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

Finally, the stroke length equation is:

As an example, assume the desired performance of a catapult is:

terminal velocity (vm)=80 ft/sec

maximum acceleration (am)=18 g

maximum rate of change of acceleration (å)=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.

(f) The equation for approximate stroke length as used in chapter 4,

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: