Physics of Skydiving

Could you see yourself jumping out of a perfectly good airplane traveling at 170 MPH 13,000 feet above the ground? Imagine being the first person to jump out of an airplane, entrusting your life to an unproven piece to technology. Over the past century, skydiving has grown from a madman's fantasy to a international sport.

As a skydiver stands at the door of the airplane, the force of their mass multiplied by gravity is directly countered by the force of the plane pushing back up on their feet, this is know as the normal force and is shown is the equation

FN = m * g

As soon as the the diver exits the plane, the normal force is removed and the diver begins to fall. Generally, a skydiver will exit the airplane at about 13,000 feet (4000 meters). To maintain a stable flight, their body must face the "relative wind". This is the direction in which the greatest air resistance is coming from. After a jumper exits, the drag force of the air counteracts the jumper's horizontal motion until the drag is only working against gravity. For a 70 kg jumper with the acceleration of gravity (9,8 m/s2), the force of gravity can be calculated with the same equation as the normal force:

Fg = 70 * 9.8 = 686 Newtons

The force of the drag caused by particles of air is calculated by this equation with:

FD=1/2 * CDr * v2 * A

FD: force of drag

CDr: coefficent of drag

v: velocity

A: surface area of the jumper

When we set the FD equal to the Force of gravity on the diver and use the drag coefficient for the density of air and use the area of a diver in the "arch" position we find that the diver find a balance of forces (no acceleration) at about 55 m/s.

When a skydiver wants to deploy their parachute, the most commonly used device used is a manually-operated pilot chute. The diver will reach back into their rig and grab a handle or small bean bag connected to the pilot chute and throw it away from them.

The small pilot chute is affected by an extra drag force attempting to keep it stationary. When this force and the force of the falling diver create enough tension in the line connected to the pilot chute, the deployment bag containing the main canopy is unstowed.

If the main canopy were to expand to full size immediately, the tensile forces between the diver and the main canopy would most likely kill the diver and/or break the lines.