 0.5 0.03 0.63 0.4062.4 31 8 0.48 0.04 0.58 0.0802.5 31 8 0.48 0 0.63 0.3652.4 31 8 0.47 0.02 0.62 0.3542.3 30 8 0.47 0 0.62 0.3542.4 31 8 0.49 0.01 0.62 0.3962.4 31 8 0.47 0.01 0.61 0.3642.4 31 8 0.46 0 0.58 0.3732.5 31 8 0.49 0.02 0.65 0.3662.5 31 8 0.48 0.02 0.62 0.3752.4 31 8 0.49 0.01 0.57 0.4462.4 30 8 0.46 0.02 0.57 0.3832.2 30 8 0.46 0 0.58 0.3732.5 31 8 0.47 0 0.61 0.3642.4 31 8 0.49 0.02 0.64 0.3762.4 31 8 0.5 0.03 0.61 0.4262.4 31 8 0.43 0.02 0.58 0.3112.6 32 8 0.51 0.01 0.6 0.4572.4 31 8 0.49 0 0.63 0.386

2.42 30.95 8 0.478 0.003 0.606 0.36792 Avg.

12 69 8 2.34 0.03 3.37 1.480

82

12.1 69 8 2.39 0.19 3.04 1.91312.1 69 8 2.28 0.16 3.38 0.08011.8 68 8 2.43 0.15 2.99 2.04611.9 68 8 2.53 0.38 2.94 2.30311.9 68 8 2.46 0.36 2.84 2.25812.2 69 8 2.75 0.22 2.65 3.04911.9 68 8 2.31 0.29 3.42 1.36711.8 68 8 2.3 0.26 3.37 1.39711.8 68 8 2.26 0.34 3.09 1.59411.9 68 8 2.45 0.2 3.14 1.93812 68 8 2.24 0.25 3.27 1.37212 68 8 2.28 0.3 3.38 1.34512 69 8 2.5 0.31 2.92 2.261

11.7 68 8 2.7 0.22 2.6 2.99611.7 68 8 2.3 0.4 3.19 1.57712.1 69 8 2.37 0.24 3.3 1.61212.1 69 8 2.28 0.23 3.59 1.13511.9 68 8 2.37 0.02 3.25 1.66211.9 68 8 2.48 0.33 2.92 2.220

11.94 68.35 8 2.401 0.078 3.1325 1.78031 Avg.

27.3 103 8 5.53 0.01 7.23 4.23126.1 101 8 6.03 0.06 6.83 5.66726.2 101 8 5.49 0.07 6.04 0.08026.9 103 8 6.17 0.22 7.2 5.58726.9 103 8 6.21 0.01 7.41 5.46026.2 101 8 5.44 0 6.4 4.87426.5 102 8 5.97 0.02 7.33 5.04326 101 8 5.05 0.49 7.99 2.476

25.7 100 8 4.64 0.51 7.58 2.03626.3 101 8 5.84 0.5 6.44 5.663

83

26.6 102 8 5.7 0.43 7.45 4.36326.5 102 8 5.16 0.43 8.34 2.35426.7 102 8 4.89 0.33 8.45 1.68526.9 103 8 6.35 0.02 7.05 6.11026.2 101 8 5.79 0.32 6.59 5.41026.2 101 8 5.5 0.03 6.57 4.82926.9 103 8 5.88 0.07 6.92 5.26626.6 102 8 5.23 0.48 8.21 2.62926.2 101 8 5.23 0.05 8.31 2.52926.6 102 8 5.41 0.61 8.45 2.762

26.475 101.75 8 5.5755 0.133 7.3395 3.95282 Avg.q V_ref Alpha NF/SF AF/AF2 PM/YM Mc/4

