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I'm a developer. I tried (mostly for fun) to create a realistic physic engine.

I try to sum all forces (here thrust) applying to an object in two composantes: an acceleration vector and the angular acceleration.

I read a lot about torque and thrust but there is still some stuff that I can't figure out.

Let's take a exemple: Imagine a plane(or space craft) with two motors each placed at the opposite side with respect to the center of gravity. If they have equals thrust I figure that I can modelise them by a single thrust vector placed on the center of gravity equals to the sum of the thrust provide by the two engines. Is that right?

What's happen if one motor delivered 10% less thrust that the other one, how my thrust decrease, how to compute resulting torque ?
Did I loose or gain efficiency if my thrusters are placed at the back of the plane and why?

I try to find a mathematic model that could work with any number of thruster placed at different position of the air-craft.

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You need to model total thrust and inertia, as well as angular thrust (torque) about the center of mass and angular inertia. For example, suppose you have two engines, each five meters left and right of the centerline, and the one on the left exerts a thrust of 90 newtons while the other one has a thrust of 110 newtons. Then you have a total thrust of 200 newtons, but the torque from the left engine is 90*5 newton-meters tending to turn to the right, while the other engine has torque of 110*5 newton-meters in the opposite direction, for a total torque to the left of 20*5 newton-meters. How fast that makes it turn depends of the angular moment of inertia about the vertical axis.

To model angular inertia, it's easiest if you model a moment of angular inertia about each of the principal axes. For example, a long slender cylinder would have a small moment of angular inertia about it's long axis, but a larger moment about each of the other two axes.

Then, determine the torque about each axis. If you have an engine whose thrust vector does not go through the center of mass of the vehicle, then it passes it at some distance. You can determine that distance by dropping a perpendicular line segment from the center of mass to the thrust vector. The length of that line, times the intensity of the thrust vector, gives you the torque, which is also a vector. You add these up over all the forces acting on the vehicle. Then you resolve that torque vector onto each of the principal axes, and together with the angular moment of inertia on each axis, you get an angular acceleration rate on each axis.

Then you use your ordinary differential equation solver (you're probably using Euler) to see how the vehicle motion evolves.

You're going to need to study up on moment of inertia and angular momentum.

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Thanks, for the quick answer, that's exactly what I looked for. However there is still something that I found a little odd. May be I just fooled myself but if both engine delivers a 100N thrust I use this energy to move forward, but if I have the same energy distributed like 90/110N. I have an additional rotation and no loose on acceleration? How with (what seems to be) the same energy can I have an additional force? – AxFab Aug 1 '13 at 9:22
Thrust and energy are not the same thing. To help you understand it, simplify the problem. Use just one engine. First let its thrust vector be on-center, so it exerts no torque. Then let its thrust vector be a little bit off-center, so there is a component thrusting forward, and a component tending to turn the vehicle. The turning component is not subtracted from the forward component. – Mike Dunlavey Aug 1 '13 at 12:22

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