Hoping that I didn't miss anything, answering to Girlinhat about engine distance from rotation axis being always good.
so, what we want to achieve is angular acceleration A.
lets say our engines output a force F.
the length of an arm is r. if we consider the body of the ship of negligible diameter compared to the length of arms, then the distance between the 2 engines we are firing is 2r=d
2 forces F equal in magnitude but opposite in direction, at a distance of d, generates a torque T=F*d
I is moment of inertia. it represents resistance to rotation on an axis. We can write
A=T/I.
so far, all good. T increases with distance. but what does I do?
since we are dealing with granular mass, we can define I as sum of all m*r^2 , where m is the mass of the elemental particle ( in this case the cubes of which our starship is made) and r is distance of the elemental particle from the axis.
what does this mean?
lets assume that the ship is rotating on the axis going from its rear to its front.
lets assume the arms are massless.
lets assume that the whole engine block has no volume. ( or, in this granular geometry, it is 1 cube big. so we don't have to deal with distributed mass)
previously, we assumed that the ship's diameter was negligible. if we keep that assumption ( which we can, since we aren't doing any number crunching yet), then moment of inertia of the ship is 0, since all mass is on the axis.
arms are massless, therefore they too contribute nothing to the moment of inertia of the ship.
all that is left is the engines, conveniently compressed.
I=2*m*r^2
where m is the mass of an engine block. it is multiplied by 2 because we have 2 such blocks, one on each side.
r is the length of an arm-
lets look back at A now
A=(2*F*r)/(2*m*r^2)= F/(m*r)
in this case, we see that as we place engines farther, our acceleration decreases!
this alone shows that it is not always best to have turning engines far away from the axis of rotation.
but is there a situation in which such outsourcing of thrust is desired?
lets rethink our assumptions, and move closer to reality.
lets assume our ship has a moment of inertia Is
lets assume the arms have a moment of inertia Ia
lets assume the engines have a moment of inertia Ie
A=(2*F*r)/(Ia+Ie+Is)
where r is length of an arm
both Ie and Ia are proportional to r^2
we can write a combined moment of inertia Ic=K*r^2, where K is a constant, depending on geometry and distribution of mass in the arms and engines.
Ms, instead, is independant from the length of the arms.
A=(2*F*r)/(K*r^2 + Is)
the only difference from the previous case seems to be Is.
what is the effect on Is on our results?
-lets assume Is is very big compared to Ic
ships can be massive, so, for low values of r this is a reasonable assumption.
We can ignore (K*r^2) since adding something small to something very big doesn't change much.
A=(2*F*r)/(Is)
now the only thing increasing by distance from the axis is torque. Which means that moving engines away is a good thing.
now lets change parameters.
-lets instead assume that Is is very small compared to Ic.
this is true for very massive engines, very light ships or, most importantly , high values of r.
we can ignore Is since it is very small compared to Ic.
A= (2*F*r)/(K*r^2)
which is the same result we got in the first case examined. now placing engines farther decreases our acceleration.
which is, needless to say, bad.
how do we apply this to a real case?
We see that, everything else being constant, there are low values of r for which A increases with distance, and high values of r for which A decreases with distance.
this mean that there is a length rc for which A is maximised. before rc, A increases, after rc it decreases.
what really matters when designing our spaceship is determining rc.
rc depends on several factors including geometry of the ship, distribution of mass ( both for Is and K), thrust/weight ratio of engines.
Which means that each ship has its own rc that has to be calculated before building it.
or you can just eyeball it. it is fine, it's just a game.