March 24, 2005

1

Critical Design ReviewCritical Design Review

Michael CaldwellMichael CaldwellJeff HaddinJeff Haddin

Asif HossainAsif HossainJames KobyraJames KobyraJohn McKinnisJohn McKinnis

Kathleen MondinoKathleen MondinoAndrew RodenbeckAndrew RodenbeckJason TangJason TangJoe TaylorJoe TaylorTyler WilhelmTyler Wilhelm

AAE 451: Team 2AAE 451: Team 2

March 24, 2005 2[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Overview

Walkaround Aircraft 3-View Constraint Diagram Physical Properties Aerodynamics Dynamics & Controls Structures, Weights, & Landing Gear Propulsion Unique Aspects of the Design Constraint Diagram Revisited

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Walkaround

March 24, 2005 4[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

5.24

ft

3.00 ft

Aircraft 3-View

Mission Requirements

15 min. endurance

Take-off distance ≤ 60 ft.

Vstall ≤ 15 ft/s

Vloiter ≤ 25 ft/s

35 ft. turn radius

Weight 1.96 lbs

Wingspan 5.24 ft

Length 3.00 ft

Height 1.50 ft

Aspect Ratio 5.24

Cruise Speed 23 ft/s

Max Thrust 1.00 lb

March 24, 2005 5[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Constraint Diagram

Design Space

Design Point

Wing Loading: 0.376 lbf/ft2

Power Loading: 32.74 lbf/hp

LiPoly Weight: 1.97lbf

Wing Area: 5.24 ft2

Power: 0.060 hp

Takeoff

March 24, 2005 6[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Tabular Summary of Parameters

Wing Area 5.24 ft2

Canard Area 1.432 ft2

Tail Area (each) 0.915 ft2

Wetted Area 23.08 ft2

Mean Chord 1.00 ft Wing Taper Ratio 0.7 Landing Gear Skis (interchangeable) Motor Type Brushless Wing Dihedral 4º Canard Dihedral -4º Center of Gravity 1.70 ft Neutral Point 1.85 ft Static Margin 14.80% Foam & Balsa Construction Pitch Rate Feedback to Elevator

March 24, 2005 7[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Concept Selection Objectives

Selected mission objectives Assigned rankings (out of 120 possible points)

Objectives Team Ranking % of votes

Endurance (high AR, fuselage - batteries) 5 8.85

Manuverability (position of control surfaces) 8a 8.13

Lightw eight 6 8.75

Robust/Accessibility 4 9.48

Low Speed 3 10.10

Cost 12a 5.00

Stylish 2 10.21

Stable (CG vs. AC) 7 8.54

Easy To Fly (size) 8b 8.13

Technically Simple 1 10.31

High Lift (w ing area/lif t distribution) 10 7.50

Ground Clearance (props, tail) 12b 5.00

March 24, 2005 8[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Weighted Objectives

For each design, objectives are ranked either: 1 - Poor, 3 - Average, 9 - Excellent

Each objective score is multiplied by corresponding weighted average

Scores for each design concept are totaledObjectives 1 2 3 4 5 6 7

Technically Simple 9 9 3 3 1 3 3

Stylish 3 9 3 3 9 9 3

Low Speed 3 3 9 1 3 3 3

Robust/Accessibility 9 9 9 3 3 3 9

Endurance (high AR, fuselage - batteries) 3 3 3 9 3 9 3

Lightweight 9 9 1 3 1 3 9

Stable (CG vs. AC) 9 3 3 9 1 9 9

Manuverability (position of control surfaces) 9 1 3 9 1 3 3

Easy To Fly (size) 3 9 3 3 9 9 3

High Lift (wing area/ lift distribution) 9 9 3 3 9 9 9

Cost 3 3 3 3 1 3 3

Ground Clearance (props, tail) 9 9 3 1 9 9 9

Total 53.86 53.34 33.33 35.24 33.63 49.12 44.64

March 24, 2005 9[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Pugh’s Method

