Re: [Flightgear-devel] Turn ball fix & JSB notes

[Tony P. <ap...@ea...>]

On Tuesday 28 August 2001 02:17 pm, you wrote:
> Jon S. Berndt wrote:
> > Well, I've got my orbital mechanics books, several books and papers
> > on flight dynamics, etc. I had never looked at the pilot accels
> > calcs, so this is a first for me. Tony is really working the
> > problem, but I want to understand it, too. I want to be able to
> > *derive* it.
>
> But the derivation is trivial:
>
> 1 Calculate the aerodynamic force in the body frame.
>
> 2 Transform to the geocentric frame, and use it to calculate an
>   acceleration in that frame using the F=ma relation.  This
>   transformation is just a rotation and translation, so it's legal.
>   The force you get will still be valid in the earth frame.
>
> 3 Use that acceleration to modify the velocity vector, still in the
>   geocentric frame.

By this, I assume you mean integrate the accels?  One downside to this 
approach is that it forces you into using moments of inertia that vary with 
the aircraft's attitude and position. (as if coming up with decent inertias 
wasn't already hard enough ... )


>
> 4 Back-transform the velocity vector into the body frame (again,
>   rotations and translations are kosher).  Go back to step one, using
>   the new velocity to calculate the aero parameters at the next step.
>
> But what the McFarland paper (and thus JSBSim) does is different.  In
> steps 2 and 3, it's using the _local_ frame to do the calculations.
> But this is a non-inertial frame, so you CAN'T USE Newton's "F=ma"
> relationship.  Instead McFarland adds a correction term to get the
> motions correct.

McFarland integrates in the local frame, JSBSim integrates in the body frame.

>
> So that's the reason the patch looks complicated.  It's undoing the
> damage done by McFarland's funny terms.  Again, the problem is not
> that JSBSim is generating bad answers for simulation questions.  It's
> generating the right answers, because McFarland's terms are correct.
> The problem is that because of the non-inertial reference frame, you
> can't assume that the acceleration felt by the pilot (which obviously
> depends only on physics and not on the characteristics of the
> reference frame it's measured in) is the time derivative of velocity.
> Acceleration is equal to V-dot ONLY in inertial reference frames.
>
> Andy

-- 
Tony Peden
ap...@ea...
We all know Linux is great ... it does infinite loops in 5 seconds. 
-- attributed to Linus Torvalds