Re: [Flightgear-flightmodel] What happens during rotation at takeoff?

[Alan T. <ajt...@v-...>]

Perhaps we should go back to our mechanics lessons at school.

When considering the rotation of a body you can take moments about any point 
on the body to produce the sum of moments. If the object is not accelerating 
then the sum of moments will be zero. If accelerating then the sum of 
moments will be equal to the angular rate of change (rotation acceleration) 
multiplied by the inertia.

Consider a simple beam with a mass at each end and a pivot at the centre. 
( e.g. a seesaw)  On one end is a a mass A, on the other end a mass B and in 
the middle is a pivot P. The distance between A and P is ap and the distance 
between B and P is bp.

   A         P          B

Take moments about the pivot and if the seesaw is balanced
Then the sum of moments is A * ap  -  bp * B = 0.

Instead take moments about A. This time P supports all of the mass a+B
Then the sum of moments is ap * (A+B) - (ap+bp) * B = 0, which is exactly 
the same as in the previous equation.

In other words it does not matter which point you choose to make the sum of 
moments about.

With the seesaw the pivot P is fixed, so if the sum of moments is non-zero, 
the resultant rotation will be about that point.

For an aircraft you sum the total of all of the aerodynamic pitch moments 
about any chosen reference point - due to wing lift, tail lift etc, all of 
the moments due to the product of all of the masses of the aircraft, fuel 
and payload and their distances from the same reference reference point and 
the moment due to the product all of the external forces such as 
undercarriage and their distances from the same reference point. The chosen 
reference point is usually near the cg datum, but could be anywhere.

If the resultant moment is non zero the aircraft will pitch up or down. If 
the pivot point is fixed because the undercarriage is on the ground, then 
the aircraft reference point will also be forced to go up and down - just as 
with our seesaw.

If you are using JSBSim then all of this is done for you. All that is 
necessary is that you choose the same reference point for all of your 
aerodynamics and the aircraft cg, fuel , payload location, and undercarriage 
location. The moments of inertia that you use should also be about the same 
reference point.

Alan