I actually wrote a frisbee simulation a few years ago, for Worldbook. If you have a copy of the Worldbook Multimedia Encyclopedia on CD-ROM for Windows, years 1999 or higher, do a search on frisbee. You'll find an interactive simulation that I wrote the physics for.

My simulation was based on the nonlinear Newton-Euler equations of motion, which are fairly complex, and an approximate aerodynamic model. I measured the moment of inertia of an actual frisbee using a trifilar pendulum to get the dynamics to be realistic.

Beyond my little plug, , I like many of the replies here. Sneftel has good advice, with the simple fake approach (though I don't know how well that fake works). And the references to theses and ultimate frisbee sites are good. There are a few links on the web that could be helpful:

Some pretty good ones:

www.afda.com/skills/physics.htm

http://www.ultimatehandbook.com/Webpages/Beginner/physics.html

Some not as good:

http://www.frisbee.com/freestyle/links/sports.html#physics

http://www.physlink.com/Education/AskExperts/ae16.cfm



Graham

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

[edited by - grhodes_at_work on May 2, 2003 5:12:25 PM]

my guess is, a frisbee thrown from the left hand (I''m a leftie) would have a natural tendancy to tilt to the right (?) because the movement of you arm would naturaly tilt the frisbee slightly when you launch it. You can do an opposite movement if you bend your wrist like mad the other way round. However, the fact that it''s rotating counter-clockwise and tilting to the right seems to keep it more stable than when it tilts to the left with the same rotational direction. Some weird-ass physics I''ve yet to comprehend.

From what I understand, the rotation of a frisbee is hardly smooth, and the gyroscpic effect helps keep it balanced. If it starts banking to the left sharply (like with a bad throw or a gust of wind), the pressure on the left side would create more lift on the left, thus making the firsbee tilt back to the right, and so on. It naturally stabilises itself, until it runs out of breath and falls like a stone. If you fire it upwards, when it comes back for you, the added speed of descent and the incline would keep the rotation and stability going.

quote:Original post by TerranFury
You''ve got to deal with gyroscopic effects, as everybody mentioned, and you also have to deal with the frisbee as an airfoil, as has also been mentioned - but in addition to that, you need to deal with the horizontal aerodynamic forces generated by the rotation! One side is moving faster relative to the air than the other side due to the rotation. If the frisbee is rotating clockwise, then it will curve to the left (I think that''s correct). Anyway, you get the point: A fresbee is an ridiculously complicated beast.

Good point about the side force; however, the effect of this is neglible compared with the interaction between the pitching moment (torque created due to pressure differential between top and bottom surfaces) and the gyroscopic effects.

The curving of the frisbee to the left or right is a result of the frisbee turning over as it flies, which in turn is a gyroscopic precession. Think about it this way. If you throw the frisbee perfectly horizontal, it creates a lift that holds in the air. But the lift acts effectively behind the center of gravity, thus creating a torque about the center of the frisbee that tries to flip the frisbee back-over-front. But this torque is merely a change in angular momentum per unit time. If the frisbee was thrown with the left hand, the frisbee has a large angular momentum vector pointing upwards. The back-over-front torque due to lift is basically an increment in the angular momentum vector that points to the left (when you view the frisbee from the view of the thrower). Add a very long vector that points straight up added to a shorter vector that points to the left and you get a long vector that points just slightly to the left. The frisbee thus turns over to the left if thrown from the left hand. Now, once the frisbee starts turning over to the left, the left generated between the top and bottom surfaces now points slightly to the left, and thus the frisbee is now being pulled to the left by the left. The gyroscopic effect continues, and when thrown from the left hand the frisbee will typically continue to turn over to the left, and will begin pulling into a tighter and tighter left-hand-turn. If thrown by the right hand, the initial angular momentum vector is very large and points downward. The gyroscopic effect in this case causes the frisbee to turn over towards the right, and the lift now pulls the frisbee towards the right, causing a tighter and tighter turn to the right. So, the basic flight of a frisbee can be explained purely using longitudinal aerodynamic forces (lift and pitching moment, even drag can be ignored to get the basic effect) and the gyroscopic effect due only to the rate of spinning about the primary spin axis. No need to dig into the more complex aerodynamic forces (side force, yaw and rolling moment, etc.) or off-axis angular momentum.

The reason some people are able to throw frisbees that don''t turn over very much is that they apply much more spin. The more spin, the higher the initial angular momentum and the smaller the change in the angular momentum axis (which basically corresponds to the primary spin axis) and thus the less the frisbee turns over during flight.

Of course, the local wind, and ground effect, can have a dramatic role in frisbee flight, and this can lead to some strange behavior that is more difficult to simulate---but that probably can be faked pretty easily.



Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

quote:Original post by Sneftel
Seems simple enough.... as the frisbee drops, it tilts forwards; and the natural precession of the axis pushes it to the right or the left, depending on which direction it''s rotating in.

Yes, that''s it exactly. I did explain this in more technical detail in my last post. I didn''t read the ultimate frisbee discussion, but perhaps the discussion there was more detailed also.



Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

quote:Original post by oliii
my guess is, a frisbee thrown from the left hand (I''m a leftie) would have a natural tendancy to tilt to the right (?) because the movement of you arm would naturaly tilt the frisbee

The tilting has to do with the spin direction, not the angle at which the frisbee is released. There are a few posts that describe the effect accurately.

But you do have a good point. Sometimes, if you work at it, you can launch the frisbee at such an angle that the lift vector is pointing in a direction opposite the direction of tilt, e.g, throw with the left hand causes a tendency to tilt to the left, but if you release it and it is already titled to the right, then the frisbee will begin flying in a rightward turning path, all the while it tilts back towards the left. I''ve seen this, and frisbees thrown in this way do have some of the more elegant flight paths!


Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.