REM@MC.LCS.MIT.EDU (Robert Elton Maas) (02/23/86)
C> Date: Thu, 20 Feb 86 14:58:17 cst C> From: John P. Cater <cater%mcchi2@mcc.arpa> C> Posted-Date: Thu, 20 Feb 86 14:58:17 cst C> Remember, that system in not in a maximally stable position when C> flying vertical and being pushed from the rear (try balancing a pencil C> on your fingertip Your analysis is completely wrong. (But then lots of nieve experts in the 40's fell for the same fallacy and tried to design rockets with engine at front instead of rear.) If you balance a pencil on your finger, the direction of force is held fixed with respect to ground (it always pushes upward presumably) so the further the pencil falls toward the side the lonnger the moment arm is (discrepancy between line from finger upward along direction of force and center of gravity) and the faster you are effectively pushing it away from vertical. But on a rocket if the engine is off-center the moment arm is constant regardless of whether the rocket is vertical or any other angle with respect to ground, because the line of force is fixed relative to the rocket instead of with respect to the ground, so rotating the spaceship with respect to ground doesn't rotate it with respect to the line of force. The rocket is in neutral equilibrium with a constant rotational offset. Putting the rocket at the head instead of tail doesn't make any difference, if the center of mass is the same distance from the rocket (in the opposite direction now) and the angle of error in the engine thrust is the same; it's neutral equilibrium with constant rotational offset just like before (except in the opposite angular direction). By comparison, hanging the rocket (or pencil) from the top with force fixed with respect to ground gives stable equilibrium, if the rocket or pencil deviates from vertical the line of force becomes offset from center of mass to push it back toward vertical. With engine fixed on rocket, there is no such adjustment. With engines mounted on rocket ship at mostly fixed position, the only equilibrium effect you can have is aerodynamic, but then the stability is with respect to the direction of the rocket through the air rather than with respect to vertical. With shuttle, there is servoing with respect to planned flight path, via radio link and/or onboard inertial navigation (I don't know which), and it may be that feedback delays cause it to oversteer and then try to compensate and oversteer the other way. It could be your conclusion is right despite analysis being totally wrong.
knudsen@IHWPT.UUCP (02/28/86)
Your analysis is good. However, while a rocket is first lifting off, and for a while afterwards, the relevant moment arm IS still that of gravity, not just the engine's thrust. So, the more a rocket leans over, the harder gravity will pull it over some more .. Oops -- you really are right on all counts! Cancel the above. But you still need to point the thrust vector thru the center of gravity (or oscillation, or percussion), which explains why space shuttles take off a bit sideways, with the orbiter a little bit under the tank. mike k