What is the equation for air resistance?

[Irrelephant]

Homework Statement

I would like to know if there is an equation/formula to find out the air resistance of any falling/moving object. This will be used in a simulator in a project I'm doing.

I've looked around and all I can find is 'Do Experiments', 'Wind Tunnels'... This is not useful for me.

One must exist, -how would an inanimate object like a cube know how fast to fall? :P

The Attempt at a Solution

http://www.grc.nasa.gov/WWW/K-12/airplane/dragco.html

That link explains the Drag Coefficient but it says get it from an experient or get it by using an equation to do with Drag force itself? (I don't know drag)

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All in all I want a simulator that a user would create any shape and just drop it (With only gravity acting) and it would say its speed (And loss of speed due to air resistance) It must be possible...

Any help would be greatly appreciated!

Thanks,

 

[PhanthomJay]

The air resistance force of a falling object of sufficient speed is usually assumed to be quadratic in nature and given by the formula D = (1/2)(C_d)(rho)A(v²), where D is the drag force, C_d is the drag or shape coefficient, rho is the density of air (if it is falling through air), A is the projected frontal area of the object, and v is the velocity. C_d is often experimentally determined since it depends on many factors, but here's a list:

http://en.wikipedia.org/wiki/Drag_coefficient

The calculation of the speed at a given point is a bit complex because acceleration is not constant. Ultimately the speed approaches terminal velocity after a few seconds, which is more easily calculated by setting the drag force equal to the weight of the object, and solving for v.

A nice calculator can be found at

http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/fallq.html

however, this is for a spherical shape...you can adjust the drag factor, but you have to come up with an equivalent area for different shapes.

 

[Irrelephant]

The air resistance force of a falling object of sufficient speed is usually assumed to be quadratic in nature and given by the formula D = (1/2)(C_d)(rho)A(v²), where D is the drag force, C_d is the drag or shape coefficient, rho is the density of air (if it is falling through air), A is the projected frontal area of the object, and v is the velocity. C_d is often experimentally determined since it depends on many factors, but here's a list:

http://en.wikipedia.org/wiki/Drag_coefficient

The calculation of the speed at a given point is a bit complex because acceleration is not constant. Ultimately the speed approaches terminal velocity after a few seconds, which is more easily calculated by setting the drag force equal to the weight of the object, and solving for v.

A nice calculator can be found at

http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/fallq.html

however, this is for a spherical shape...you can adjust the drag factor, but you have to come up with an equivalent area for different shapes.

Yeah that all sounds good but still for a simulator for ANY shape it's pretty useless.

Is there a formula for 'drag or shape coefficient'? (Not experimentally)

 

[PhanthomJay]

Is there a formula for 'drag or shape coefficient'? (Not experimentally)

Not really, because the drag coefficient is in part a function of the Reynolds Number, which, in turn, is a function, in part, of the speed and length of the object. The best you can do is to use the approximate Cd factors noted for various shapes, low for spheres, very low for airfoils, bullets, birds, and 'bird shaped' cars, very high for flat surfaces, and somewhere in between for other shapes. For example, if the drag factor for a cylinder is 1, and for a flat surface it is 1.6, for a polygon shaped surface it is 'in between'.

 

[Irrelephant]

There must be one. Bah, wheres Steven Hawking when you need him.

 

[Dadface]

Why must there be one?It seems obvious that the shape and size of an object and all of the other mentioned factors(plus other unmentioned factor such as winds)must affect air resistance and there can't be one single fits all equation.There are numerous examples in science where we have to content ourselves with answers that are rough approximations only.

 

[Irrelephant]

A rough approximation equation would be nice ;)

But yeah in time (Dunno how long) there must be one, -how would nature itself know how an object falls?

 

[PhanthomJay]

A rough approximation equation would be nice ;)

But yeah in time (Dunno how long) there must be one, -how would nature itself know how an object falls?

Nature does tell us how it falls..then we try to figure it all out.