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twin engined phyics problem unequal thrust

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can somebody with free time explain to me please this problem. you have unequal thrust on a twin engined plane, because one engine is suffering a bit. How much thrust do we get in the direction of travel, and how much thrust goes to drive torque?

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my difficulty in understanding this is this:

are the torque separate to thrust or is the fact that its free and not pegged like a catherine wheel make it more complex.

Would a catherine wheel firework spin as fast if it was pegged or just set loose?

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I see what you are saying steve, it''s not particularly easy. I use an open source physics library which does a good job of this for my twin engined vehicle: http://www.q12.org/ode check it out

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well it wasnt actually, but never mind. i''ll guess that the torque of a free body is seperate from the thrust factor.

perhaps if dt is small it is modeled well, since a plane obtains no new linear momentum as the single engine pushes it around - or rather a loose catherine wheel would not.

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Well, the question in that thread was, paraphrased, "how much of a force goes to linear and how much goes to torque.", which is *essentially* what you have asked. You simply have two forces instead of one. The principle of superposition is the only required step to take the info from that problem to yours.

"since a plane obtains no new linear momentum as the single engine pushes it around
This would only be true in uniform circular motion (thrust is directed toward the center of the circle the plane is moving in). How many planes do you see flying like that (besides the space shuttle in orbit).

A single force whose line of action does not pass through the center of gravity of an object affects both the linear and angular momentum of the object. It is not "split up" as I posted in the other thread. Read Baraff''s paper (link in other thread). He derives this relationship.

As a side note, if a four engine plane loses one engine, the throttle back on the oppisite engines so that the net torque is 0. A twin engine plane that loses an engine must use the rudder and other control surfaces to produce the needed torque to keep the plane from spinning out of control.

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well i found the 32 pages to read through depressing.

i went to end and it seems to suggest that linear momentum and angular momentum are separate: it said that the force seems to be being considered twice.

to confirm. if this twin engined plane was running in the an airless situation - is the angular momentum build up the same as if the position of the plane was contrained by a sort of bar through the yaw axis?

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quote:
to confirm. if this twin engined plane was running in the an airless situation - is the angular momentum build up the same as if the position of the plane was contrained by a sort of bar through the yaw axis?

Correct. It seems a bit un-intuitve, but its the way things are.

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Think of the problem this way. Subtract from both engines the power produced by the under-performing engine. So that now, you only have to consider the effect of the over-performing engine. Since the power produced by this engine is not balanced it generates a moment about the yaw axis of the aircraft. The effect is to generate a yaw motion. If left unchecked this yaw induces a roll with the wing carring the under-powered engine dropping (since the wing carrying the over-powered wing is travelling at a higher speed during the yaw). The aircraft will enter a spiral dive. The effect of a slight under-powered engine on a twin (mutli-) engined aircraft can be compensated for by trim in the yaw axis. If the yaw effect is significant a large amount of opposite rudder must be maintained to counter the yaw.

Alternatively, by keeping a neutral rudder but applying opposite roll through the ailerons, the over-powered engine can propel the aircraft through a flat turn. This would look like a smooth circular arc flown with level wings. It''s a basic skill learned when learning to fly. It can be produced in single engine aircraft by applying rudder and opposite aileron.

I hope this helps you to visualise what is happening to the aircraft in your problem and thus helps you understand the physics of the problem.

Cheers,

Timkin

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