[psf] [mph] [deg] [lbf] [lbf] [in lbf] [in lbf]0.1 7 12 0.05 0.01 0.04 0.0640.1 7 12 0.05 0.01 0.03 0.0740.1 7 12 0.02 0.01 0.01 0.0800.2 8 12 0.04 0.01 0.02 0.0630.1 7 12 0.04 0.01 0 0.0830.1 7 12 0.06 0.02 0.03 0.0940.1 6 12 0.07 0.01 0 0.1450.1 6 12 0.04 0.01 0 0.0830.1 6 12 0.03 0 0 0.0620.1 6 12 0.03 0 0.02 0.0420.1 7 12 0.04 0 0.02 0.0630.1 7 12 0.04 0.01 0.04 0.0430.1 6 12 0.04 0.01 0.02 0.0630.1 6 12 0.04 0.02 0.03 0.0530.1 7 12 0.04 0.02 0.02 0.0630.1 7 12 0.03 0.02 0.01 0.0520.1 7 12 0.03 0.01 0.02 0.0420.1 6 12 0.03 0.02 0.03 0.032

84

0.1 7 12 0.02 0.01 0 0.0410.1 7 12 0.04 0.01 0.03 0.053

0.105 6.7 12 0.039 0.01 0.0185 0.06476 Avg.

2.5 31 12 0.54 0.06 0.62 0.4992.4 31 12 0.59 0.06 0.58 0.6432.6 32 12 0.55 0.01 0.66 0.0802.4 31 12 0.52 0.02 0.61 0.4682.4 31 12 0.46 0.08 0.55 0.4032.4 31 12 0.51 0.01 0.67 0.3872.6 32 12 0.68 0 0.66 0.7492.6 32 12 0.46 0.07 0.59 0.3632.5 31 12 0.54 0.06 0.71 0.4092.4 31 12 0.44 0.02 0.55 0.3622.4 31 12 0.52 0.03 0.58 0.4982.5 31 12 0.56 0.05 0.55 0.6112.5 32 12 0.54 0.04 0.57 0.5492.5 32 12 0.57 0 0.6 0.5812.6 32 12 0.51 0.04 0.59 0.4672.7 33 12 0.51 0.07 0.64 0.4172.5 31 12 0.59 0.01 0.55 0.6732.5 31 12 0.44 0.05 0.59 0.3222.6 32 12 0.51 0.08 0.62 0.4372.4 31 12 0.53 0 0.62 0.4782.5 31.45 12 0.5285 0.036 0.6055 0.46982 Avg.

11.7 68 12 2.79 0.21 2.91 2.87211.8 68 12 3.06 0.21 3.5 2.84211.6 67 12 2.69 0.01 2.49 0.08012.1 69 12 2.81 0.11 2.99 2.83411.7 68 12 3.31 0.22 3.18 3.680

85

11.8 68 12 2.54 0.21 3.05 2.21412 68 12 2.66 0.02 3.41 2.103

11.8 68 12 3.24 0.14 3.09 3.62511.7 68 12 2.95 0.1 2.68 3.43411.8 68 12 2.34 0.03 3.24 1.61012.1 69 12 2.78 0.21 3.03 2.73211.8 68 12 3.12 0.18 3.76 2.70611.8 68 12 2.7 0.07 2.09 3.50611.9 68 12 3.2 0.19 2.95 3.68211.9 68 12 3.35 0.13 3.11 3.83311.7 68 12 2.84 0.15 3.75 2.13611.8 68 12 2.67 0.04 3.74 1.79411.7 68 12 2.8 0.2 3.58 2.22312.3 69 12 3.06 0.12 3.68 2.66211.8 68 12 2.72 0.22 2.88 2.757

11.84 68.1 12 2.8815 0.1155 3.1555 2.66616 Avg.

26.7 102 11.9 6.79 0.68 8.63 5.44226.1 101 11.9 6.84 0.07 7.03 7.14626 101 11.9 7.04 0.13 9.19 0.080

27.1 103 11.9 7.05 0.45 7.19 7.42127.4 104 11.9 8.34 0.44 8.33 8.95526.2 101 11.9 7.37 1.2 8.41 6.86427.2 103 11.9 7.51 0.94 9.72 5.84426.3 102 11.9 6.63 0.34 5.75 7.99125.9 101 11.9 7.05 0 7.97 6.64125.7 100 11.9 7.05 0.69 9.62 4.99126.5 102 11.9 6.3 1.01 8.91 4.14725.6 100 11.9 6.67 0.27 7.34 6.48427.9 104 11.9 6.91 0.27 8.96 5.36126.9 103 11.9 7.22 0.3 9.83 5.133

