(2)

10-5 for removers)

Where *a* is the maximum rate of change of

acceleration. The use of equation (2) is demonstrated

(2) Equation (4) is a simplification of equation

by the following calculation which was made to

(31) presented in Chapter 5.

The

determine the stroke time of the M5 catapult. The M5

derivation of the constants used in

catapult has the following performance characteristics:

equation (4) is presented in "Refinements

to First Order Equations," in Chapter 5.

(3) To use the curves of figure 21 in

approximating the propellant charge in a

catapult (the M5 catapult for example)

find the intersection of the terminal

velocity (64 fps) abscissa and the catapult

curve. The ordinate of this point (0.26

gm/lb) is the ratio of the charge weight to

the propelled weight. Since the propelled

weight is 312 pounds, multiply the ratio

The stroke for the M5 catapult actually is 0.220 seconds.

found in figure 21 by 312 pounds and the

approximate charge weight is found to be

pressure, *P*, and piston area or tube area, *A*, may be

81 grams. This is a reasonable estimate

estimated by using Newton's Law (*F*=*ma*) and

since the actual charge weight of the M5

substituting *PA *for force, *F*, where *m *is the propelled

catapult is 84.5 grams.

(4) A similar procedure is followed when

(3)

estimating the charge weight of a

Equation (3) may be used to determine the piston or

remover, except the remover curve is

tube area if a specific pressure is desired, or it may be

used.

used to determine the peak pressure if the area is

established.

(1) Figure 22 is used, in a manner similar to

that outlined above, to estimate the

again in the following calculation as an example of how

propellant charge for a thruster. Two

to use equation (3). The propelled mass is 312/*g *slugs

curves are presented in figure 23,

and the tube area is 2.65† + square inches. Therefore:

showing two groups of propellants of

different impetus which are used in

stroking devices. The curves are plotted

from equation (5) which is derived in

The actual peak pressure in the M5 catapult is 1800 psi.

Where:

(1) A first order design approximation of the

propellant charge weight for catapults and

removers may be found by using figure

21. This figure is based on the equation:

Where:

† Refer to footnote on page 24.

‡ Chosen on the basis of installed dimensions and dimensions) of standard tubing.

Different constants are used for catapults and removers since the characteristic propellant composition and energy losses for

these two types of devices are different.

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