MEAM 22 Modelling and Simulation How does a parachute deployment drastically change a falling human’s dynamics, and how can this life-critical transition be modeled and simulated using MATLAB/Simulink?
Model the vertical motion of a parachutist falling from 3000 m who deploys a parachute at 1500 m, causing a sudden change in aerodynamic drag area. Derive the governing differential equation including gravity and quadratic air resistance, compute the maximum velocity analytically, then build a Simulink model with a height-triggered switch that changes drag area during descent. Plot height vs. time and velocity vs. time, and verify that the computational maximum speed matches the analytical result.
John Williams answered .
2026-01-26
The motion is governed by gravity and quadratic air drag:.......
Before deployment, the area (A=A_S) is small, so drag is low and velocity increases until terminal velocity where drag equals weight:
At height (h_1), the parachute opens and area switches to (A_O). Drag rises sharply, causing rapid deceleration and a new, much lower terminal velocity. The height–time curve shows fast descent first, then a clear slope change after deployment; the velocity–time curve shows a high constant speed followed by a sudden drop and stabilization at a safer speed.