Review of Basic Concepts The Vocabulary of Design Dr. Danielle Soban [email protected] Weber Bldg Room 306

Review of Basic ConceptsThe Vocabulary of Design

Dr. Danielle Soban

[email protected] Bldg Room 306

2Dr. Danielle Soban Fixed Wing Aircraft Design I

The Disciplines

Many disciplines need to be considered in the balanced design of an aircraft. People who specialize in these areas are called “disciplinarians”

Aerodynamics

Structures

Propulsion

Performance

Design

Stability and Control

This list is not comprehensive by any means. This are just the heavy hitters.

The Big Three


Airplane Components


Airplane Components

The whole tail assembly is called the “empennage”


Airplane Components


The Airplane in Motion

A set of mutually perpendicular axes are defined within the airplane, with their center being at the aircraft’s center of gravity, or c.g.

X

Y

ZNote: with Z pointing down, this is NOT a right-handed system.


Six Degrees of Freedom

The aircraft is considered as a rigid body with six degrees of freedom: three linear velocity components and three angular velocity components (pitch, roll, yaw).

Longitudinal Axis“Roll”

controlled by ailerons

Lateral Axis“Pitch”

controlled by elevator

Vertical Axis“Yaw”

controlled by rudder


Pilot Controls

Stick or Yoke

Foot Pedals

Left-Right Ailerons RollForward-Back Elevator Pitch

Left-Right Rudder Yaw


Elevators and Stabilators

The horizontal stabilizer is fixed to the aircraft and doesn’t move. The elevator is attached to the horizontal stabilizer and moves up and down. This causes the aircraft to pitch (the nose moves up and down around the lateral axis).

Sometimes, the elevator and the horizontal stabilizer are combined into one, called a stabilator. The whole stabilator moves, instead of just the elevator.

Chapter 1- Flight


Aircraft Notation

angle of attack flight path angle pitch angle

yaw angle sideslip angle (note sign change. This just by convention)

Ref: Shaufele


Aircraft Notation

φ

bank (roll) angle

Y

In a roll about the flight path, the angle between the Y axis and the horizontal is bank angle.This picture shows the aircraft nose pointed in the same direction as the flight path. This is not always the case.


The Four Forces of Flight

V

always in the direction of the local flight of the aircraft. Shows flow velocity relative to the airplane

This is RELATIVE WIND

L

W

perpendicular to by definition

V

always acts towards the center of the earth

T

D

parallel to by definition

V

not necessarily in the flight direction

Lift, Drag, Weight, Thrust Lift and Drag are for complete airplane


Some Speed Terms

Mach Number M =V

aa is speed of sound

Subsonic M < 0.8

Transonic 0.8 < M < 1.2

Supersonic M < 1.2

When M = 1, the velocity is the same as the speed of sound. In general, “supersonic” means M >1, but when an airplane is flying at exactly this speed, there could still be parts of it that are flying subsonically. So generally the superonic regime is defined as M > 1.2. This ensures the entire aircraft if flying at a speed greater than the speed of sound.


Only 2 Sources of Aerodynamic Force

A body immersed in an airflow will experience an Aerodynamic Force due to:

Pressure

S

p=p(s)

=(s)S

Shear Stress

acts perpendicular to the surface

acts parallel to the surface

Integrate around the surface of the bodyto get the total force:

R = S S

Sdk Sdn p

nk

dS


Aerodynamic Lift, Drag, and Moments

V

RL

D

“free stream velocity” or “relative wind”

(defined as parallel to V )

(defined as perpendicular to V )

(not perpendicular to V )

AERODYNAMIC FORCES MOMENTS

c

MMLE

c4

By convention, a moment which rotates a body causing an increase in angle of attack is positive.

L is LiftD is DragM is Moment


Bernoulli’s Principle

As air velocity increases, pressure decreases

Venturi Tube

V P V P

V P

Total Pressure = static pressure + dynamic pressure = constant


Bernoulli Applied to an Airfoil

WindHigher VelocityLower Pressure

Lower VelocityHigher Pressure

P

P

There is a decrease in pressure on the top of the airfoil


Two Types of Lift

Induced Lift: caused by pressure difference betweenupper and lower surface of airfoil, dueto camber. We know it as Bernoulli’slift.

Dynamic Lift:

Wind

Action

Reaction

From Newton’s 3rd Law:for every action there is anequal and opposite reaction

accounts for about 15% of lift


Creating Even More Lift

In general, there are four ways to create more lift

A larger wing will lift more weight(up to a point)

Increasing the camber of the airfoil will increase the lift

Increasing the speed of the wing will increase the lift


Increasing the Angle of Attack

Tilting the airfoil into the wind will increase the lift, up to a point.

