Is this a comprehensible explanation? Comments/improvements/corrections
welcome and solicited:
--------------------
It is important to point out the differences in the coordinate frames and
point of origin used for defining the particular flight model for an
aircraft, and the way the aircraft is visually modeled in a 3D modeling
program for display.
The flight dynamics model (FDM) determines where in the world the aircraft
is – and by “aircraft”, it is really the aircraft center of gravity (CG)
that is being tracked. The FDM cares about modeling where the aircraft CG
is, and the 3D model wants to be in the correct spot in the world, too, but
how does one decide where to place the visual model? Can one simply take the
FDM-reported CG and place the aircraft origin (0,0,0) point there? No,
because the various aircraft modelers might use for a coordinate frame
origin any point they see fit when creating their aircraft model. There is
no universal convention for that.
FlightGear developers discussed a possible convention. The idea is that the
forward most center portion of the aircraft would be the MODEL REFERENCE
POINT ("MRP" hereafter - not to be confused with the JSBSim AERODYNAMIC
REFERENCE POINT). If the FDM can report the real world position of the MRP
(and it can), the scene code on the FlightGear side can place the aircraft
very nicely where it is supposed to be.
This is a slight problem for the FDM, though. The FDM has to make sure that
it knows where the MRP is IN RELATION TO THE CG. It is very important to
remember that the FDM reports the lat/lon/alt of the aircraft CG. As fuel
burns off the aircraft CG moves. So, the vector to the MRP will change with
time. It's not a big issue, just a little work for the FDM.
Some definitions:
Aerodynamic Center: The idea of the aerodynamic center is similar to the
idea of the center of gravity. It is the location on the aircraft through
which the total lift and drag can be said to act, just as the center of
gravity is the point through which the total weight acts.
Each part on the aircraft has its own aerodynamic center. In the subsonic
regime, the aero center of the wing airfoil section is generally near the
0.25 chord point. But it moves aft as the aircraft increases speed into the
transonic regime, typically as far back as the
0.5 chord.
Aerodynamic Reference Point (ARP): Think about all the sources of
aerodynamic pitching moment. The largest of those are the wing and the
horizontal tail. That due to the tail comes largely from the tail lift
multiplied by the tail moment arm. But how do we define the tail moment
arm? The aero center of the wing seems like a natural choice, but doesn't
really work since it moves in flight. So typically a point on the wing is
arbitrarily chosen to be the moment arm zero or reference point. That's the
point that I've dubbed the aero reference point. By convention, that point
is typically along the 0.25 chord line on the wing. Spanwise, it is
typically defined to be at the spanwise location of the MAC or mean
aerodynamic chord. The MAC is often computed using:
cbar/croot=2/3*(1+lambda+lambda*lambda)/(1+lambda) where lambda is the wing
taper ratio, ctip/croot. Once this length is computed, the spanwise
location can be found by finding the point on the wing which has that chord.
In the design phase, this point needs to be chosen early and all CFD and
tunnel data reduced using it.
Structural Frame: This is the manufacturer’s frame of reference used to
define locations of items on the aircraft. These items would include the
center of gravity, the locations of all the wheels, the pilot eyepoint,
point masses, thrusters, etc. The items in the JSBSim configuration file are
located using this frame. In this frame the X-axis increases from the nose
towards the tail, the Y-axis increases from the fuselage out towards the
right (when looking forward from the cockpit), and of course the Z-axis then
is positive upwards. Typically, the origin for this frame is near the front
of the aircraft (at the tip of the nose, at the firewall, or in front of the
nose some distance); the X-axis is typically coincident with the fuselage
centerline and passes through the propeller hub (thrust axis).
Note that the origin can really be anywhere for a JSBSim-modeled aircraft,
because JSBSim internally only uses the distances between the CG and the
various objects – not discrete locations themselves.
Body frame: As used in JSBSim the body frame is similar to the structural
frame, but rotated 180 degrees about the Y axis, with the origin coincident
with the CG. This is the frame where the aircraft forces and moments are
summed and the resulting accelerations are integrated to get velocities.
Stability frame (or wind axes): This frame is similar to the body frame,
except that the X axis points into the relative wind
Model Reference Point (MRP): This is the reference point that is agreed
upon by both the aircraft modeler and the 3D model builder.
-- Jon Berndt (some material supplied by Tony Peden)
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