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:
The winch needs a burst of energy. In the example above, the
energy spent during the 7 seconds of winch operation is more than 100
kJ. A little AA battery contains about 4 kJ. You would need more than
25 AA batteries (this makes less than 1 kg) or just 8 of them for the 2
first
seconds. That seems doable but an AA battery needs a minimum of 1 hour
to release
all its energy. Systems capable of doing that in a few seconds do
exist, but...
The winch is "a moving part". It's reliability is disputable.
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:
At an accurately measured height above the ground, the load would
be released from the parachute and start a bungee free fall towards the
ground.
Once the length of the elastic rope is attained, it begins to
stretch and exerts a force that tends to bring the parachute and the
load back together.
The load, pulled upwards by the elastic rope, will slow down to a
low speed, it can even get motionless for a short while or go
upwards. If everything goes like planed, the load is supposed to touch
the ground at that moment.
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:
The weight of the elastic is 40 kg.
The "landing altitude" is quite unpredictable. Small differences
in the parameters can change it dramatically. For example the
temperature will change the elasticity of the rope, the flackerings of
the parachute are unpredictable...
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...
The bungee
parachute
