In article ,
Iain McClatchie wrote:
Henry the optimal thrust direction is *not* tangential.

Can you suggest, or give a reference that would suggest, a better
parameterized model for pointing during launch?

*Launch* is a somewhat different story than low-thrust orbit maneuvering.

Generally, while within the atmosphere, it is obligatory to point into the
wind (maintaining angle of attack at 0) to avoid excessive aerodynamic
loads on the vehicle. Usually this is done with a precalculated pitch
program, but sometimes refinements like active sensing and pointing are
added to reduce wind-gust loads. (The Saturn V was precalculated, the
shuttle does some active pointing.) After max Q has passed, sometimes
it can be worth incurring a bit of loading by cranking in a little bit
of pitch-up, so as to get some body lift.

After exiting the atmosphere, it is common to use closed-loop optimizing
guidance algorithms which don't lend themselves to simple description.
(The closed-loop guidance on the Saturn V did amazing things after the
Apollo 6 double engine failure. It did reach orbit, but the guidance data
was a sight to behold.)

That said, a first approximation is to drive the pitch angle (above the
local horizontal) theta to satisfy tan(theta) = A + B*t where t is time,
A is an initial pitch (usually somewhat above the flight path) and B is
usually negative (so pitch declines with time and is zero or slightly
negative at insertion).

Finally, just before insertion it is usual to freeze the pitch angle and
limit optimizing guidance to controlling cutoff time. Trying to actively
chase the last little errors in position and velocity can lead to wild
gyrations as the error magnitudes shrink rapidly and the error directions
become almost random.

...I'm at a loss to explain why pointing not along the
velocity vector would be anything but less efficient, since
E = F*d
Any force orthogonal to motion would appear to add no energy to the
vehicle...

True, but there are two other issues.

One is that although it does not add energy, the thrust component
perpendicular to the velocity rotates the velocity vector, which can be
desirable if you are in the vicinity of some large hard object (e.g. the
Earth) that you don't want to smack into while maneuvering. This is an
important issue for launch.

The other is that your goal is not to optimize the instantaneous rate of
energy addition, which is F dot v , but to optimize the total energy
added, which is integral(F dot v dt) . And because the problem is
nonlinear, these two strategies are *not* equivalent for low-thrust orbit
maneuvering: energy added yesterday changes the orbit and thus changes
v today, so it can be better to accept a lower rate of energy addition
yesterday if it will give better conditions today.
--
MOST launched 30 June; first light, 29 July; 5arcsec | Henry Spencer
pointing, 10 Sept; first science, early Oct; all well. |