# Wing pitching moment ( torque not around cg ) - head hurts

1. Jun 22, 2013

### chipmeisterc

Wing pitching moment ( torque not around cg ) - head hurts!!

Hi all! :)

First post! I am currently coding up a basic flight simulator for fun. It is all going well so far - and certainly improving my rusty physics knowledge. I break the wing down into elements calculate the lift and drag on those elements apply the forces and watch the plane fly - which it does pretty well.

The integration is done by a physics engine so I can use AddForce AddForceAtPosition (which will cause a torque also if not at cg ) or AddTorque

This is great because using AddForceAtPosition all of my lift and drag forces then naturally generate the correct pitch/roll/yaw torques about the cg etc.

This means I have been blissfully ignorant about torques directly up until this point (other than having to use the torque in working out relative wind for angle of attack )..

What is hurting my head however is that a wing doesn't just produce lift and drag, but it also has a pitching torque/moment about it's aerodynamic center.

My question is how do I take this torque and apply it to my aircraft - AddTorque only cares about a vector where xyz is the axis of rotation and the magnitude is the force.. (so it is assuming torque around cg) applying the aerodynamic center torque around the cg is clearly not correct... I guess it should be a combination of a torque and a linear force which takes me back to AddForceAtPosition - but what and where this force is I have no idea how to calculate:

Here is a diagram:

Edit my cp label should actually read ac or aerodynamic center.
The purple arrow shows rotation for pitching moment - so how do I take this conceptual torque around ac and convert it into a form that can be actually applied to my rigid body around its cg.

Edit 2 : cg could be anywhere fore or aft of it's current position depending on weight distribution it is not necessarily inline with the ac as it appears in that diagram.

Edit3 : That lift vector was supposed to look 3d - even if it was 3d i think it still looks wrong :)

Thankyou :)

I look forward to hearing from you!

Last edited: Jun 22, 2013
2. Jun 22, 2013

### Filip Larsen

Assuming you are using Unity (which I don't myself), then I believe the AddTorque takes just the torque expressed as a vector, meaning you should just provide the torque you have since a pure torque around one axis is equal to the same pure torque around another axis.

3. Jun 22, 2013

### chipmeisterc

Hi Filip,
Thanks for taking the time to reply!
Will there not be a translation from pitching moment being offset from the cg then? i.e will the plane not pitch around this point rather than around the cg?

Edit - I have just done a bit more reading and I realise torque and moment aren't entirely interchangeable terms - it sounds like torque is 'independant of reference point' whilst moments are not.

So my question is - is this wing pitching moment, independant of reference point? Or do I need to do some maths to convert it so that I can find what the torque would be about my cg reference point instead?

Last edited: Jun 22, 2013
4. Jun 22, 2013

### Filip Larsen

Pitching moment is a torque and you do not need to transform it to apply it to a particular point of reference, like the CM.

You can either model the lift on your wing segment as a single force without torque acting at the center of pressure, CP (which, by definition, is the point where there is no pitching moment from the lifting force) and keeping in mind that the position of the CP depends on airspeed and wing geometry, or you can transform this force to another (likely more fixed) reference point like CM as a lift force and pitching moment.

For the code you mention in your first post, it means you either have to use AddForceAtPosition for the CP position, or translate the force to another reference point and then use AddForceAtPosition for that position together with an AddTorque for the torque around this position. Both approaches should give same result of course, its just a matter if you want to calculate the position of the CP as function of airspeed and other state or you want to calculate pitching moment. In textbooks on aerodynamics you often find the pitching moment approach because you can then separate the dynamics into translation and rotation which is easier if you have to analyze the involved equations. In a numerical context, where you want to integrate both translation and rotation at the same time anyway, it doesn't matter quite as much which approach you use.

5. Jun 22, 2013

### chipmeisterc

Thanks Filip! :) Appreciate you taking the time to explain all this - I think I am slowly getting there :)

I already have the lift and drag working, the aircraft flies along quite nicely using just lift and drag from the aerodynamic center but I want to include the pitching moment properly!

and all i need to do is calculate the pitching moment and use AddTorque to my rigidbody to apply it, because reference frame does not matter..

Alternatively I can presumably calculate the CP from the AC using the pitching moment somehow? And then AddForceAtPosition(liftFromCP) here instead??

In the second scenario would the drag also act from CP or still from AC?? I think I will stick with just adding torque to my rigid body if that will do the job :)

6. Jun 22, 2013

### Filip Larsen

Correct. When you choose the AC as your (fixed) reference point you have the benefit that the pitching moment stays constant when the lift changes; for any other fixed reference point you would have to recalculate the pitching moment as a function of lift. As you describe your setup, I don't see any need for you to move your lift reference point to the CP or the CM instead of the AC.

By the way, I'm not sure it makes much sense to let drag act through the AC. Calculation of total drag for a particular airplane in a particular configuration is, as far as I know, usually based on some fixed reference point. If you want to calculate this per wing (lifting) and body (non-lifting) section, I suggest that you apply lift at the AC (for wing sections), drag at the CM (for all sections), and then add one or more torques depending of nature of the section.

In principle, if you model your sections small enough you could replace many of the "variable contributions" to the pitching, rolling and yawing moment as small forces located at particular points, e.g. at the ailerons, flaps, rudder, elevator, gear, engine, and so on. However, if you try to establish model data from existing airplanes, I believe it will be harder this way as most such data that I know of is formulated as contributions to the moments of the airplane as a whole.

Oh, and in my first reply I forgot to say: Welcome to PF, chipmeisterc!