86

27.4 103 11.9 7.22 0.83 8.74 6.22327.2 103 11.9 7.22 1.14 8.51 6.45328.6 106 11.9 7.53 0.35 9.14 6.46626.4 102 11.9 6.59 0.32 8.9 4.75827.3 103 11.9 6.74 0.51 8.34 5.62927 103 11.9 6.66 0.02 6.31 7.493


[psf] [mph] [deg] [lbf] [lbf] [in lbf] [in lbf]0.1 7 16 0.01 0.01 0.02 0.0010.1 7 16 0.05 0.01 0.02 0.0840.2 8 16 0.02 0.02 0.03 0.0800.1 7 16 0.04 0.02 0.02 0.0630.1 7 16 0.01 0.01 0 0.0210.1 7 16 0.03 0.01 0.01 0.0720.2 8 16 0.03 0.01 0.03 0.0320.1 7 16 0.02 0.01 0.03 0.0110.1 8 16 0.03 0.02 0.02 0.0420.1 7 16 0.03 0.01 0.01 0.0520.1 7 16 0.03 0.01 0.01 0.0520.1 7 16 0.03 0.02 0.03 0.0320.1 7 16 0.04 0.01 0.04 0.0430.2 8 16 0.01 0.01 0.01 0.0110.1 7 16 0.03 0.01 0.01 0.0520.1 6 16 0.03 0.01 0.03 0.0320.1 7 16 0 0.01 0.03 0.0300.1 7 16 0.02 0.02 0.03 0.0110.1 7 16 0 0.01 0.02 0.0200.1 7 16 0.01 0.01 0.01 0.011

0.115 7.15 16 0.0235 0.0125 0.0195 0.03263 Avg.

87

2.5 31 16 0.61 0.01 0.66 0.6042.2 30 16 0.56 0.03 0.55 0.6112.3 30 16 0.59 0.01 0.65 0.0802.2 30 16 0.6 0 0.63 0.6142.4 31 16 0.54 0.04 0.63 0.4892.5 31 16 0.53 0.03 0.66 0.4382.5 31 16 0.59 0.03 0.62 0.6032.3 30 16 0.61 0.01 0.67 0.5942.3 30 16 0.48 0.05 0.54 0.4552.4 31 16 0.53 0.04 0.6 0.4982.5 32 16 0.57 0 0.7 0.4812.4 30 16 0.53 0.01 0.59 0.5082.5 31 16 0.59 0.04 0.63 0.5932.3 30 16 0.54 0.04 0.62 0.4992.4 31 16 0.56 0.01 0.63 0.5312.5 31 16 0.53 0 0.65 0.4482.5 31 16 0.53 0.05 0.66 0.4382.5 31 16 0.61 0 0.73 0.5342.3 30 16 0.55 0.04 0.57 0.5702.4 30 16 0.55 0.06 0.65 0.490

2.395 30.6 16 0.56 0.02 0.632 0.50396 Avg.

11.5 67 15.9 2.66 0.08 3.24 2.27311.9 68 15.9 2.72 0.11 3.11 2.52711.9 68 15.9 2.74 0.09 3.17 0.08011.9 68 15.9 2.75 0.07 3.19 2.50912 69 15.9 2.83 0.06 3.39 2.475

11.8 68 15.9 2.67 0 3.17 2.36411.8 68 15.9 2.74 0.08 3.2 2.47911.9 68 15.9 2.41 0.1 2.97 2.02511.6 67 15.9 2.66 0.07 3.05 2.463

88

11.8 68 15.9 2.61 0.1 3.06 2.34912.1 69 15.9 2.61 0.02 3.1 2.30911.9 68 15.9 2.55 0.16 3.17 2.11512.1 69 15.9 2.87 0.01 3.16 2.78812.1 69 15.9 2.81 0.09 3.15 2.67412 69 15.9 2.72 0.05 3.31 2.32712 69 15.9 2.64 0.1 3.3 2.171

12.1 69 15.9 2.82 0.01 3.19 2.65411.8 68 15.9 2.73 0.05 3.19 2.46812.1 69 15.9 3 0.18 3.49 2.72811.9 68 15.9 2.82 0.07 3.49 2.354

11.91 68.3 15.9 2.718 0.075 3.205 2.30662 Avg.

