Use of "Ideal" acceleration vs. time curves to estimate stroke length.

The equation for terminal velocity, vm, is:

Referring to the acceleration-time curve,

For any constant acceleration system, the distance traveled, s, in time, t, is related to the initial velocity, v0, and the

acceleration, a, by:

As the telescoping length is equal to s1 + s2 and the inner tube is equal to S3, and they are assumed to be of equal length

Simultaneous solution of equations (22) and (23), with simplification, results in:

which can be solved for t2-3 given the requirements of maximum acceleration, am, maximum rate of change of

acceleration, å, and terminal velocity, vm. The time, t1-2, can be found from the revision of equation (22).