Finally, the stroke length equation is:
As an example, assume the desired performance of a catapult is:
terminal velocity (vm)=80 ft/sec
maximum rate of change of acceleration ()=150 g/sec
From equations (19), (20), and (21)
The approximate stroke length then is determined from equation (26)
S=6.47 ft or 77.6 in.
(c) These quantities (t0-1, t1-2, and t2-3) are used to define the acceleration-time curve of figure 46. If the
velocity-time and travel-time curves are desired, they can be determined by first and second
integrals of the acceleration-time curve.
(d) These curves, then, define the approximate stroke length and stroke time for a three tube catapult
operating with a constant internal pressure after t1 and designed in accordance with assumptions in
(b) 1 and 2 above. This method may be modified if the tube lengths are known or are related in
some manner, or if the tube areas are known or related in some manner, by minor changes in
equations (22) through (26).
(e) Since it is not possible to match the acceleration-time curve of figure 46 exactly, the value of the
stroke length should be increased by approximately 10 percent. To reach the desired separation
velocity of 80 fps, the stroke should be approximately 86 inches.
was based on equal tube areas for the inner and telescoping tubes (essentially a two-tube catapult).
The reduction and simplification of equation (26) using a tube area ratio of 1 result in the following
equation:
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