Figure 46. "Ideal" pressure, acceleration, velocity, and travel vs time curves for a three-tube catapult.

Figure 46. "Ideal" pressure, acceleration, velocity, and travel vs time curves for a three-tube catapult.

The second term may be eliminated, since the value of 24å is so large that it makes the term am

insignificant. Firing tests have indicated that for a closer approximation of stroke length, equation

(27), with the elimination of the second term, should be modified by increasing the values by 20

percent. The equation then becomes

which is plotted in chapter 4 (fig. 20) showing stroke length as a function of terminal velocity for

several values of maximum acceleration.

(g) It should be noted that these parameters (acceleration, velocity, and travel) are independent of the

mass to be accelerated. The mass fixes only the required pressure and tube areas as will be shown

in b below.

b. Pressure and Tube Area Relationships.

(1) The pressure and tube area relationship is based upon the equation of motion

Substituting am for a and eliminating αmg (since αamg <<PA), the equation relating piston area to peak

pressure becomes: