By Elijah Harrington

Faculty Mentor: Mickey Skamangas

Abstract

Modeling projectile motion is important because it helps us predict trajectories with varying conditions and visualize how forces like gravity, lift, and drag shift the outcomes. Though it is possible to model projectile motion using classical Newtonian methods, this produces a closed-form, extremely simplified result that assumes no resistive forces and a simple parabolic trajectory. In order to construct a more realistic model with no closed-form solution and the ability to incorporate drag and lift, a numerical method is needed. In this study, a closed-form solution was first coded into MATLAB as a baseline for later comparisons. The Runge-Kutta numerical method was implemented to integrate the equations of motion. Using simple initial conditions, the Runge-Kutta results were compared to the closed-form solution to confirm accuracy and identify errors in the code. Once confirmed, aerodynamic drag was added to the model, and trajectories were simulated across a range of drag coefficients. The results were then compared to the closed-from solution to compare deviations in range, flight time, and trajectory shape. Preliminary findings indicate that drag significantly reduces both horizontal range and flight duration, with the effects becoming more pronounced at higher velocities and lower launch angles. Lift was then incorporated and tested with varying angles of attack, to which flight time and distance increased even in the presence of drag.