On high-altitude projectile motion

Abstract

In this study, the formulas for projectile velocity components and coordinates in a vacuum were derived with the altitude decrease in gravitational acceleration factored in. A model of cannon shell motion in the air is presented that accounts for the altitude dependence of gravitational acceleration, air density, the speed of sound up to an altitude of 84 km, and the speed dependence of the drag coefficient at trans- and supersonic speeds. The drag coefficient function is obtained by fitting to experimental data taken for the US M101 155 mm shell. The model gives flight parameters that agree with the published ones. The motion of the Paris Gun projectile is then modeled. The model shows that a range of 120 km is possible if the projectile mass is about 150 kg. A flat Earth approximation was used in the computations. Changing the launch angle to 90°, super high-altitude vertical ascent and free fall are modeled.