ConceptsObjectives

1 2 3 4 5 6 7 8 9

Technically Simple S - - - - - S S

Stylish + - S + + S S +

Low Speed S - S + + - - -

Robust/Accessibility S S S + + S S +

Endurance (high AR, fuselage - batteries) S - S + + S S -

Lightweight S - - - - S S +

Stable (CG vs. AC) S - + - S S + +

Manuverability (position of control surfaces) - S S - S S S -

Easy To Fly (size) + S S + + S S -

High Lift (wing area/lift distribution) S - S + + - - -

Ground Clearance (props, tail) S - S - + S S -

S + 2 0 1 6 7 0 1 4

S - 1 8 2 5 2 3 2 6

S s 8 3 8 0 2 8 8 1Total 1 -8 -1 1 5 -3 -1 -2

D

A

T

U

M

All other designs’ objectives are compared to design 1 (datum) + (better), - (worse), s (same)

Sum of each scoring criteria taken Design strengths and weaknesses determined

March 24, 2005 10[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Aerodynamics Overview

Airfoil Selection Twist Distribution Mathematical Model Launch Conditions L/DMAX

March 24, 2005 11[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

SELIG – WORTMANN COMPARISON

Selig 1210: M.S.Selig,J.J.Guglielmo,A.P.Broeren and P.Giguere,"Summary of Low-Speed Airfoil Data, Volume 1 – Wind Tunnel DataWortmann FX 63-137: M.S.Selig,J.F.Donovan and D.B.Fraser,"AIRFOIL AT LOW SPEEDS – Wind Tunnel

Airfoil Selection: Wing

March 24, 2005 12[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Airfoil Selection: Wing

Wortmann FX63-137

Wortmann FX 63-137: M.S.Selig,J.F.Donovan and D.B.Fraser,"AIRFOIL AT LOW SPEEDS – Wind Tunnel

March 24, 2005 13[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Airfoil Selection: Canard

NACA 0012

March 24, 2005 14[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Airfoil Selection: Vertical Tails

Flat Plate Non-Lifting Surface No Volume Needed Ease of Construction Light Weight

March 24, 2005 15[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Wing Twist Distribution

Root: 1o

Tip: -7o

March 24, 2005 16[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Mathematical Model Prandtl’s Classical Lifting Line Theory

Elliptical Loading

Parasite Drag – Component Buildup Method

22

1

-b

yo

-- 2

2

2

2

)()(b

b

b

bdyyVdyyLL

)()( yVyL

SV

LCL

2

21

eAR

CCC L

LiDi

2

- -

2

24

1)( b

bo

oi dy

yy

dyd

VV

yw

misc

cc

o Dref

wetccfD C

S

SQFFCC

S

March 24, 2005 17[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Mathematical Model

From Prandtl’s Classical Lifting-Line Theory

*LLL CCCo

615.0oL

C 1deg067.0 -L

C

io DDD CCC 0.043

oDC

eAR

CC L

Di

2

44.1cos9.0 25.0maxmax clL CC

March 24, 2005 18[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Mathematical Model

Re=147,820

March 24, 2005 19[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Mathematical Model

*4

MMM CCCoc

033.0-oMC

1deg014.0 --MC

cohowfoo MMMM CCCC

0MM

MM

MMM

o

o

fowowfo C

CCCC

CMo calculated using Roskam Vol. VI and CMα calculated from flatearth.m

March 24, 2005 20[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Launch Conditions

αLo = -9o

Vtake-off = 1.2Vstall = 18 ft/s Climb Angle = 20o

Angle of Attack = 4.5o

-9o

20o

4.5o

March 24, 2005 21[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

L/DMAX

L/DMAX=10.75

αL/Dmax=0.60o

Re=147,820

March 24, 2005 22[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

L/DMAX

L/DMAX Velocity Loiter Straight:

VL/Dmax= 21.97 ft/s

Re=147,820

Operation Point

March 24, 2005 23[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Dynamics & Controls Overview

Tail Sizing Control Surface Sizing Static Margin Trim Diagram Dihedral Angle Feedback System

March 24, 2005 24[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Tail Sizing (Class 1)

Constants cHT = 0.50 cVT = 0.05 Cw = 1 ft Sw = 5.24 ft LHT = 1.83 ft LVT = 0.75 ft

Horizontal tail (canard) Area = 1.432 ft2

Vertical tail Area = 0.915 ft2 (each)

March 24, 2005 25[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Tail Sizing (Class 2) Vertical Tail

Plot Cnβ versus Svt Svt = 0.912 ft2

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1Vertical Tail Sizing

Vertical Tail Area Svt

(ft2)

