Aerodynamic Forces (Lift)

Question 1

Define the following (of a wing):

• Chord line
• Mean camber line
• Camber
• Thickness
• Leading edge radius

Answer 1

• Line joining leading and trailing edge
• Line equidistant from upper/lower surface of the wing
• Thickness between MCL & chord line
• Distance between upper and lower surface
• Radius of the curvature of the leading edge

Question 2

Describe the meaning of the 1st, 2nd & 3rd/4th digits in the NACA system

Answer 2

1st digit: Max camber as a percentage of the chord
2nd digit: Location of max camber from the LE as a 10th percentage of the chord
3rd/4th digit: Max thickness of the aerofoil as a percentage of the chord

Question 3

What is the trend for the NACA system for symmetrical aerofoils?

Answer 3

The first two digits are 0 as the MCL=chord so you are unable to determine the location of the max thickness

Question 4

Draw the pressure envelopes of -4* AoA through to 20* AoA & the forces of an aerofoil

Answer 4

Refer to notes for diagrams

Question 5

What is the pressure coefficient equal to (Cp)?

What is Cp?

Answer 5

Cp= (P-Pfs)/q
P: local pressure
PNS: freestream static pressure
Q: dynamic pressure
A dimensionless quantity measuring ratio of local pressure and freestream pressure to dynamic pressure

Question 6

What is the line of zero lift?

Answer 6

The edgewise straight line through the aerofoil, parallel to the airflow, when the aerofoil points downwards and produces no lift.
Does NOT mean no moment.
Will occur on cambered aerofoils

Question 7

What are the 3 possible components to airflow over an aerofoil?

Answer 7

Chordwise
Spanwise
Vertical

Question 8

Describe an infinite aerofoil

Answer 8

Only has flow in 2 dimensions… chordwise and vertical.
Has no wingtip (elliptical) or is infinitely long. This is as these limit development of spanwise flow.
A high AR wing is considered infinite.
Are considered “idealised” wings.

Question 9

Describe a finite aerofoil

Answer 9

Has airflow in all 3 dimensions.
Is a wing with a limited wingspan or with a wingtip.
Are considered “real” wings.

Question 10

Explain how Bernoulli’s theorem explains the production of lift.
Include any limitations

Answer 10

Ps+Pd=Pt
Airflow in streamline speeds up over the wing and reduces below.
As a result pressure reduces above the wing increases below the wing and a/c is sucked up into this region of low pressure.
Limitations include:
-only considers 1 dimension (chordwise)
—>no vertical as any elevation is insignificant compared to the size of the a/c… so assumes level flow and no spanwise flow
-all limitations of benoullis theorem discussed earlier
-no boundary layer seperation
-unable to explain up/downwash

Question 11

Explain how Newton’s theorem (momentum/impulse) explains the production of lift.
Include any limitations

Answer 11

It states the net force on an object is equal to the rate of change of momentum and utilises Newton’s 3rd law (equal/opposite).
Horizontal air velocity is equal before/after aerofoil so there is no overall momentum change so therefore no horizontal force component on the airstream.
There is a change of momentum in the vertical plane, as the vertical component, w, changes direction by 180* because of up/down wash (but assumed magnitude remains equal). So Ft=mv can be rewritten as Ft=-2mw (think of ball against wall example). So impulse is x2 momentum in vertical direction… the - means the direction of the force is downwards. If Newton’s 3rd is applied, the reaction force of the airflow gives to the aerofoil (upward) = the force the aerofoil produced by deflecting the airflow downward.
Refer to notes for variables of equations explained.
Limitations include:
-2D flow (does not explain spanwise flow)
-Flow must be non viscous
-Flow must not seperate

-However compared to Bernoulli’s theorem it recognises up/downwash as contributing to lift production.

Question 12

Do we need to know about Euler’s & Navier Stokes equation?

Answer 12

Nooooooooope.

Just that it explains 3D flow and requires supercomputers to solve partial differential equations.

Question 13

Explain the how there is a circulation in the circulation theory of lift

Answer 13

It can be assumed the freestream air velocity is horizontal and uniform and that an object travels at a constant speed.
So… (refer to notes for the labels for each bullet point)
-upwash is the Vfs+small vertical velocity
-local air velocity above the aerofoil is Vfs+small horizontal velocity
-downwash is the Vfs-small vertical velocity
-local air velocity below the aerofoil is Vfs-small horizontal velocity
So if we superimpose the 2 air flows (uniform horizontal airflow where V=Vfs and the circulation) we get the streamlined flow of air over an aerofoil (refer notes for diagram)

Question 14

List the assumptions with the circulation theory of lift

Answer 14

• object travels at a constant speed
• MUST be of a thin & symmetrical infinite aerofoil
• air particles leave the TE evenly (uniform) downward
• does not account for boundary layer separation
• does not account for friction
• must apply a superposition
• 2D flow of air only (no spanwise)

Question 15

What is the equation for circulation?

Do the air particles rotate?

Answer 15

C= V x path C=m^2s^-1. But in exam use the funny symbol one which you will need to refer to notes for. Note C has a unique symbol.

No, although there is a circulation in the airstream the air particles are irrotational (do not rotate).

Question 16

Explain how the Kuta Joukowski theorem links to the circulation theory of lift

Answer 16

The theorem states “force per unit length acting at right angles to the airstream is equal to the product of the air density, air velocity and circulation (F=CpV in Nm-1)”
Lift per wingspan L=pVC
Induced drag per wingspan D=pwC

Question 17

What does each finger represent in the RH rule when applying KJ theorem?

Answer 17

Thumb: direction of force
Index: direction of airspeed/velocity
Middle: direction of circulation… find this but curling fingers in direction of circulation on RH & thumb is the direction of circulation

Question 18

Which way does the force act on the airflow “over” the aerofoil?
What about on a basketball that has been shot?

Answer 18

Upward

Upward

Question 19

What is the diameter of circulation assumed to be?
What equation do we get as a result?
How can this be used to derive L=pvw x Pi x S ?

Answer 19

Diameter approximates chord… then downwash is proportional to circulation
So C=w x Pi x C (w velocity and circulation/circumference is piC)

kJ states F=L=CpV
If C=wc x Pi 
L=pV x wcPi ... across wingspan b
L=Cl x 0.5pv^2 x S= pVw x Pi x S
Where c is chord & C is circulation

Question 20

What is Cl and CD equal too? What are they approximate to? (inc AoA).
How are the two proportional?

Answer 20

Cl= (2 x Pi x w)/V = 2 x Pi x AoA. So Cl prop AoA
CD= (2 x Pi x w^2)/V^2 = 2 x Pi x AoA^2
Where AoA is in RADIANS and is approximates w/v when AoA is small on a thin symmetrical aerofoil. This is explained in pencil in notes how this is achieved.

CD prop Cl^2/Pi

Question 21

What equations of KJ theorem allow for wing geometry (camber/AR etc)?

Answer 21

Cl= K x Pi (AoA0 + AoA) or Cl0 + 2K Pi AoA
Where AoA(0) is a zero lift AoA
Cl0 is Cl at 0 AoA
K(l) is related to aerofoil features (Thickness)

Question 22

What is the Cd due to downwash?

Answer 22

K x (Cl^2)/piAR      OR
Cl^2/piARe
Where k/e is a constant due to wing efficiency

Question 23

Does a symmetrical aerofoil have Cl?

Answer 23

Yes, but not at 0* AoA