(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.
c. Use of Estimated Acceleration vs Time Curve to Determine Approximate Propellant Web.
(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:
(a) The actual pressure-time curve of a catapult deviates from the theoretically optimum pressure-time
curve as shown in figure 46.
(b) In most actual catapults, the propellant web burns out some time before tube separation.
(c) The theoretical web was based upon the burning rate curve of the propellant (M2) at +160 F.
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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