Cn

Cn variation

Desired Cn

Size of Vertical Tail

March 24, 2005 26[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Tail Sizing (Class 2) Horizontal Tail

Plot Xcg and Xac versus Sht

Sht = 1.36 ft2

March 24, 2005 27[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Canard & Tail Sizing

Class 1 Sizing Class 2 Sizing

Canard Area Sht 1.43 ft2 1.36 ft2

Vertical Tail

Area Svt (each)0.92 ft2 0.91 ft2

March 24, 2005 28[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Control Surface Sizing

Span (ft) Chord (ft) Area (ft2)

Aileron (each) 1.40 0.20 0.28

Elevator 1.00 0.33 0.33

Rudder (each) 0.75 0.58 0.44

March 24, 2005 29[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Desired Static Margin

Static Margin (Raymer) Typical Fighter Jet: 0-5% Typical Transport Aircraft = 5-10% Model aircraft usually more stable

Goal: Static Margin = 15%

March 24, 2005 30[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Actual Static Margin

Xcg = 1.70 ft

Xnp = 1.85 ft Static Margin = 14.80%

March 24, 2005 31[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

-5 0 5 10 150

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

(deg)

CL

c=-10o

c=-5o

c=0o

c=5o

c=10o

-0.3-0.2-0.100.10.20.30

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

CM

Xref

CL

CL Max

Trimmed Maximum CL

(xref = xcg)

α CL Max

α = 0o

Trim Diagram

March 24, 2005 32[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Outer Panel Dihedral

Wing: 4 deg outer panel dihedral, B=4 deg and x at 0.9 ft Canard: -4 deg outer panel dihedral, B=4 deg and x at 0.08 ft

Dihedral Angle

kBAEVD

March 24, 2005 33[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Dihedral Angle

EVD of the wing and canard: Wing EVD:

Canard EVD:

deg 72.3)4)(93.0(0

93.0 ,25.0/

26.03166.0/08.0/

deg 36.3)4)(84.0(0

84.0 ,35.0/

35.062.2/9.0/

EVDc

kLxfor

Lx

EVDw

kLxfor

Lx

March 24, 2005 34[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Loop Closure Description

Pitch Rate feedback to the Elevator

Objective: Establish longitudinal stability by

using pitch rate feedback by varying damping ratio of the short period mode from 0.83 to 0.99.

March 24, 2005 35[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Block Diagram

He(s) q(s)/e(s)

H (s)K

S

PilotInput

ElevatorServo Aircraft

e(s) q(s)

+ _

Pitch RateGyro

FeedbackGain

March 24, 2005 36[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Aircraft TF / Natural Frequency and Damping Ratio

Aircraft Transfer Function (Flat Earth Predator)

Undamped Natural Frequency (Short Period)

Damping Ratio (Short Period)

004912.06.14387.939.23236.25

10147.101007.09.3815.61821.90

)(

)(2345

19234

-----

-

sssss

ssss

s

sq

e

rad/sec 16.201 1

- MU

MZ qnsp

0.836 2

1

-

spn

q

sp

MUZ

M

March 24, 2005 37[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Gain Calculation, k

Gain Calculation: - Flat Earth Predator

- SISOTOOL k = 0.0857 - Root Locus Plot

For k = 0 For k = 0.0857

%83.0

sec/ 15

836.0

p

n

M

rad

%0

sec/ 5.16

99.0

p

n

M

rad

March 24, 2005 38[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Root LocusRoot Locus

Real Axis

Imagin

ary

Axis

-18 -16 -14 -12 -10 -8 -6 -4 -2 0 2-10

-8

-6

-4

-2

0

2

4

6

8

100.160.340.50.640.760.86

0.94

0.985

0.160.340.50.640.760.86

0.94

0.985

24681012141618

System: untitled1Gain: 0Pole: -12.5 + 8.2iDamping: 0.836Overshoot (%): 0.83Frequency (rad/sec): 15

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Root LocusRoot Locus

Real Axis

Imagin

ary

Axis

-18 -16 -14 -12 -10 -8 -6 -4 -2 0 2-10

-8

-6

-4

-2

0

2

4

6

8

100.160.340.50.640.760.86

0.94

0.985

0.160.340.50.640.760.86

0.94

0.985

24681012141618System: untitled1Gain: 0.0857Pole: -16.3 + 2.27iDamping: 0.99Overshoot (%): 0Frequency (rad/sec): 16.5

