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Exterior Ballistics of a Projectile in Vertical Flight

INTRODUCTION 
The Materials Application Division at aWIRC is currently engaged in the 
development of experimental artillery shell. The projectile features new com- 
ponents, assemblies, materials and methods cf manufacture. After the prototype 
rounds: are fabricated, a number of models are test fired to determine the ade- 
quacy of the design. At launch, high-speed motion pictures are taken as the 
round emerges from the muzzle and during the early stages of free flight. Also, 
the time of flight is recorded for several selected ranges. This information is 
then used to assess the sufficiency of the experimental rounds . 
If the coefficient of drag and its variation with velocity is known for the 
projectile configuration, then the time of flight is readily calculated as a 
function of the range. The magnitude of the deviation between the measured time 
of flight and the calculated time of flight— consistent vith the accuracy of 
the drag coefficient data— serves as a reliable index of projectile performance. 
Thus, substantial increases of the measured time of flight over the calculated 
allowable time band would suggest excessive yaw, probably induced by some major 
component malfunction or projectile break-up, whereas modest deviations would 
indicate less severe problems. 
The program presented in this report, in conjunction with the experimentally 
determined coefficient of drag, permits the time of flight to be calculated at 
any range for vertical firings as a function of muzzle velocity and projectile 
weight.

Projectile Motion 
The velocity and time of flight versus range were calculated for the experi- 
mental shell for both the upward and downward trajectories using the applicable 
equations developed earlier. The calculations were performed for increments Of 
200 feet. Over each increment, the drag coefficient and air density were assumed 
to be constant, corresponding to the velocity and range values at the beginning 
of the increment. At the start of each new increment, the values were recomputed. 
Thus the terminal conditicns for one increment form the initial conditions for 
the succeeding increment. The equations were programmed for the 1108 UNIVAC 
computer. 
The altitude, velocity, time cf flight, air density, and drag coefficient 
are calculated for an assumed muzzle velocity of 1800 fps. The computer results 
for both the upward and downward motion are given in Appendix A. The FORTRAN 
listing of the program is given in Appendix B.