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# The Math Behind a Frisbee

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Does anyone have any information or links to information on the math behind the flight of a frisbee? I searched the forums and google and found a few decent articles but they just describe the physics without ever telling me how the math behind it works. The one post I found on here looked like it was going to be good but the guy never finished posting to it after he got back from SIGGRAPH. I''m really interested in learning about the frisbee flight and the math behind it. The_Ethernopian

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Oooooo, do I smell an Ultimate Frisbee game in the works?

-- John

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The deal here is, don't expect to find any nice, simple math. This is aerodynamics, and aerodynamics is reeeeally difficult.

Luckily, you can fake it. I suggest the following:

1. Rotational speed "a" decays exponentially. This is complete fakery.

2. Vertical air resistance is proportional to (1-tilt)(1 - (1/a)), where "tilt" is 0 for a flat frisbee and >0 otherwise. This is also complete fakery.

3. Horizontal air resistance is 0. Absolute, total fakery.

4. Acceleration is the projection of the normal vector of the frisbee onto the XY plane. Not sure if this is fakery, but I assume it is.

How appropriate. You fight like a cow.

[edited by - sneftel on May 1, 2003 5:11:12 AM]

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Seems to me if you know the physics, you should know the "math" involved.

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quote:
Original post by Hoser
Seems to me if you know the physics, you should know the "math" involved.

No, not necessarily. Physics is like knowing what the phenomena is, while the math is quanitative model describing it.

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i read a paper about a boomrang once... if a frisbee is een nearly as complicated, youre in trouble .

but if you have a decent general understanding of physics, you should be able to come up with some aceptable faking indeed.

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Haha even completey removing aerodynamics, a 3D rotating body runs you right into the moment of inertia tensor. Its no wonder no one explained the math! I dimly remember doing it in an advanced mechanics class, but its all so foggy now

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Yeah, you could go for gyroscopic effects and precession (which, of course, frisbees do) but I think a few simple rules like I described earlier would be more than adequate, given some studious parameter tweaking.

How appropriate. You fight like a cow.

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quote:

1. Rotational speed "a" decays exponentially. This is complete fakery.

2. Vertical air resistance is proportional to (1-tilt)(1 - (1/a)), where "tilt" is 0 for a flat frisbee and >0 otherwise. This is also complete fakery.

Not sure if I agree with those. I''m positive rotational speed does not decay exponentially. It''s also difficult to measure the "Vertical Air Resistance," because a frisbee flies mostly by generating lift.

Yeah, I know. You weren''t trying to be absolutely precise or anything. But I figured I''d put my 2 cents in

-- John

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well, the rotational velocity decrease would correspond to the friction of the outer edge of the frisbee with the air. The faster it turns, the more the friction. So friction force and fluid dynamics... too complicated for me. Then, if it''s exponential or not...

From my crude understanding of physics, As the frisbee rotates, the air under it is pushed towards the edges of the frisbee, due to the friction of the air with the bottom and inner edge of the frisbee and the gyroscopic effect (ever wondered why your clothes in a washing machine end up stucked to the edges?), which in turn, is pushed down due to the curvature of the edge. The more it rotates (i.e. the more it spins), the faster the air is shoveled to the edges, the better the lift. And as the frisbee falls down, the air pressure under it increase, thus creating more lift and slowing the rate of descent, but also increasing the friction and slowing the rotation, which in turn decrease the lift, ect...

Which would explain why the frisbee I''ve got have a smooth and shiny top surface, and a rough bottom surface. Arggh! Why does it have to be so complicated?

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