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Descent speed


Author: John Coppens ON6JC/LW3HAZ
Even more than pressure and height calculations, it's not easy to obtain reliable formulas to calculate parachute descent speeds. There are a few siteson the web that have interesting information on the construction of parachutes. I found one site that had a Java calculator.

These formulas are probably correct, but are not too useful to determine the total descent time: all are based on a constant air density (1.225 kg/m3) which is the density at 0 meters, and at 15°r;C. For a payload, falling from 30 km high, where the density is 150 times lower, and temps are 50 degrees below 0, the result is far from correct.

Disk calculator for parachutes

A few years ago I received through a publication, a graphic calculator (designed by the people at the University of Minnesota), which enables you to make a much more logical approximation to the problem: apart from weight and 'chute diameter, it takes into account the air density of the starting point. The result is the total descent time.

Here'sthat graphic calculator. The link gives a .GIF (55k) with a resolution of 300 dpi, ready to be printed, each disk separately.

Formulas

It's just a little impractical to have to know the pressure at the start of the fall, and, in these computerized times, those graphical things have lost some of their charm (though they do have their advantages!)

So, after some number juggling, I've derived a formula that takes into account:

The formula is a numerical appoximation, resulting from integrating the flight path from 0 to 40 km. How to obtain it, is probably of little interest to most.

MIND: All the formulas use metric units! (like hectoPascal (hPa), g in m/s², height in meters (m), etc.)

Original formula - descent speed \(r=\sqrt\frac{2*g*W}{0.75*\rho*A}\)
\(A=\frac{\pi*\rho^2}{4}\)
Descent time: First calculate \(a_n=-20.0508+\frac{3.166*10^6}{h+57140}\)
\(t=a_n*h*\sqrt{\frac{0.03*D^2}{W}}/60\) (minutes)

A
Parachute area (m)
h
Height in m
D
Diameter of the parachute (m)
W
Total weight (parachute+payload) (gr)

Slide calculator

Finally, I decided to make a slide calculator to determine:

-Final descent speed
-Weight
-Parachute diameter
-Descent time
-Height

Here's an image of the calculator: (Click to enlarge)
The slide rule

If you're interested in reproducing the calculator, here are 300 dpi images ready to be printed:

Slider
globocalc_slider.jpeg
Fixed
globocalc_sleeve.jpeg

References

1er Simposio de Comunicaciones Satelitales y Digitales para Radioaficionados
AMSAT Argentina - 22/23 de setiembre de 1990
National Balloon Symposium Proceedings
Denver, Colorado. August 20,21,22, 1993
JAVA-aided Design of Parachutes
[WWW::link http://www.cs.auc.dk/~dorf/Kites/Plans/JavaChute/ http://www.cs.auc.dk/~dorf/Kites/Plans/JavaChute/]
Hemisphere Parachute Design
[WWW::link http://www.sct.gu.edu.au/~anthony/kites/parafauna/chute_design/ http://www.sct.gu.edu.au/~anthony/kites/parafauna/chute_design/]

(c) John Coppens ON6JC/LW3HAZ mail