27.5 104 15.9 8.9 0.36 11.71 6.73526.7 102 15.9 10.3 0.29 10.21 11.13728.3 105 15.9 10.96 0.01 12.85 0.08027.7 104 15.9 8.36 0.45 12.11 5.21626.5 102 15.9 9.25 0.38 12.92 6.25126.1 101 15.9 10.22 1 12.05 9.13126 101 15.9 10.05 0.29 14.5 6.32926 101 15.9 8.82 0.91 8.26 10.019

28.6 106 15.9 10.63 0.41 13.27 8.76127.9 104 15.9 9.48 0.44 8.34 11.30727.9 104 15.9 11.09 0.6 13.44 9.54426.6 102 15.9 7.96 0.27 11.35 5.14726.8 102 15.9 11.27 0.58 10.41 12.94726.4 102 15.9 8.93 0.04 9.18 9.32725.6 100 15.9 9.32 0.53 10.72 8.59626 101 15.9 9.01 0.44 12.93 5.743

26.4 102 15.9 8.62 0.62 9.15 8.71528.5 106 15.9 10.24 0.81 8.94 12.282

89

28.1 105 15.9 11.83 0.54 10.78 13.73827.3 103 15.9 11.34 0.28 12.51 10.992

27.045 102.85 15.9 9.829 0.3035 11.2815 8.59987 Avg.

3D Wing Calculations

V = 6MPH q

NF/SF

AF/AF2

PM/YM Sin Cos Tan

V = 6MPH

[psf]

[lbf]

[lbf]

[inlbf] 4

0.06976

0.9975

6

0.0699

3Lift(lb)

Drag(lb) CL CD

6.5MPH

30MPH

68MPH

102MPH

Angleof

Attack

(deg)

40.1

0.0295

0.003

0.015 3

0.05234

0.9986

3

0.0524

1

Angleof

Attack

(deg)

4

0.0296

4

0.0009

3

1.23

0.039

Angleof

Attack

(deg)

4

0.0389

5

0.036659

0.035407

0.034165

00.1

0.0065

0.007

0.006 2

0.03490

0.9993

9

0.0349

2 00.0065

0.007

0.27

0.292 0

0.291646

0.052413

0.046389

0.0531

7

40.11

0.005 0

0.009 1

0.01745

0.9998

5

0.0174

6 4

0.0049

9

0.0003

5

0.19

0.013 4

0.0132

1

0.080175

0.082557

0.075841

80.12

0.031

0.011

0.004 0

0.00000

1.0000

0

0.0000

0 8

0.029167

0.015207

1.01

0.528 8

0.527993

0.109417

0.143553

0.142839

12

0.105

0.039

0.01

0.0185 1

0.01745

0.9998

5

0.0174

612

0.036069

0.0178

9

1.43

0.710

12

0.709871

0.241807

0.250571

0.250374

1 0. 0.0 0.0 0.0 2 0.034 0.9 0.0 1 0.0 0.0 0. 0. 1 0.6 0.3 0.2 0.3

90

6 115

235

125

195

90 9939

3492

6 19144

18493

69

670

6 69997

01965

87299

72422

30.052

34

0.9986

3

0.0524

1

V = 30MPH 4

0.06976

0.9975

6

0.0699

3V = 30MPH

50.087

16

0.9962

0

0.0874

9

Angleof

Attack

(deg)

4

2.415

0.0815

0.027

0.0295 6

0.10453

0.9945

2

0.1051

0

Angleof

Attack

(deg)

