Landing the LM Aug 31, 2011 13:48:25 GMT -4
Post by Bob B. on Aug 31, 2011 13:48:25 GMT -4
That's going to be a problem in any plane change if you use simple vector addition. For small plane changes the effect is negligible. For large plane changes the problem can be eliminated by rotating the thrust vector during the burn so that the thrust is always at right angles to the velocity vector. (Edit: Rather than continuously rotating the thrust vector, the same thing could be accomplished by adding one or more doglegs.) This second method changes the direction of the velocity vector without ever changing its magnitude, however more delta-v is required. In the first case, the amount of delta-v required to perform the plane change is given by the following equation:
Δv = 2*Vi*sin(θ/2)
where Vi is the initial velocity and θ is the angle of the plane change.
In the second case it would be:
Δv = Vi*θ*π/180
The equation for a combined altitude/plane change maneuver using simple vector addition is:
Δv = SQRT[ Vi2 + Vf2 – 2*Vi*Vf*cosθ ]
where Vf is the final velocity.
I don't have a combined equation for the second case, but I'm sure if it were an issue, the direction of the thrust vector could be controlled during the burn to assure the velocity never drops below a critical value.