“An Approximation Model for Projectile Motion under Air Resistance Proportional to a Power of the Speed,” co-authored by Robert Kantrowitz ’82, the Marjorie and Robert W. McEwen Professor of Mathematics, appears in the April 2023 issue of the international research journal Rendiconti del Circolo Matematico di Palermo. The article addresses a ballistics problem concerning the motion of an airborne projectile that is subject to the forces of both gravity and air resistance proportional to some power of its speed.
Inasmuch as an application of Newton’s law gives rise to an initial value problem for which explicit formulas for the exact solutions are not available, Kantrowitz and co-author Michael M. Neumann of Mississippi State University focus on projectiles having a relatively low launch angle. These small-angle approximations provide a model in which the problem is tractable, and the article compares its solution to the exact solutions.
Kantrowitz says that the comparison shows that the trajectories of the exact solutions are always dominated by those of the small-angle approximations, which in turn are always majorized by the parabolic Galilean flight paths that are traced in the absence of a retarding force.
