# What two types of forces contribute to the lift on a wing?

FZ+
If this is a trick question on fundamental forces, then are we saying EM and gravity?

Random guess...

i'm sure by now someone has got it. we just need to wait for greg to catch up.

Matt
Yeah, Greg or Enigma - I think Enigma came up with the question.

enigma
Staff Emeritus
Gold Member
I guess I can answer it now.

You're going to kick yourself.

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Air friction is the other contributor.

Like I mentioned above, Newton's laws are the way to tally up the Lift on the wing (airfoil, airplane, etc.) by measuring deflection of the air (or other more complicated methods), but they don't provide the fundamental forces. The information of the underlying cause is swept under the rug.

Similarly, the formula for lift L = CL*q[oo]*S doesn't provide the fundamental forces either. All the force information is bundled up into the experimentally obtained value for CL for a specifically shaped airfoil.

The only types of forces which cause interaction between two human sized objects except for electrical/magnetic or gravitational interactions are friction and pressure. Even point loads are simply approximations to a large pressure distributed over a small area. This holds true also for airplanes, only the friction is very small under normal circumstances.

Drawing from "Fundamentals of Aerodynamics, third ed." by John D. Anderson, Jr. (Chapter 1.5 Aerodynamic Forces and Moments)

Definitions:

L = lift = component of the resultant force (R) perpendicular to the freestream velocity (V[oo])
D = drag = comp. of R parallel to V[oo]

N = normal force = comp. of R perpendicular to the chord
A = axial force = comp. of R parallel to the chord

' - value per unit span
[the] = difference in angle between chord and the surface of the airfoil (clockwise positive)
p = pressure
[tau] = shear due to friction
[alpha] = angle of attack
TE = trailing edge

pressure always acts perpendicular to the surface, and shear due to friction always acts opposite the direction of motion of the wing (so, to the back of the wing)

Going over the top surface of the wing, looking at a differentially small portion of the surface, the normal and axial forces per unit span are:

dNu' = -pu*dsu*cos[the] - [tau]u*dsu*sin[the]

dAu' = -pu*dsu*sin[the] + [tau]u*dsu*cos[the]

Similarly, on the lower surface:

dNl' = pl*dsl*cos[the] - [tau]l*dsl*sin[the]

dAl' = pl*dsl*sin[the] + [tau]l*dsl*cos[the]

Putting it all together and integrating,

N' = - [inte] {LE,TE}: (pu*cos[the] + [tau]u*sin[the])*dsu + [inte] {LE,TE}: (pl*cos[the] - [tau]l*sin[the])*dsl
A' = [inte] {LE,TE}: (-pu*sin[the] + [tau]u*cos[the])*dsu + [inte] {LE,TE}: (pl*sin[the] + [tau]l*cos[the])*dsl

From there, lift and drag can be obtained by taking the angle of attack into account:

L = N*cos[alpha]-A*sin[alpha]
D = N*sin[alpha]-A*cos[alpha]

Like I said above, friction's contribution to lift can be safely disregarded in many situations, since [alpha] & [the] are both typically small, and |[tau]| is usually << |p|, but there are situations where neglecting the friction can cause values to be off by 10% or more. An example of this would be supersonic or hypersonic flows about non-symmetric airfoils (or airfoils at non-zero AoA) where the friction is a significant fraction of the pressure.

EDIT: Fixing sub/sub
EDIT2: Fixing a - sign

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Matt
Owww! Just head-butted the monitor - too hard to kick myself.