March 24, 2005 40[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Gyro and Servo Selection

Futaba GYA350 gyro Weight: 0.92 ounces Remote gain function

JR S241 sub micro servos Weight: 0.32 ounces Torque: 17 oz/in

March 24, 2005 41[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Structures Overview

Material Properties Structures Landing Gear Center of Gravity Weight and Cost Estimation V-n Diagram Wing Loading Analysis

March 24, 2005 42[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Material Properties

Density (lbf/ft3) Young’s Modulus (ksi) Yield Stress (psi)

Balsa 11 625 1725

Spruce 34 1500 8600

EPS Foam 1.5 320-360 72.5

EPP Foam 1.3 1000 4000

Epoxy 0.0625 lb/ft2 500 14500

Ultrakote 0.0156 lb/ft2 N/A N/A

Values from Fall ’04 AAE 451 projects and http://www.matweb.com

March 24, 2005 43[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Structural Geometry

Primarily EPP Foam Balsa fuselage structures

March 24, 2005 44[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Wing – Fuselage Attachment

March 24, 2005 45[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Fuselage Structure

Formers Outer Fuselage (each):

Three - 1” radius Main Fuselage:

Four - 2” radius

Stringers Outer Fuselage (each):

Seven – 1/8” x 1/8” x 36” One – 3/8” x 1/2” x 36” (for landing gear mounts)

Main Fuselage:Eight – 1/4” x 1/4” x 20”

March 24, 2005 46[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Tail Structure

Flat Plate Non-Lifting Surface No Volume Needed Ease of Construction 1/8” Balsa –

Lightweight EPP Foam Rudder

March 24, 2005 47[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Landing Gear

Wire mounting Rigid Lightweight Inexpensive Easy to construct

Interchangeable Smooth takeoff and

landing on AstroTurf®Pictures courtesy of http://www.dubro.com

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Location Front gear by canard Back gear by wing

Configuration Wire strut attached to

stringer in outer fuselage with mounting bracket

Interchangeable with wheels, skis, and floats attached to mounting blocks

Gear Configuration

Pictures courtesy of http://www.dubro.com

Fuselage Attachment Wheel/Ski/Float Attachment

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Weight Estimation

Weight (lbf)Wing 0.6460

Fuselages 0.4260Tail 0.1493

Canard 0.1190Landing Gear 0.0625

Motor 0.1250Batteries 0.1125

Servos 0.0675Rate Gyro 0.0573

Speed Controller 0.0469Receiver 0.0400

Propellers 0.0060Misc 0.1000

Total 1.9580

Tail 8%

Wing 35%Fuselages 23%

Propellers 0%

Receiver 2%

Rate Gyro 3%Speed

Controller 3%

Canard 6%

Landing Gear 3%

Motor 7%

Batteries 6% Servos 4%

March 24, 2005 50[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Cost Estimation

CostsMotor and Controller $134.00

Gyro $124.99Receiver $69.00

Servos $65.96Battery $29.90

EPP Foam $60.00Propellers $22.00Ultrakote $18.00

Balsa $15.00Landing Gear $15.00

Total $553.85(Team Cost) $130.00

(Purdue Cost) $423.85

Balsa12%

Landing Gear12%

Propellers17%

EPP Foam45%

Ultrakote14%

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V-n Diagram Level Flight

Turning Flight

Max Load Factor

Vdive ~ 50% higher than Vcruise

nmax=2.7778-g @ Vloiter = 25 ft/sec

22max stallVVn

W

SVCnL L

22

1

maxmax

SVCWL stallL2

21

max

Typical limit load factors for general aviation (npositive = 3.0-g, nnegative = -1.5-g)from Raymer, Daniel P., Aircraft Design: A Conceptual Approach p.407

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Wing Loading Analysis

Analysis Load Distribution and Maximum Wing

Loading Maximum Wing Root Bending Moment Maximum Torsional Moment Maximum Wing Tip Deflection Maximum Bending Stress

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Bending

Worst case simplification Cantilevered beam Negligible weight, outer fuselage mass/support Elliptical load distribution

March 24, 2005 54[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Twisting

Moment due to lift found from moment coefficient

212 mM C V S

March 24, 2005 55[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Constraints

Twisting: less than one degree of twist

Bending: bending stress less than EPP foam yield stress (w/ safety factor of 2)

ML

GI 21

2 mM C V S

My

I

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Analysis

Maximum wing load: 1.97 lbs of lift, elliptical loading, load

factor of 2.77 yields 5.45 lbs Maximum bending moment (at root):

3.623 ft-lbs

Maximum torsional moment (from Cm): 0.194 ft-lbs

March 24, 2005 57[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Results

Maximum wing stress: 361.80 psi

Maximum tip deflection: 0.16 in.

