Hello there, I have a problem. I''m designing a flight simulator and I have worked out how much force the elevator is producing up or down in Newtons. What I need to know is how do I convert this into an angular pitch rotation? What I mean is, how do I know how much of an angle do I rotate the vectors around the centre of gravity based on the force produced by the elevator??? Thanks in advance

I''ll post you some fully commented simple framework code of a non-linear flight-model hopefully within a couple of days if no-one else answers. It''s not a simple thing that one can "just answer" without writing a bit of an essay.

Anthony

What do elevators have to do with aeroplanes? Perhaps I''m missing something. Anyway, rotation is handled by off-axis elements of your Inertia matrix. Check out the equations for the moments of inertia.

Cheers,

Timkin

Timkin, elevators are flight controls located on the tail of the aeroplane. When the pilot pulls back on the control column the elevators move up, causing the nose of the aeroplane to pitch up.

Prospero, I look forward to seeing this code, thanks very much

generally you can calculate the torque T produced by a force F which acts on a point with distance r from the mass center by

T = r x F (cross product)

where r is the radius vector.
similar to linear movement there''s an equation about the angular acceleration alpha:

T = I*alpha


I is the moment of inertia. for a given body and a given axis you can get the moment of inertia by integration over
r^2*dm
where r is the distance to the axis and dm is the infinitesimal mass element; of course you would do it by dividing your plane into some small parts which can be treated as mass points and make a sum from the integral.

alpha is the change of the angular velocity per time unit, the angular velocity itself is the change of the angle per time unit.


just some general words about forces not acting on the center of mass - I guess Prospero will post some more useful things for your specific problem.

GA

Prospero,

Thanks for your post. Please do consider posting your code, or a link to it. This type of question comes up from time to time, and if I like your code I may put a link back to this thread (and another one or two) in the forum FAQ.

Timkin,

(some of the details here are not for your sake, since I know that you will understand this right away. In fact, I know thatyou understood more than you implied in your reply, . )

As you say, the off-axis terms of the inertia matrix are associated with rotation in the equations of motion. As TolTol alluded, the elevator is the control surface that is used to cause generation of a lift force by the horizontal stabilizer. When the pilot pulls back on the stick, the elevator rotates upward at the trailing edge of the stabilizer, effectively creating negative camber on the stabilizer. The negative camber leads to a lift force that acts downward, basically pushing down on the rear end of the airplane. When the rear of the airplane moves downward, the nose rotates upward. The main wing then has a higher angle of attack and as long as it is not near stall, more lift is generated and the airplane is able to climb. (The negative lift from the tail is much less than the additional lift of the main wing and so the net change in lift is positive.) There is also a component of thrust that can contribute to helping the airplane climb to a higher altitude.

Of course, the actual rotation of the airplane is accomplished via physics that are represented mathematically by the Newton-Euler equations of motion. Through Newton''s 2nd law of motion, the lift force causes an acceleration that leads to an increase in the airplane''s upward velocity that changes the airplane''s vertical position. And the lift force on the horizontal stabilizer, located away from the center of gravity, generates a pitching moment about the center that causes a rotational acceleration, thanks to the rotational acceleration and pitching moment being coupled by the off-axis terms of the inertia matrix. This acceleration leads to a rotational velocity about the pitch axis that in turn leads to the actual angular rotation. Prospero''s code should actually simulate all of this.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

quote:

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Original post by TolTol
Timkin, elevators are flight controls located on the tail of the aeroplane.

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OMG! Where did my brain go??? When you said elevator, all I could think of was a box suspended by a cable in a building... and this from a person that used to hold a pilots license.

Oh, the shame of it! 8^(

Timkin

quote:

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Original post by Timkin
Oh, the shame of it! 8^(

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My father tells me that humility is good for you! Actually, I''m a bit relieved. Thought you had gone loopy, .

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

quote:

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Original post by grhodes_at_work
My father tells me that humility is good for you! Actually, I''m a bit relieved. Thought you had gone loopy, .

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Oh, I went loopy a long time ago... it''s just that I can normally keep people fooled! I guess the secret''s out now!

Timkin