4

0.083185

0.021249

0.14

0.037

0

2.345

0.2295

0.0295

0.241 7

0.12187

0.9925

5

0.1227

9 00.2295

0.0295

0.41

0.052

4

2.375

0.362

0.0205

0.4715 8

0.13917

0.9902

7

0.1495

4 4

0.359688

0.045703

0.63

0.080

82.42

0.478

0.003

0.606 9

0.15643

0.9876

9

0.1583

8 8

0.473766

0.063554

0.82

0.109

12

2.5

0.5285

0.036

0.6055

10

0.17365

0.9848

1

0.1763

312

0.509466

0.145095

0.85

0.242

16

2.395

0.56

0.02

0.632

11

0.19081

0.9816

3

0.1943

816

0.532794

0.173582

0.93

0.302

12

0.20791

0.9781

5

0.2125

6V = 68MPH

13

0.22495

0.9743

0.2308

V = 68MPH

91

7 7

14

0.24192

0.9703

0

0.2493

3

Angleof

Attack

(deg)

4

12.05

0.4125

0.1315

0.072

15

0.25882

0.9659

3

0.2679

5

Angleof

Attack

(deg)

4

0.420668

0.102405

0.15

0.035

0

11.99

1.149

0.1335

1.2795

16

0.27564

0.9612

6

0.2867

5 01.149

0.1335

0.40

0.046

4

11.81

1.8245

0.107

2.3715 4

1.812591

0.234016

0.64

0.083

8

11.94

2.401

0.078

3.1325 8

2.366778

0.411395

0.83

0.144

12

11.84

2.8815

0.1155

3.1555

Planform

Area:

34.562

5in^2

12

2.7945

2

0.712075

0.98

0.251

16

11.91

2.718

0.075

3.205

0.240017

ft^2

16

2.592037

0.821276

0.91

0.287

V =102MPH

V =102MPH

Angleof

Attack

(deg)

4

26.74

0.9895

0.289

0.2665

Angleof

Attack

(deg)

4

1.007249

0.219272

0.16

0.034

0

26.995

2.703

0.3445

3.186 0

2.703

0.3445

0.42

0.053

4 26 4.1 0.1 5.5 4 4.1 0.4 0. 0.

92

.45

92 895

935

68569

81472

66

076

8

26.475

5.5755

0.133

7.3395 8

5.502729

0.907665

0.87

0.143

12

26.77

7.0365

0.149

8.341

12

6.8517

6

1.608717

1.07

0.250

16

27.045

9.829

0.3035

11.2815

16

9.5319

2.417493

1.47

0.372

V = 6 MPH q Mc/4 Mc/4 M' cm1/4

[psf] [in lbf] [ft lbf] lbf

Angleof

Attack

(deg)

4 0.1 0.048 0.004 0.0048 0.0000410 0.1 0.015 0.001 0.0016 0.0000134 0.11 0.014 0.001 0.0014 0.000013

8 0.12 0.065 0.005 0.0066 0.000067

12 0.105 0.065 0.005 0.0066 0.000059

16 0.115 0.033 0.003 0.0033 0.000032

V = 30 MPH

Angleof

Attack

(deg) 4 2.415 0.139 0.012 0.0141 0.002900

0 2.345 0.228 0.019 0.0231 0.0046054 2.375 0.266 0.022 0.0269

93

0.005437

8 2.42 0.368 0.031 0.0373 0.007670

12 2.5 0.470 0.039 0.0476 0.010118

16 2.395 0.504 0.042 0.0510 0.010398

V = 68 MPH

Angleof

Attack

(deg)

4 12.05 0.752 0.063 0.0761 0.078025

0 11.99 1.041 0.087 0.1055 0.107563

4 11.81 1.369 0.114 0.1387 0.139299

8 11.94 1.780 0.148 0.1803 0.183120

12 11.84 2.666 0.222 0.2700 0.271941

16 11.91 2.307 0.192 0.2336 0.236660

V = 102 MPH

Angleof

Attack

(deg)

4 26.74 0.991 0.083 0.1003 0.228245

0 26.995 2.302 0.192 0.2331 0.535245

4 26.45 2.973 0.248 0.3010 0.677319

8 26.475 3.953 0.329 0.4003 0.901529

94

12 26.77 5.976 0.498 0.6052 1.378176

16 27.045 8.600 0.717 0.8709 2.003621

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SUBSONIC WIND-TUNNEL WALL CORRECTIONS ON A … · SUBSONIC WIND-TUNNEL WALL CORRECTIONS ON A WING WITH A ... 2D Airfoil Data (Pressure) ... 78 Figure 5.4 Values