Numerical-analytical Algorithm for Constructing the Envelope of the Projectile Trajectories in Midair

TL;DR

This paper develops a numerical-analytical method to construct the envelope of projectile trajectories considering air drag, providing simple formulas for maximum range estimation, demonstrated through baseball motion analysis.

Contribution

It introduces a novel analytical approach for envelope construction of projectile trajectories with air resistance, enhancing accuracy over traditional methods.

Findings

Derived simple analytical formulas for trajectory envelopes

Validated approach with baseball motion example

Provided a method to determine maximum flight range

Abstract

A classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon is reviewed. The air drag force is taken into account with the drag factor assumed to be constant. An analytic approach is mainly used for the investigation. Simple analytical formulas are used for the constructing the envelope of the family of the point mass trajectories. The equation of envelope is applied for the determination of the maximum range of flight. The motion of a baseball is presented as an example.