Airfoil StallWhen the angle of attack gets too high, the flow doesn’t have enough energy to follow the curve. It “separates” from the airfoil, causing loss of lift, turbulence, and drag.

Wind

angle of attack

loss of lift


Flaps-What do they do?

Flaps are moveable surfaces at the trailing edge of the wing. When these surfaces are moved, it increases the camber of the wing, which increases the lift.

By increasing the lift of aircraft with the flaps, the aircraft can fly slower and still maintain flight. Flaps are especially useful for takeoff and landing.

Finally, flaps increase drag. They act like big doors that open into the airstream. This will also make the aircraft fly slower.

Flap

Chapter 1- Flight


Aerodynamic Coefficients

From intuition and basic knowledge, we know:

aerodynamic force = f (velocity, density, size of body, angle of attack, viscosity, compressibility)

L = L(, V , S, , , a )

D = D(, V , S, , , a )

M = M(, V , S, , , a )

To find out how the lift on a given body varies with the parameters, we could run a series of wind tunnel tests in which the velocity, say, is varied and everything else stays the same. From this we could extract the change in lift due to change in velocity. If we did this for each parameter, and each force (moment), we would have to conduct experiments that resulted in 19 stacks of data (one for each variation plus a baseline).

This is bad: wind tunnel time is very expensive and the whole process is time consuming.



Instead, let’s define lift, drag, and moment coefficients for a given body:

CL =L

q SCD =

Dq S

CM =M

q Sc

and q is defined as the dynamic pressure:

q = V 212

c is defined as a characteristic length of a body, usually the chord length

Now define the following similarity parameters:

Re = V c

Reynold’s Number(based on chord length)

M =V a

Mach Number



Using dimensional analysis, we get the following results. For a given body shape:

CL = f1( , Re, M )

CD = f2( , Re, M )

CM = f3( , Re, M )

If we conduct the same experiments, we can now get the equivalent data with 10 stacks of data.

But more fundamentally, dimensional analysis tells us that, if the Reynold’s Number and the Mach Number are the same for two different flows (different density, velocity, viscosity, speed of sound), the lift coefficient will be the same, given two geometrically similar bodies at the same angle of attack.

This is the driving principle behind wind tunnels.

But…be careful. In real life, it is very difficult to match both Re and M.

7


Side Force CoefficientsYou may have noticed by now that we have only talked about forces and moments in two of the three axes. These are the ones usually used in analysis. However, once you start getting into stability and control characteristics, the side force coefficients become extremely important. Motion about the Z-axis and Y-axis is symmetrical. When we have motion about the X-axis, we have asymmetrical flight.

Side Force =Cy Sq

Yawing Moment =Cn Sb

q

Rolling Moment =Cl Sb

q

Note: moments for asymmetrical flight is based on b (wingspan) instead of c (chord)


Reference Area, S

S is some sort of reference area used to calculate the aerodynamic coefficients.

S as wetted area - not common, but is the surface upon which the pressure and shear distributions act, so it is a meaningful geometric quantity when discussing aerodynamic force.

S as planform area - the projected area we see when looking down at the wing or aircraft (the “shadow”). Most common definition of S used when calculating aerodynamic coefficients.

S as base area - mostly used when analyzing slender bodies, such as missiles.

The Point: it is crucial to know how S was defined when you look at or use technical data!

8


Airfoil Nomenclature

Mean Camber Line

Camber

chord, c

Leading Edge

Trailing EdgeThickness


Center of Pressure

Question: At what point on the body do the lift and drag (or R) act?

Answer: The forces act at the centroid of the distributed load, called the

center of pressureL

D

c.p.

NO moment!

L

D

M c4

c4

= =

Same force, but move it to the quarter chord and add a moment

L

MD

LE

Same force, but now it’s at the leading edge, along with a moment about the leading edge

Question: So why don’t we use center of pressure as reference point in aircraft dynamics?

Answer: Because c.p. shifts when angle of attack is changed. Use quarter chord.


Aerodynamic Center

Aerodynamic Center - point about which moments are independent of angle of attack

L

M c/4

a.c

xacc/4

xac

c=

d cmc/4

d

d cl

d

= -m0

a0


Lift Curve

cl or

CL

(angle of attack in degrees or radians)

clmax or CLmax

Lift curve slope(usually linear)

When you are only looking at the airfoil, you use lower case cl. This implies a 2 dimensional analysis.

If you use capital CL (or CD, CM, etc) you are implying that you are looking at the whole aircraft using a three dimensional analysis.

The shape of the lift curve slope is the same for both. Be sure you understand what you are looking at.



