Calculating Wing pitching moment/torsion using Cm?


Well-Known Member
Dec 31, 2009
Barcelona, Spain.
Hi everyone!

I am trying to understand how to compute the different loads over the wing? Intuitively my force diagram would include Lift, Drag at the center of pressure, and Moments around the quarter chord. The most straightforward way, to compute moments around the aerodynamic center, would be that of using the formula: M = 1/2*p*v^2*S*Cm*C, and pick the CM value from TOWS, XFLR5...

However I am a bit surprised, that some reference authors do not use Cm, or moments around the 1/4 chord at all, in their force diagrams.

It is assumed that the maximum loads happens at maximum Cl on a pull out. However, the maximum pitching moment (I understand this to be the maximum possible torsion on the wing, too), is originated at maximum speed/in a dive.

Given that at maximum speed, the center of pressure shifts to half of the wing mean aerodynamic chord. Peery and Azar in their Aircraft Structures book, take moments around the center of gravity located at 1/3 chord, and the center of pressure at half chord; they do not consider moments around the aerodynamic center.

Frati, in his glider design book, calculates the loads on a two spar aircraft wing, by distributing the loads of the center of pressure in between those; ignoring too completely moments around the 1/4 chord.

Heintz is very confusing, because he uses a diagram picturing lift, drag and moments, all located at 1/4 chord.

Given the examples above, am I wrong by drawing a force diagram, with the resultant lift and drag at the center of pressure, weight at 1/3 chord and moments at 1/4 chord?
Is it perhaps that by taking moments from the resultant lifting force, is like taking moments from the aerodynamic center, so that both methods are equivalent?

Sorry if this has been covered before, or if it is a silly question but I am lost here.