Maximum rotation: 0.13 degrees

March 24, 2005 58[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Moments and Products of Inertia

Balsa Components:

Volume = 86.51099 (+/- 0.00014) cubic inches

Volume Centroid = 4.025129,2e-007,1.06559 (+/- 8.6e-006,2.2e-006,1.2e-005)

Volume Moments:

Volume Moments of Inertia about World Coordinate Axes Ix: 3479.97 (+/- 0.0035) Iy: 9483.726 (+/- 0.014) Iz: 11292.75 (+/- 0.012)

Volume Moments of Inertia about Centroid Coordinate Axes Ix: 3381.738 (+/- 0.011) Iy: 7983.872 (+/- 0.045) Iz: 9891.13 (+/- 0.035)

Foam Components:

Volume = 1048.1777 (+/- 0.00012) cubic inches

Volume Centroid = 2.468645,1.1e-005,0.7137613 (+/- 3.5e-006,2.7e-006,2.4e-006)

Volume Moments:

Volume Moments of Inertia about World Coordinate Axes Ix: 222524.954 (+/- 0.0066) Iy: 98029.872 (+/- 0.043) Iz: 317314.68 (+/- 0.042)

Volume Moments of Inertia about Centroid Coordinate Axes Ix: 221990.954 (+/- 0.017) Iy: 91108.06 (+/- 0.11) Iz: 310926.87 (+/- 0.097)

Calculated from CAD Model Multiply by material density to determine

Mass MOI

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Propulsion Overview

Propeller Selection Component Trade Study Motor & Battery Selection

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Prandtl & Goldstein

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15Radial Thrust Distribution

dC

Td

x

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.02

0.04

0.06

0.08Radial Power Distribution

nondimensional radial location

dC

Pd

x

PrandtlGoldstein

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0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9Effect of Advance Ratio on Propeller Efficiency

Advance Ratio

Pro

pe

ller

Effi

cie

ncy

2 Blade3 Blade

Propeller Efficiency and Advance Ratio

Operation Range J = 0.35 - 0.45

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Thrust Coefficient and Advance Ratio

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.60

5

10

15

20

25Effect of Advance Ratio on Thrust Coefficient

Advance Ratio

Th

rust

[oz]

2 blades3 blades

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Propeller Efficiency and Advance Ratio

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9Effect of Advance Ratio on Propeller Efficiency

Advance Ratio

Pro

pe

ller

Effi

cie

ncy

2 Blade3 Blade

March 24, 2005 64[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Propeller Selection

2 Blades 8 in Diameter 5 in Pitch

Phase Flight Speed

[ft/s] Thrust [oz]

% Throttle *

Propeller Efficiency

Power [W] **

Take-off 18 3.15 50% 63% 10 Climb 18 4.00 55% 59% 14 Level Flight 22 2.93 51% 70% 10 Turn 23 3.24 54% 70% 12

Aerobatic 25 8.00 77% 59% 38 3 Blades 8 in Diameter 6 in Pitch Take-off 18 3.15 40% 65% 10

Climb 18 4.00 44% 61% 13 Level Flight 22 2.93 41% 72% 10 Turn 23 3.24 43% 69% 12

Aerobatic 25 16.00 83% 49% 92 * max motor RPM is 9350, direct drive ** power required from the battery (assumes75% motor efficiency)

March 24, 2005 65[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Component Trade Study• Graupner Speed 500 60% too powerful, unreliable data

• Each “Tier” represents a battery / motor combination

• More selection with Li & Brushless

• Connectors for brushed motors and Li batteries are not compatible. It would not be wise to have a Li & brushed combination.

