Pierce Nichols wrote:
>
> On Thu, 2003-10-23 at 00:15, David Masten wrote:
>
> > I had figured that to yaw left decrease left engine thrust and increase
> > right engine thrust simultaneously. Since opposite motors generate
> > torque in the same direction this should mean no (little) torque change.
>
> Neither the strategy you propose nor John's strategy eliminate
> cross-axis coupling. Both strategies still produces coupling to the roll
> axis when maneuvering in both pitch and yaw at the same time. Neither
> addresses the coupling that occurs when rolling is combined with
> manuevers in those axes. However, I think John is right about being able
> to mostly ignore the cross-coupling. If you keep the engine cants small
> and make only small control actions, then whatever coupling occurs
> should be simply damped out by the control system, assuming that it is
> fast and well-damped.
> If precision pointing is required, as for a sounding rocket carrying a
> telescope or earth-sciences package, then this will not be enough, of
> course.
Hmmmm.... in a vehicle with 4 alternate-canted base-mounted engines,
I think Pierce is right... there _is_ gonna be a weird cross-coupling:
Assume:
\
A B << +Pitch
C D
^ \
^ \
| +
Roll
+
Yaw
I.e. positive Roll is the way it twists when you fire engines A,D, etc.,
so we have, for a given R, Yaw, Pitch and Thrust (positive T is all
4 firing equally), and mix with appropriate signs to get engine commands
from maneuver inputs:
A = T + Y + P + R
B = T - Y + P - R
C = T + Y - P - R
D = T - Y - P + R
So if you put in T=2 P=+1 Y=+1 R=0 for a pitch maneuver while climbing:
A = 2+1+1+0 = 4
B = 2-1+1-0 = 2
C = 2+1-1-0 = 2
D = 2-1-1-0 = 0
So B and C will combine their lateral forces into a roll torque and
a thrust, but A (not balanced by D during the yaw-pitch maneuver)
will introduce an unbalanced lateral force at the vehicle base, since
it's one of a canted pair and the other isn't firing. This force is
going to push sideways on the base - i.e. - at right angles to the
intended maneuver.
So I ask myself, why doesn't this manifest if we just pulse
a yaw pair or a pitch pair for example? Answer - it does, but
it's on-axis, so it doesn't skew you sideways - it makes the
vehicle either harder or easier to steer in yaw than in pitch,
depending on the orientation of the nozzle tilt rectangle - i.e.,
whether the yaw or the pitch pairs get a more favorable tilt
relative to the axis of action of that pair.
This would suggest that for easiest steering, the orbital vehicle
should in fact make its "horizon turn" as a maneuver on either the
pitch or roll axis (depending on which way came out "easy") after
selecting the desired azimuth in a vertical roll.
-dave w
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