Freefalling and body aerodynamics

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Beside the adrenaline rush, skydiving involves some aerodynamic challenges which are not directly evident to the distant observer. Beside establishing and maintaining flight stability which is highly dependent on the arc position and the symmetrical application of the aerodynamic forces around the human body, the free fall velocity (terminal speed) has to be adjusted when considering formation skydiving. A look on basic aerodynamics follows:

W=mg\\ D_{ff}= \frac{1}{2} \rho V^2 S_{exp} C_{D}

At terminal velocity condition and considering a vertical free fall (L=0):

W=D_{ff}\\ mg= \frac{1}{2} \rho V_{term}^2 S_{exp} C_{D}

In order to establish a formation with jumpers of various weights, the terminal velocity (V_{term}) has to be the same for all. This requires different body exposed surface (S_{exp}) for each jumper:

V_{term}= \sqrt{\frac{2mg}{\rho S_{exp} C_{D}}}

For example, for myself being currently on the “heavy side” of the jumpers, the exposed surface has to be larger, which is not directly implied by the increased body mass. In order to do so, arms and legs need to be extended in wider angles without sacrificing free fall stability. Drag coefficient might also experience a slight increase due to the more extended arc position, but the vast increase in drag comes from surface. The “light side” jumpers on the other side need to fall in a less extended position and sometimes even add weight zones to increase their mass…

In other words… sounds like fun!!!

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