# The Naked Scientists Forum

### Author Topic: Is there a formula for parachute size?  (Read 6364 times)

#### chris

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##### Is there a formula for parachute size?
« on: 17/05/2013 10:32:09 »

"I am making my own rockets; I am wondering how to work out how large to make the parachute to recover the rocket. Is there a formula that can tell me the right size to use?"

I advised the young man who called in that he could do some simple experiments, varying the mass of a payload falling over a set distance, to find out how much drag he needed to achieve a satisfactory recovery velocity. But I also promised I'd ask everyone here for some suggestions regarding how he should calculate the dimensions of his parachute to achieve a descent speed suitable for his rocket.

Chris

#### David Cooper

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##### Re: Is there a formula for parachute size?
« Reply #1 on: 17/05/2013 18:50:40 »
It is a good question. It would be interesting to know how the density of the atmosphere affects it too, and if there's a difference between area and the type of parachute - the old round ones (which you'd use with a rocket) look a lot bigger than the steerable kind used by people today.

#### chris

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##### Re: Is there a formula for parachute size?
« Reply #2 on: 17/05/2013 22:48:27 »
Do you know, David, that's exactly how I opened my answer on the radio - mentioning that one should, when making rockets, also consider atmospheres on other planets and celestial bodies since some, like Mars, have a thin atmosphere and will require a much bigger 'chute, while other places - like Titan - have very thick atmospheres where said parachute can afford to be much smaller.

But that's sort of the point where my wisdom ran dry and I had to admit that the best I could advise would be a series of simple experiments, varying the load and parachute area to see how the two are related; I would expect, over a smallish range of the two, that the relationship should be linear shouldn't it...?

#### evan_au

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##### Re: Is there a formula for parachute size?
« Reply #3 on: 18/05/2013 01:49:28 »
There is more to it than just area:
• It needs to be as strong and light as possible (a lead parachute would not be very effective, regardless of the area)
• You need to let the air out of the parachute in a controlled manner, or you will end up with wild oscillations or even collapse of the parachute. This is why there is often a small hole at the top, see http://en.wikipedia.org/wiki/Parachute#Round_types
• It needs to be reinforced so that the load is distributed evenly, and so it doesn't rip (or if it does tear, the size of the tear is limited)
Here is an interview with a designer on the Mars Curiosity parachute, which had to deal with opening at supersonic speeds (requiring holes around the middle), and difficulties in doing a realistic test programme before deployment! (1 hour podcast) http://omegataupodcast.net/2012/12/110-curiositys-landing-on-mars/

#### damocles

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##### Re: Is there a formula for parachute size?
« Reply #4 on: 18/05/2013 03:05:42 »
For a reliable introduction to the subject of air resistance and "terminal velocity", check out these websites:

http://batesvilleinschools.com/physics/APPhyNet/Dynamics/Newton's%20Laws/air_resistance/air_resistance_ap.htm
http://batesvilleinschools.com/physics/PhyNet/Mechanics/Newton2/air_resistance.htm

The formula you are looking for depends very much on how you choose to model the situation. The first thing that you will have to decide is what is the acceptable terminal velocity. This in turn will be governed by the sort of terrain in the "drop zone" and whether you are wanting to allow for the contingency of missing it. Obviously the terrain of the drop zone will affect the acceptable terminal velocity: snow > water > field > rocky terrain.
For a spent rocket the dominant term in the air resistance equation will probably be the v2 term, so that the necessary area will not be directly proportional to the mass.
The (only) good news is that the viscosity of the gas mixture will not depend on the exact mix of gases present (ideal gas approximation), but it will depend both on the pressure and the temperature.

#### chris

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##### Re: Is there a formula for parachute size?
« Reply #5 on: 18/05/2013 10:37:03 »
As Evan is turning out to be quite a radio star (just via the web the special podcast from yesterday has already been downloaded 1000 times!) I would really like to audio record the opinions and perspectives of our forum-goers who are so good at answering these questions.

We've got a channel account with AudioBoo; this has an interface to allow you to record Boos into the site: http://audioboo.fm/channel/nakedscientistspodcast

Could you guys each do us a brief "boo" - not more than a minute or so, on what you think the pertinent points are?

Chris

#### evan_au

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##### Re: Is there a formula for parachute size?
« Reply #6 on: 19/05/2013 05:05:38 »
One "boo" delivered...

#### chris

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##### Re: Is there a formula for parachute size?
« Reply #7 on: 19/05/2013 12:10:12 »
Thanks - and it's lovely; now let's convince everyone else to boo too!

#### David Cooper

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##### Re: Is there a formula for parachute size?
« Reply #8 on: 19/05/2013 20:26:06 »
I don't like the sound of my voice and have a very bad microphone which makes it sound even worse. Fortunately, you shouldn't need my contribution.

#### chris

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##### Re: Is there a formula for parachute size?
« Reply #9 on: 19/05/2013 22:07:01 »
Oh, go on David; you make interesting points, and if the sound quality is poor we'd not use it.

C

#### David Cooper

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##### Re: Is there a formula for parachute size?
« Reply #10 on: 20/05/2013 19:02:51 »
Which means you wouldn't use it. I expect you'll have heard the expression, he has a radio face. Well, I really do have a book voice (and a radio face to boot).

#### The Naked Scientists Forum

##### Re: Is there a formula for parachute size?
« Reply #10 on: 20/05/2013 19:02:51 »