# Free Fall Speed Calculator

This is a fun but technically correct tool. You can use it to broaden your understanding of how fast you can free fall and what would it take to make that happen, like what would it take to fall at the speed of sound. After you exit the aircraft, gravity accelerates you until your aerodynamic drag (upward force) just exactly matches your weight (downward force). This balance of forces occurs at a speed called terminal velocity. Once you have reached terminal velocity you will not go faster no matter how far you fall unless you change your body shape/position to lower your aerodynamic drag.

The first input is your “all up” weight, including your equipment.

Next input is your frontal area in square inches. Frontal area is defined as the area of your silhouette as viewed from the spot you are moving toward. Note that some books use different area definitions to do the same calculation so be careful about the exact names if you look up other references on the subject. Here is a way of measuring frontal area that we have found easy and accurate enough (there are very precise laser beam scanners to do this if you can find access to one). Lie or stand on a big sheet of paper in a body position which represents how you intend to fly. Use a carpenter’s square or a long carpenter’s level held vertical to transfer/draw the perimeter of your body shape onto the paper. Then fill the interior of this outline with a square gridwork of lines one inch apart in both directions. Finally, count how many squares are inside your outline. This number is your frontal area in that body position. Obviously you can do this again for a variety of body positions. As a sanity check, standing (head up or head down doesn’t make any difference in the area measurement) you will get about 250 square inches and lying down you will get about 850.

Next input is coefficient of drag or Cd, a dimensionless shorthand way of describing how well streamlined you are or aren’t. Accurate determination of Cd requires putting the shape into a wind tunnel with an force measuring system. This has been done for a human body standing straight up, sitting, and lying down. All you ever wanted to know about drag including this is described in the “bible” of aerodynamic drag, a book called “Fluid Dynamic Drag,” by S.F.Hoerner, which you ought to be able to find in most libraries. Motorcycle racers, ski jumpers, etc., who have big budgets actually get into a wind tunnel to measure their Cd. But ballpark estimates are accurate enough to give you some interesting food for thought. In very rough terms, Cd is around 1. Well streamlined shapes like a race car or a sky diver falling head down with arms at sides would have Cd well below 1, maybe as low as 0.3 or 0.4. A very blunt shape like a ball or spread eagle sky diver with a floppy suit would have a Cd higher than 1, maybe as high as 1.3 or 1.4. A circular parachute is generally considered to have a Cd of about 1.4, High Cd means slow free fall and low Cd means fast free fall.

The last input is altitude. The reason you must select an altitude is that air density changes as altitude changes. Density increases as you fall, thereby increasing your aerodynamic drag. This changes your terminal velocity. For example, if you assume a constant body position at exit and don’t change it you reach terminal velocity, the fastest you can possibly go, at about 12 seconds after exit. From that altitude until you pull you are slowing down because the air is getting denser as you fall. NOTE: You must select an altitude from the calculator menu to recalculate the output, even if the value you want is already displayed in the window on the table.

OUTPUT:

**Rho**: Rho represents the density of the air in slugs per cubic foot at the selected altitude. A slug is a mass which weighs 32.2 pounds, a term you may not be familiar with. One half times rho times the square of the velocity in feet per second gives you the dynamic pressure (also known as ram pressure) against your body at that altitude, in pounds per square foot

**Frontal area:** Your input divided by 144 to convert to square feet

**Loading:** Your weight divided by your frontal area. Small, heavy people have high loading and fall fast.

**Velocity:** Your terminal velocity is calculated and presented in both feet per second and miles per hour. International

jumpers whose heads work in meters per second should divide feet per second by 3.28; or velocity in meters/second is about a third of the answer in feet/second. And remember, the free fall speed you calculate is only momentary as you pass through the selected altitude.

Chuck Eastlake

Professor of Aerospace Engineering

Embry-Riddle Aeronautical Univeristy