# Parachute Physics Equation

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Does anyone know if there is a relation between the weight of an object with how large of a parachute it will need or anything like that?

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Yes there is.

First you have to determine what your maximum impact speed is. This will be the terminal velocity of your object-parachute system. Set this to whatever feels right within your game/demo. You will probably have to experiment to get this to feel right.

Now for a little bit of basic physics. (Basic meaning easy math). An object in free fall has two forces effecting it. Gravity and Air Resistance. Gravity is "pulling" down and air resistance is "pushing" up so when the two forces equal each other we've reached an equilibrium (no more acceleration). This is the point where terminal velocity occurs or the maximum impact speed. We can solve for this point to determine the relationship between weight and a parachute's size. So...

The force from air resistance can be expressed as R=(1/2)DpAv^2.
R: Air resistance
D: Drag coefficent constant. This constant is dependenet on the objects shape. For example a spherical object has a value of about 0.5 and can get as big as 2 for irregular objects.
p: Density of air (which is 1 in this case). Note this is not a 'p' its the greek letter 'ro', not that it really matters.
A: Cross-sectional area of the object - this would be the area of your parachute in this example.
v: Velocity of the object.

You also have the weight of the object which is its Mass*Acceleration due to gravity (9.8).

So you set the two equations equal to each other...
mg = (1/2)DpAv^2
You've set the velocity to some arbitrary value you've picked. D, g and p are constants (experiment to figure out a value of D that feels right). Which leaves us with m (the mass) and A (the size of the parachute). We've related the weight of an object and the size of a parachute, yay!

The method I've presented is not perfect. It ignores numerous minor factors such as the effect of the object dangling from the parachute on airflow. However, this method should be more than accurate enough for any game or realtime app which I'm assuming is what your asking the question for. If you need more accuracy, we can talk further though I don't know how much I can help beyond this.

Good Luck,
Squirell

[Edited by - Squirell on November 28, 2006 8:57:32 PM]

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Thank you much, I don't have much time to read the reply but I skimmed it and it looks very helpful. I'm off to my EGR and CS classes, so hlpefully I'll have some time to read your post thoroughly a little bit later. Thanks.

Edit: BTW I see you are from Dallas. You wouldn't happen to be a Cowboys fan, I used to live in Plano and I love the Cowboys. They are having an excellent season.

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Haha, yeah I follow the Cowboys.

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This topic is 4036 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.