Nonlinear Dynamics of Skydiving with Variable Atmospheric Density and Gradual Parachute Deployment
DOI:
https://doi.org/10.70028/cpir.v2i2.109Keywords:
Skydiving Dynamics, Aerodynamic Drag, Terminal Velocity, Atmospheric Model, Parachute DeploymentAbstract
This study investigates the vertical motion of a skydiver under the influence of aerodynamic drag and variable atmospheric conditions. A mathematical model is developed based on Newton’s second law, incorporating a quadratic drag force that depends on air density, velocity, drag coefficient, and reference area. Unlike simplified approaches, this study accounts for altitude-dependent air density using a standard atmospheric model, allowing for more realistic simulation of high-altitude descent. The transition between freefall and parachute deployment is modeled using a logistic function to represent gradual canopy inflation. The resulting nonlinear differential equations are solved numerically using the fourth-order Runge–Kutta (RK4) method. Simulation results show that aerodynamic drag plays a dominant role in limiting velocity, leading to the formation of terminal velocity during freefall and a significantly reduced steady-state velocity after parachute deployment. Additionally, the inclusion of variable air density improves the accuracy of velocity predictions, particularly at higher altitudes where density variations are significant. The findings demonstrate that combining aerodynamic modeling, atmospheric variation, and numerical methods provides a more comprehensive understanding of skydiving dynamics.
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Copyright (c) 2026 Brandon Lee Kosaido, Kushendarsyah Saptaji, Djati Wibowo (Author)
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