Pierce Nichols wrote:
> > I think
> > there would still be a slight lateral force, but not the yaw/pitch
> > torque that would occur with base-mounted engines.
> 
>         I don't see how -- please explain.

Well, let's rotate the vehicle 45 degrees, to make the ASCII 
art easier - assume we're looking down from above.


        <B

    ^
    A         D


         C>

Let the symbols ^<> indicate the horizontal component of each engine's 
thrust. (A is firing 100%, B and C are firing 50%, and D is shut off, 
as in the previous example).

So the vertical component of A's thrust, unbalanced by D, will tend to tilt 
the vehicle in such a way as to lift the corner where A is mounted... this
is the same 45 degree yaw-pitch maneuver we were considering earlier.

The vertical components of B and C will combine to produce 
a lifting-but-not-tilting force. The left-pushing (in the 
image plane) horizontal component of B's thrust, combined 
with the right-pushing component of C's thrust, will produce 
a counterclockwise-rotating torque, but will cancel out as far 
as producing a net translational force (i.e., we're not pushing 
the vehicle either to the left or to the right).

However, what's the horizontal component of A's thrust going to do?
It produces a torque that cancels that of B+C, but it's also going
to push the vehicle "B-ward" (i.e., toward the top of the page in the
ASCII art plane). If the engines were base-mounted, this is the force
unbalance that would produce the "cross-maneuver" torque discussed 
earlier... with the engines mounted at the CG plane, there will still 
be a side force even though it's not producing a yaw/pitch torque.

-dave w
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