Example Airfoil Data-NACA 2415

Note: this is just airfoil drag, not the drag of the whole airplane


Subsonic Drag-Airfoils

Section drag, also called profile drag, is what you see in typical airfoil cl vs cd data, like the NACA airfoil data.

cd = cf + cd,p

profile drag = skin-friction + pressure drag

drag due to separation

Skin friction drag due to frictional shear stress acting on the surface of the airfoil

55

Pressure drag due to flow separation caused by the imbalance of the pressure distribution in the drag direction when the boundary layer separates from the surface

(form drag)


Subsonic Drag-Finite Wings

Now we need to add in induced drag, which is a form of pressure drag.

For a high aspect ratio straight wing, use Prandtl’s Lifting Line Theory to get:

CDi =CL

2

e AR

CDi = Di

qS

e is efficiency factor

0 < e < 1 function of aspect ratio and taper

Realize that induced drag and lift are caused by the same mechanism: change in pressure distribution between top and bottom surfaces.

So, it makes sense that CDi and CL are strongly coupled.

Induced drag is the “cost” of lift.

58

Induced Drag


Finite Wing Geometry

Wingspan, b

Planform area, Sct

cr

Aspect Ratio is defined as

AR = b2

S


Wing Tip Vortices and Downwash

Question: Is the lift coefficient of the finite wing the same as that of the airfoil sections distributed along the span of the wing?

Answer: NO, due to the downwash of a finite wing. Lift will be less.

Front View of Wing

High Pressure

Low Pressure

V

Wing Tip Vortices

33


Summary of Subsonic Drag

skin friction drag - due to frictional shear stress over the surface

pressure drag due to flow separation (form drag) - due to pressure imbalance caused by flow separation

profile drag (section drag) - sum of skin friction drag and form drag

interference drag - additional pressure drag that is caused when two surfaces (components) meet.

parasite drag - term used for the profile drag of the complete aircraft, including interference drag.

induced drag - pressure drag caused by the creation of wing tip vortices (induced lift) of finite wings

zero-lift drag - parasite drag of complete aircraft that exists at its zero-lift angle of attack

drag due to lift - total aircraft drag minus zero lift drag. It measures the change in parasite drag as changes from L=0


Area Rule

66

To reduce transonic drag, area rule the fuselage


Supersonic Drag

Shock waves are the dominant feature of the flow field around an aircraft at supersonic speeds.

Wave drag caused by pressure pattern around aircraft, so it is a pressure drag.


Swept Wings

Purpose of using a swept wing is to reduce wave drag at transonic and supersonicspeeds

V

V

u

wV

uw

V== 0

Here, u = V cos Since u for swept wing is less than u for straight wing, the difference in pressure between top and bottom surfaces of the swept wing will be less than the difference in pressures on the straight wing. Result: swept wing has less lift.


Supersonic Swept Wings

Compare:

M M

Wing is inside Mach cone. Component of M perpendicular to leading edge is subsonicsubsonic leading edge

Weak shock at apex, NO shock on leading edge

Behaves as subsonic wing even though M >1

Wing leading edge is outside of Mach conesupersonic leading edge

Shock wave attached along entire leading edge

Behaves as supersonic flat plate at angle of attack

Mach Angle: =arcsin (1/M)Leading Edge Sweep:


The Drag Polar

We now focus on the drag of the complete aircraft, which is presented in the form of a drag polar

Drag Breakdown

74


The Drag Polar

For every aerodynamic body, there exists a relationship between CL and CD. This relationship can be expressed as either an equation or a graph. Both are called “drag polar”.

Virtually all information necessary for a performance analysis is contained in the drag polar.

Total Drag = parasite drag + wave drag + induced drag

CD = CD,e + CD,w + CL2

e AR

78

If you break each term down into its components, and gather up terms that are caused by the same phenomena, you can rewrite this equation in classic Drag Polar form.


Drag Polar

CD = CD,0 + K CL2

CD

CD,0

K CL2

total drag coefficient

zero lift parasite drag coefficient or “zero lift drag coefficient”

drag due to lift

Equation is valid for both subsonic and supersonic

At supersonic, CD,0 contains wave drag at zero lift, friction drag, form drag.The value for wave drag due to lift is part of K

CL

CD

K CL2CD,0

zero lift dragcoefficient

drag polar


Graphic Drag Polar

CL

CD

0

The slope of the line from the origin to any point on the drag polar is the L/D at that point. It will have a corresponding .

A line drawn from the origin tangent to the drag polar identifies the (L/D)max of the aircraft.

Sometimes called the “design point”Corresponding CL is called “design lift coefficient”

Note (L/D)max does NOT occur at point of minimum drag


General Drag Polar Notes

Note how drag polar shifts as Mach number changes


The Propeller

Like a wing, a propeller produces friction drag, form drag, induced drag, and wave drag. Thus, it is a loss mechanism and the power output of the engine/propeller combination will always be less than the shaft power.