• Our Aircraft needs to weigh less than 32 oz

Battery & Motor Weight vs Total Aircraft Weight

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 20 40 60 80 100 120

Total Aircraft Weight (oz)

Est

imat

ed C

om

po

nen

t W

eig

ht

(lb

)

Brushless & Li Brushed & Ni Brushed & Li

www.hobby-lobby.comwww.balsapr.com

Our Aircraft

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Thrust, Power, and Endurance

Δt

EP

E

)req(input)req(input

tNN

Preqinput

propmotor

reqoutput

..

..)(

mAhΔtVolts

WattsmAh hoursbrushless 300

Phase Time (s) Energy (ft-lb) Power (hp) Power (W) mAhTake-off 5 27 0.01 7.29 1.37Climb 5 36 0.01 9.72 1.82

Level Flight 445 2791 0.01 8.50 142.05Turn 445 3119 0.01 9.50 158.73Total 900 5973 N/A N/A 303.97

Brushless Nmotor=85%, Nprop=74%

Phase Speed Friction Coefficient Thrust Required (oz)Take Off N/A 0.3 2.4Take Off N/A 0.5 3

Climb 18 N/A 4Loiter 20 N/A 3Turn 20 N/A 3.2

Airspeed

Amps

“Sedate” Mission 15min

Airspeed

Amps

“Trainer” Mission 23min

March 24, 2005 67[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Motor & Battery Selection

ComponentsProp 2 Code• Calculates near 900mAh necessary to fly mission

• Fails to include component energy requirements

• Components need approximately 150mAh across our mission

• 1050mAh battery necessary

• Kokam 1200mAh battery chosen on grounds of weight & preferred vendors

Component Product Name Weight (oz) PriceMotor AXI 2212/20 2.00 $58.20

Speed Controller Jeti 18amp 0.32 $75.80Prop Graupner 2 Blade 0.10 $4.50Prop Graupner 3 Blade 0.14 $6.50

Battery Kokam 1200mAh 1.80 $29.90Total 4.22 $185.90

Brushless Motor Selection

March 24, 2005 68[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Unique Aspects of the Design

Twin Boom Design EPP Foam Robust Interchangeable Landing Gear Brushless Motor 3-Bladed Prop Alternative

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Remaining Design Problems

Updating SURFCAM Possible Wing Area Updates Landing Gear Position

March 24, 2005 70[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Constraint Diagram Revisited

Design Space

Current Design Point

Weight: 2.06 Lbf

Wing Area 5.30 ft2

Power: 0.06 hp

Wing Loading: 0.39 lbf/ft2

Power Loading: 34.33 lbf/hp

Desired Design Point

Takeoff

March 24, 2005 71[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Summary

Walk Around Aircraft 3-View Constraint Diagram Physical Properties Aerodynamics Dynamics & Controls Structures, Weights, & Landing Gear Propulsion Unique Aspects of the Design Constraint Diagram Revisited

March 24, 2005 72[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Questions?

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Appendix

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Turning Conditions

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L/D Mathematical Model

41

22

2

2

***

-

turn

LL

turn

rgCCS

WV

o

2

222 ***

2

1* turnL

turn

turnturn VCSg

r

VWL

* Raymer, Daniel P., Aircraft Design: A Conceptual Approach p.493

***

21

LL

straight

CCS

WV

o

March 24, 2005 76[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

L/DMAX

L/DMAX Velocity Loiter Straight:

VL/Dmax= 21.97 ft/s

Loiter Turn: VL/Dmax= 23.12 ft/s

Re=147,820

March 24, 2005 77[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Effect of Control Surface Deflection: Lift

ic c

cL c L

SC C

S

1 slipc

cc

Sx

S

c ic c

L LC a C

'L

c Theory

Theory c l

l Cb l

l l C

aC ka K C

C C a

Roskam,Jan, Airplane Design PartVI: Prelimenary Calculation of Aerodynamic, Thrust, and Power Characteristics, 2000

CTL ic cL L c L cC C i C

CTLo LLLL CCCC

*

March 24, 2005 78[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ][ 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 ]

Effect of Control Surface Deflection: Pitching Moment

ctl ic cM M c M cC C i C

ic cM L c cC C V

c

cc ac cg

SV x x

S

c ic c

M MC a C

Roskam,Jan, Airplane Design PartVI: Prelimenary Calculation of Aerodynamic, Thrust, and Power Characteristics, 2000

CTLorefx MMMM CCCC

*