Aerodynamic Forces (Lift) Flashcards
Define the following (of a wing):
- Chord line
- Mean camber line
- Camber
- Thickness
- Leading edge radius
- 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
Describe the meaning of the 1st, 2nd & 3rd/4th digits in the NACA system
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
What is the trend for the NACA system for symmetrical aerofoils?
The first two digits are 0 as the MCL=chord so you are unable to determine the location of the max thickness
Draw the pressure envelopes of -4* AoA through to 20* AoA & the forces of an aerofoil
Refer to notes for diagrams
What is the pressure coefficient equal to (Cp)?
What is Cp?
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
What is the line of zero lift?
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
What are the 3 possible components to airflow over an aerofoil?
Chordwise
Spanwise
Vertical
Describe an infinite aerofoil
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.
Describe a finite aerofoil
Has airflow in all 3 dimensions.
Is a wing with a limited wingspan or with a wingtip.
Are considered “real” wings.
Explain how Bernoulli’s theorem explains the production of lift.
Include any limitations
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
Explain how Newton’s theorem (momentum/impulse) explains the production of lift.
Include any limitations
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.
Do we need to know about Euler’s & Navier Stokes equation?
Nooooooooope.
Just that it explains 3D flow and requires supercomputers to solve partial differential equations.
Explain the how there is a circulation in the circulation theory of lift
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)
List the assumptions with the circulation theory of lift
- 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)
What is the equation for circulation?
Do the air particles rotate?
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).
Explain how the Kuta Joukowski theorem links to the circulation theory of lift
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
What does each finger represent in the RH rule when applying KJ theorem?
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
Which way does the force act on the airflow “over” the aerofoil?
What about on a basketball that has been shot?
Upward
Upward
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 ?
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
What is Cl and CD equal too? What are they approximate to? (inc AoA).
How are the two proportional?
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
What equations of KJ theorem allow for wing geometry (camber/AR etc)?
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)
What is the Cd due to downwash?
K x (Cl^2)/piAR OR Cl^2/piARe Where k/e is a constant due to wing efficiency
Does a symmetrical aerofoil have Cl?
Yes, but not at 0* AoA
