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Inertia tensors, flight simulation

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Ok, say I am creating a linear model, (i dont have any L D M curves) and I know the following components of my tensor.. I_xx, I_yy, I_zz, and I_xz, how do I compute the other five tensor elements from this information? For instance, in the UIUC aircraft models, they state these four tensor elements in the aircraft configuration files along with the mass of the aircraft etc., but they dont have any of the other tensors. How is it you can develop a linear flight model by A] using the limited information above to somehow calculate the entire inertia tensor matrix as in the UIUC models? or.. B] not knowing all the masses, sizes, etc. of the aircraft parts to properly calculate the COM and inertia tensors Can someone please give me a little explanation? Its driving me nuts!!

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The inertia tensor is:

[Ixx Ixy Ixz]
|Iyx Iyy Iyz|
[Izx Izy Izz]

The inertia tensor is actually a symmetric tensor, which means there are only 6 independent terms. For example, Ixy = Iyx. So you can really simplify the tensor to:

[Ixx Ixy Ixz]
|Ixy Iyy Izy|
[Ixz Izy Izz]

Note the terms are Ixx, Iyy, Izz, Ixy, Ixz, and Izy

These 6 terms are all independent, and you cannot derive the unknowns from the 4 you are given. HOWEVER, you can use what you know about the geometry of the typical aircraft. The typical airplane is symmetric left-to-right (along the y axis), with identical mass distribution on either side. So any component of the tensor involving y and something else will be zero. This means Ixy and Izy are zero. You are only left with only Ixx, Iyy, Izz, and Ixz (exactly what the UIUC models provide) being nonzero.

If you have a bizarro aircraft, such as Burt Rutan''s asymmetric design that has the cabin one one side of center and the engine on the other side of center, then Ixy and Izy are not zero. You must either be given these or calculate them from known information about the distribution of mass.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

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Thanks for the responses, they really helped.

Hey, penetrator, your site is pretty cool, it has some good information.

Now, i have to ask you a few questions about it. I notice you said you upgraded to a dynamic coefficient flight model, first I want to say I wish I could test out your sim, but I dont have XP or 2k, argg!

Anyhow, when you do your force calculations for ailerons, elevator and rudder input, do you simply add to the lift coefficient with some specified force as in the linear model, or do you have coefficients specifically for wing/rudder/elevator input changing the lift characteristics of the wing creating a lift imbalance and thus a roll/yaw/pitch? Now being as such, would this not require a complete set of coefficient data including

1]data for main wing, mid, and wing tips (if needed)
2]data for above said wings when flaps are deployed, ailerons activated, and with spoilers engaged?
3]data set for elevators and rudders as well?

It is my best guestimation that having the complete set of coefficient data is fairly impossible for those without the funds, therefore much liberty is taken with simulated flight models, and a combination of dynamic coefficient information and a linear flight model are used to approximate most aircraft.

Second, how do you account for fuel loss/ weapon discharge within your inertia tensor matrix? If you lose fuel in the left wing for instance, dont you have to recaluclate the inertia tensor every so often to account for this loss of fuel? With having pre-calculated inertia tensors such as with UIUC data, how do you go about accounting for this?

Finally, what are your sources for obtaining F-18 data dynamic coefficient data etc? I hear there are complete sets of dynamic coefficient data out there for specific aircraft, 747 and F16 being a few of them, which might explain why Falcon4, and Aerowinx simulators are more realistic in nature than a more approximated flight model as in microsofts yearly product. Would you have a book name, or link etc. that would happen to lead me to such dynamic coefficient information or data that you have obtained? I read about a nasa report as well, aircraft handling quality data etc. which contains the linear flight models, but I think that many of these are already used in UIUC''s aircraft models, but I still cant find a source to download that report, or buy it for that matter.

Ok, thank you much for any reply :-)

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Hi Famine,

1) no i do not have coefficients specifically for wing/rudder/elevator input, i just increase/decrease lift/drag coefficient with linear formulas
2) about inertia tensors, i do make calculations for it, taking into account fuel consumption. If you want i can send you some code ...
3) I''ll look for you about F-18 dynamic coeff. data, i think i have them somewhere ...


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