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Fall speed

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**Descent spd**

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/m^{3}) 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.

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*.

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 changing pressure, according to the definition of the standard atmosphere.
- The temperature that varies according to the same definition.
- And, of course, the weight of the payload, and the diameter of the parachute.

**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)

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)

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

**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 |