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

[Andy R. <an...@ne...>]

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.

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.

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

-- 
Andrew J. Ross                NextBus Information Systems
Senior Software Engineer      Emeryville, CA
an...@ne...              http://www.nextbus.com
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