
SIZING A PARACHUTEby Levi Westra GoalDetermine the size of a parachute needed to deliver a specified payload at a specified speed Basic ConceptsWhen released from rest, a parachute will accelerate before reaching a steady speed. This steady speed is called terminal velocity. Terminal velocity is a consequence of equilibrium. That is, the sum of the forces on the parachute is equal to zero. Forces acting on a parachute are shown in Fig. 1. Figure 1 Weight (W) acts downward, through the center of mass. The resistance of the ambient air creates a drag force D. These forces are balanced once terminal velocity is reached. W = D WeightWeight is given by W = mg, where m is the mass of the payload plus the mass of the parachute. DragDrag force is the retarding force acting upon a body as it moves through a fluid. Engineers commonly predict drag using. where Cd, the coefficient of drag, is found from experiments. Values for a parachute are 0.8 < Cd < 1.2. Note that Cd is unitless. The term Ap is the projected area of the object. Imagine shining a light directly on an object. The surface area of the shadow equals projected area. Thus, for a hemisphere, the projected area equals the area of circle of radius r. Calculation of radius for a ParachuteTo find the radius of a parachute, we equate weight with drag: Using the drag formula gives
Solving for radius gives
ExampleGiven an object of mass m = 100 g, find the radius of parachute needed to provide a terminal velocity of V = 7.5 m/sec. Assume Cd = 1.2
Note that this radius corresponds to the parachute as a threedimensional object. If one was to cut a round parachute out of a sheet of plastic, the radius of the plastic would need to be larger than this value.

