(2) the required pressure-time curve, which will provide the desired acceleration-time relationship, can be

determined by continuing the example of the preceding paragraphs. Assume the catapult must accelerate

a 360-lb load vertically upward. From a mechanical design standpoint and based on space envelope

limitations, optimum tube areas are established at 3.10 in.2 and 2.56 in.2 for the telescoping and inner

tubes, respectively. The maximum pressure needed corresponding to am and a telescoping tube area of

3.10 in.2 is:

The pressure-time curve can then be constructed as shown in figure 46.

(1) The propellant web may be estimated if either the burning rate vs. pressure curve for the propellant or the

constants B and n in the burning rate law (r=BPn) are known.

(2) The burning rate curve of the propellant may be used by selecting small intervals of time ∆t, on the

pressure-time curve of a propellant actuated device, and taking an average pressure over ∆t. Then find a

burning rate to match this average pressure and find the product of r∆t. The propellant web, *w*, can then

be defined as:

The propellant web may also be defined as:

Returning to the example and the acceleration-time curve of figure 46, equation (29) may be integrated to:

9

where A = average area of telescoping and inner tubes.

(See appendix IV for the derivation of this equation.) Application of this equation to

-3

the example, assuming a propellant (M2) with constants, B= 1.525 X 10 in./ sec/psi and

n=0.855, results in a web of 0.33 inch.

(3) This calculated web is slightly larger than should be used for initial testing purposes. This can be ascribed

to the following:

curve as shown in figure 46.

Operation of the catapult at -65F. will result in a longer burning time because of the lower burning

rate and reduced pressures. The web may then have to be reduced to allow generation of all of the

propellant gas during the ballistic cycle. For these reasons, testing should begin with propellants

having a web of approximately 85 to 90 percent of that calculated by the above methods.

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