Closed -Form Expressions forPredicting Certain Projectile Trajectories

Accurate prediction of the trajectory of a projectile passing through air almost always requires the aid of computer-assisted numerical procedures. Herein are derived closed-form expressions for a certain class of such trajectories, which can provide insights not readily obtainable with computer codes alone. For example, the expressions reveal errors in widely-promulgated formulas for predicting the effects of Coriolis acceleration and of uphill or downhill launches. An example is presented showing negligible differences between results from expressions derived herein and those from a well-developed and widely-used code that uses numerical integration. Such agreement can be expected for flat trajectories of projectiles with shapes resembling that of a standard, so-called G-7 projectile, in the supersonic speed range.