What determines Fall Rate?
by Jan Meyer
Everything in relative work hinges on fall rate. Formations must be built with people who have exactly the same fall rate. Floaters need a slow fall rate at the beginning of a dive to allow the base jumpers to catch up to them. Divers need a faster fall rate, at first, to catch the base jumpers. Before you take grips on a formation you must have the right fall rate. It can't be too fast, else you'll fall out from the formation. If your fall rate is too slow then you'll float above the formation. Neither of these situations is desirable.
If you get below a formation you must slow your fall rate. Similarly, if you are above a formation then you must increase your fall rate. Fall rate depends on your weight and your drag-area. For a given jump, you cannot change your weight, therefore you must change your drag-area to adjust your fall rate. (Fall rate dependance on body weight is not discussed in this article.)
What is drag-area? Drag-area is a combination of your body shape and size. Scientists and engineers have defined two numbers that represent your body shape and body size. Your body shape is represented by a fudge factor called a drag coefficient. Your body size is represented by an arbitrary reference area. Amazingly, aerodynamics can accurately be predicted from these made-up numbers. The trick works because the product of these parameters is the important number and not either number by itself. It's the drag-area that is important, not the drag coefficient (body shape) or the reference area (body size) by itself. Fall rate is determined from the combination of body shape and body size, not by either one alone.
The drag coefficient (body shape) represents how hard it is for the air to get around you. When it's real difficult for the air to go around you, the air will push harder on you and your fall rate will decrease. Likewise, when the air easily flows around your body, your fall rate increases. In the first case you have a high drag coefficient and in the second case you have a low drag coefficient. Your body shape determines your drag coefficient.
Shapes that allow air to flow smoothly and easily past them are called streamlined. These shapes are found on wings, rudders, stabilizers and struts of aircraft. The motion of the air follows nice, orderly paths as shown in Fig. 1a. These shapes have very low drag coefficients and produce very small drag forces. Streamlined shapes can pass through the air very fast.
Shapes that significantly disturb the air flow are called bluff bodies. The air does not travel smoothly past bluff bodies. The air flow on the downwind side of the body is chaotic and random. The air goes this way and that way. This region is called a wake or as skydiver's like to call it, a burble. The middle of the wake, close to the bluff body, actually has some air flowing directly towards the backside of the bluff body. Because of this air flow, the very near wake region is called the recirculation zone. This is the place where hesitating pilot chutes hang out. Part of the flow over a bluff body is orderly, but a substantial portion of it is disordered, as shown in Fig. 1b. Bluff bodies have high drag coefficients and produce large drag forces. Bluff bodies pass through the air rather slowly.
Some shapes catch air on the upwind side and create a wake region on the downwind side, as shown in Fig. 1c. Bowls with the opening into the wind will do this. Conventional round parachutes catch air on the upwind side and generate a large downwind wake. These shapes have still larger drag coefficients.
You can vary your shape. This changes the drag coefficient. The more you resemble streamlined shapes the lower your drag coefficient will be. Your drag coefficient increases when your shape resembles a bluff body. This occurs when you're in an RW stable position. When you de-arch and roll your shoulders forward you will catch air in front of you. This will make your drag coefficient increase even more. Increasing your drag coefficient will tend to slow your fall rate.
As mentioned before, your body size is related to an arbitrary reference area. Sometimes a fixed area is calculated from some obvious geometric dimensions of the body. Aircraft reference areas use the wing span times the average chord length to get a planform area. This area is used no matter what flight configuration the aircraft may be flying in. Skydivers could define a reference area as height times width.
Sometimes an area related to flight configuration is desirable. In these instances, projected area is normally used as the reference area. Projected area is the amount of area you would see if you looked at a jumper while in his flight path, as shown in Fig. 2. You would see the head and shoulders of a diving jumper. This is a small area. A tracking jumper would have a slightly larger projected area. You'd be able to see the front side of a tracking jumper at a steep angle while observing from his trajectory. A face-to-Earth jumper would have an even larger projected area. The largest projected area is when you have your arms and legs extended and in the same plane as your body. Your ankles, knees, hips, wrists, elbows and shoulders all lie in the same plane too. This position can easily be demonstrated by lying down (face up or down, your preference) on a flat surface with your arms and legs extended. This is a spread eagle position with no arch. The angular orientation of your limbs does not effect the projected area. Your arms could be at your sides, one arm out and one arm in, or both arms bent, as long as they're touching the surface your torso is on, then your projected area will be the same. Jumpers doing dead spiders have smaller projected areas than this maximum. In fact, the dead spider projected area is about the same as the normal face-to-Earth projected area.
Fig 2: Projected Area of skydivers in several freefall positions. Top shows position. Bottom shows projected area.
Drag-area determines fall rate, for a fixed weight. The combination of body shape and body size are used to adjust fall rate. Neither body shape or body size, by itself can determine fall rate.
Your body shape determines your drag coefficient. The more streamlined you are the lower your drag coefficient and the faster you will fall. Your body size is represented by your projected area. The larger your projected area the slower you will fall.
Your body size and shape work together to determine your fall rate. If your increase your body size, but make your body more streamlined, the net effect could be to increase your fall rate. This is exactly what you do when you change from a dead spider position to an RW stable position.
It's important to realize that it's drag-area that determines your fall rate, not just your body size (projected area) or just your body shape (drag coefficient). A good example of this dependence is when you go from a slow RW face-to-Earth position to a dead spider position. Suppose that you had 100% of your maximum body size (projected area) in your RW position. Then in your dead spider position, you only had 70% of your maximum body size (projected area). You have decreased your body size (projected area). This alone should decrease your drag-area and should make you fall faster, not slower. Since you catch air with your torso, your drag coefficient (body shape) increases and should make you fall slower. Your drag coefficient increases much more than your projected area decreases. The overall effect is to increase your drag-area and slow your fall rate.
Originally published in Sport Parachutist's Safety Journal V2, #5 Jan./Mar. 1991.
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