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(>-------------------------oThe bungee parachute









A parachute is an excellent way to land a free-falling person safely on the ground. A typical parachute diameter for this would be 8 meters, which is about 50 m2 surface. The landing speed will be about 5 m/s. To land probes on Mars or very heavy weights on Earth, though, the parachute surface needed appears to be too gigantic (the Martian atmosphere is very thin). So, the parachute is complemented by a rocket motor system and/or huge airbags. The parachute brakes most of the fall speed, then the rockets and/or the airbags allow a soft landing.

Another way to land a load using a small parachute would be to use a long rope between the parachute and the load. Once close to the ground, a winch rolls up the rope very fast. This increases the speed and the drag of the parachute. The fall speed of the load will be much slower, it can even hover above the ground or go back upwards for a short while (say to avoid an impractical landing zone).

Next graph shows the result of a rough numerical simulation. A 100 kg load is attached to a 5 m2 parachute by a 100 meters long nylon rope of 2 millimeters diameter. The parachute starts at an altitude of 3.00 km, the load is 100 meters below.





At t = 5 seconds, the system stabilized at a descent speed of 20 m/s. The winch is started and rolls up 15 meters of rope per second. The load quickly stops falling, rises a little bit in the air, then gets on descending very slowly. If the ground was at that altitude of 2.80 kilometers, the load would land like a plume. At t = 12 approximately, the rope is rolled up and the system gets back descending at the 20 m/s speed.

This system has two drawbacks amongst others:
While pondering on the subject, I thought it would be fine if the rope could be a stretched elastic. The elastic would be released once close to the ground, to pull the parachute and the load towards each other. But... what would keep the elastic stretched? Maybe use a nanotechnology rope that contracts like a muscle? Maybe use a hollow elastic, inflate it like a kid baloon and deflate it suddenly? Maybe stretch the elastic, freeze it stretched and use an electric current to soften in back to life? Then I thought of a simple way to stretch the elastic: just let the load fall to the ground, like a bungee jumper. This would be the sequence:




The graph below shows the result of a numerical simulation of a system dropped from 3 kilometers altitude. The parachute has a surface of 5 m2 (diameter of 2.5 m), the load has a weight of 100 kg and the rope is a 100 m rubber elastic with a diameter of 2 centimeters.





At t = 5 seconds, the parachute and the load stabilized at a descent speed of 20 m/s. The load is released and begins its free fall while the 100 meters of elastic rope deploy. At t = 15, the load is braked to a slow 2 m/s.

A low load speed is maintained for approximately 3 seconds, on a descent height of 20 meters. This can seem excellent, but:
So, real world systems, using less rope weight, will need something to tune the landing height during the bungeeing. Maybe a fast little winch can be powered by some length of elastic that was rolled up stretched. Conversely, a powerless system can release short lengths of rope calculated in real time...


The simulations were not cross-verified. If you'd like to go hunting big errors, check the level of approximation or try simulations with other dimensions, the source code of the routines can be downloaded here. You need an Ada compiler and the XGRAPH plotting software (both are free).

The idea of pulling on a parachute dates from when I was a kid. I imagined the parachute would be around a harpoon and the load would shoot the harpoon back high in the air, each time the rope was winched up. That way the load would stay in the air...



Eric Brasseur  -  September 3 2008
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