Reciprocating Engine

Shaft Power

PPA

PA P

Propeller efficiency is defined as:

PA = Ppr pr 1

Realize, like Wilbur Wright did in 1902, that a propeller is nothing more than a twisted wing.

Hub

Root

Leading EdgeTrailing Edge

Tip


Propulsive Efficiency and Engines

Propeller provides large m but small Vj - V so has high efficiency

Gas turbine jet engines gives a smaller mass of air a larger increasein velocity, but at a lesser efficiency.

Q: so why don’t we use propellers on faster aircraft?

Turbofans try to combine the thrust generating capabilities of the jet engine with the efficiency of a propeller. Similarly, the turboproptries to achieve the same.

A: as speed increases, the tip speed increases. At high enough speeds, shock waves will form. This increases drag, which increases the torque on the reciprocating engine, which reduces the rotational speed (rpm) of the engine, which reduces power obtrained from the engine, which reduces thrust. Also, shock waves on the propeller airfoils increase drag, reducting thrust.

speed

low

high


Turbojet Engine

Diffuser- slows the air, with increase in pressure and temperature

Compressor- work is done on the air by the rotating compressor blades, greatly increasing pressure and temperature

Burner (combustor)- air is mixed with fuel and burned at essentially constant pressure

Turbine- burned air-fuel mixture then expands through a turbine, which extracts work from the gas. The turbine is connected to the compressor by a shaft, and the work extracted by the turbine is thus used to operate the compressor.

Nozzle- the gas expands through a nozzle an is exhausted into the air with velocity Vj.


Generation of Thrust

The thrust generated by the engine is due to the net resultant of the pressure andshear stress distributions acting on the exposed surface areas, external and internal


Example of a Turbojet


Turbofan Engine

Strives to combine the high thrust of a turbojet with the high efficiency of a propeller

Core of turbofan is a turbojet. However, the turbine drives not only the compressor but a large external fan.

Most jet-propelled airplanes today are powered by turbofans.

flow here takes advantage of the propeller

flow here generates high thrust


Bypass Ratio

Bypass ratio =mass flow through the fan

mass flow through the core

The higher the bypass ratio, the higher the propulsive efficiency

Typical bypass ratios are on the order of 5.

Typical values of TSFC are 0.6 lbhp h

(almost half of a conventional turbojet)


Turboprop

A turboprop is a propeller driven by a gas turbine engine

The turbine powers both the compressor and the propeller

Most available work is extracted by the turbines, leaving little available for jetthrust. Only ~5% of total thrust is through jet exhaust.


Specific Fuel Consumption

SFC - How efficiently the engine is burning fuel and converting it to power

c = weight of fuel burned per unit power per unit time

= weight of fuel consumed for given time increment(power output)(time increment)

Units:

[c] = lb or [c] = N

(ft lb)/s)(s) W s

Often, however, you will see:

[SFC] = lbhp h

Note: for calculations, if given data inSFC, you must convert to c.

Specific fuel consumption is a technical merit for an engine, similar to L/D or T/W


Some References

S.F. Hoerner, Fluid Dynamic Drag, Hoerner Fluid Dynamics, Brick Town, NJ 1965

S.F. Hoerner and H.V. Borst, Fluid Dynamic Lift, Hoerner Fluid Dynamics, Brick Town, NJ 1975

Ira H. Abbott and Albert E. Von Doenhoff, Theory of Wing Sections, McGraw-Hill, New York, 1991.

John D. Anderson, Jr. Introduction to Flight, 3rd Edition, McGraw-Hill, New York, 1989

John D. Anderson, Jr. Fundamentals of Aerodynamics, 2nd Edition, McGraw-Hill, New York, 1991

Joseph Katz and Allen Plotkin, Low-Speed Aerodynamics, McGraw-Hill, New York, 1991

Deitrich Kuchemann, The Aerodynamic Design of Aircraft, Pergamon Press, Oxford, 1978

Daniel P. Raymer, Aircraft Design: A Conceptual Approach, 2nd Edition, AIAA Education Series, American Institute of Aeronautics and Astronautics, Washinton, 1992.


Some References

Schaufele, Roger D. The Elements of Aircraft Preliminary Design, Aries Publication, 2000.

Stinton, Darrol, The Design of the Aeroplane, BSP Professional Books, 1983.

Mattingly, Jack D., Heiser, William H., Daley Daniel H., Aircraft Engine Design, AIAA Education Series, 2000.

Torenbeek, Egbert, Synthesis of Subsonic Airplane Design, Delft University Press, 1982.

Documents

Review of Basic Concepts The Vocabulary of Design Dr. Danielle Soban [email protected] Weber Bldg Room 306