The Physics Behind Skydiving

The Physics Behind Skydiving

The motion of a skydiver can be easily explained with a little physics. As a skydiver falls from about 13,000 ft. they start to accelerate downwards. This continues until the terminal speed is reached. This is the speed at which the drag from air resistance exactly balances the force of gravity pulling the skydiver down. The air resistance as the diver falls is dependent on two things; the speed and the cross-sectional area of the skydiver.

Where:

• g is the acceleration due to gravity, which is 9.8 m/s2
• m is his mass
• D is the drag force acting upwards
• W is the force of gravity pulling him down
• v is the speed at which he falls
• vt is the constant (terminal) speed he reaches when D = W

Key Equations

- drag acting on a body is represented by:

Where:

• C is the drag coefficient, which can vary along with the speed of the body. But typical values range from 0.4 to 1.0 for different fluids (such as air and water)
• ρ is the density of the fluid through which the body is moving (in this case, the fluid is air)
• v is the speed of the body relative to the fluid
• A is the projected cross-sectional area of the body perpendicular to the flow direction (that is, perpendicular to v)

- the force of gravity pulling the skydiver down:

- when terminal speed is reached, D = W, so we have:

- to solve for terminal speed v_t we have:

One important observation is that, the smaller the cross-sectional area A is, the higher the terminal speed. Therefore, if a skydiver wants to catch up to another skydiver close by, he can do so by decreasing his A value. One way to do that is to re-orient your body so that your head is facing down. The typical speed of a skydiver is around 120 mph in the spread-eagle position, but he can reach speeds up to 200 mph if he orients his body with head pointing down, while therefore decreasing A.

During their fall, a skydiver can perform many different acrobatic maneuvers such as spinning, moving forward, moving backward, just by changing the shape of his body to "catch" the wind a certain way. This works because they are essentially changing the direction of the drag force acting on their body.

After the parachute is released, the skydiver experiences their last drag force, which slows their descent enough for them to land back on the ground safely.

Sources

1. http://www.physicsclassroom.com/mmedia/newtlaws/sd.cfm

2. https://www.real-world-physics-problems.com/physics-of-skydiving.html