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If you toss a tennis ball up in the air, neglecting air resistance, but it didn''t go straight up. It went off to the side, so when it came down, it''s path was an upside down U. Two questions: ___ / \ / \ / \0<- ball goes up, then down A. Is the ball''s path vertically symetric at the highest point? B. Suppose the ball had air resistance..it''s path would be similar(as in geometry), but not congruent. Thanks

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A. If you mean if you drew a line at the top of the path to the ground, would both sides be the same, just flipped over, then yes. A ball thrown up like that forms a parabola, not an upside-down U

B. Err, yes, no, maybe. Depends on how strong the wind is and which way it''s blowing. In most cases, the path the ball follows is similarly shaped to the path it would''ve followed if there was no wind.

Hope that helps a little.

"We are the music makers, and we are the dreamers of the dreams."
- Willy Wonka

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Part B of your question is a vector and magnitude issue. As BitBlt said, it depends not only on the magnitude of the wind, but also on the direction the wind is blowing form. For part A, it is symmetric, and forms a parabola like BitBlt stated.

Edem Attiogbe

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...and to extend the realities of Part B in your question, when you add air, you may also want to consider other things like Magnus forces caused by the ball''s surface friction with the air.

If you''re unfamiliar with Magnus forces (and I DON''T want to hear any X-Men jokes ) then you just need to watch a good baseball pitcher or read an article about baseball pitching. They almost always try to explain the effect of object spin on an object path when they discuss the slider or breaking-ball.

---------------
-WarMage
...gravity is Universe''s way of trying to tell you that spandex is BAD...

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quote:
Original post by WarMage
...and to extend the realities of Part B in your question, when you add air, you may also want to consider other things like Magnus forces caused by the ball''s surface friction with the air.

(This response may be becoming over-the-top but gph-gw and others may find it useful.)

Yes, this can add to the realism for good benefit (especially in a sports game) with a little additional computational expense. Magnus force is really the same thing as lift, and it is caused by pressure differences due to air circulation, which is generated as a result of the surface friction WarMage mentioned. I wish I could draw a picture... I''ll give you a secret equation for calculating an estimate of the lift/magnus force on a spinning baseball. It is called the Kutta-Joukowski theorem. Actually, this equation shows up during the derivation of the theorem:

lift force (a vector) = rho * circ * diam * (U cross e)

Here, rho is the scalar air density, U is the velocity vector of the wind---relative to the ball''s center of mass, e is a unit vector indicating the direction of ball rotation, diam is the diameter of the ball, and circ is scalar air circulation given by:

circ = pi * diam * rotational_velocity

where pi is, you know, and rotational_velocity is the magnitude of the rotational velocity of the ball in radians/unit time.

The drag force could also be considered, and it can be estimated as:

drag force magnitude = 0.5 * rho * (U dot U) * CD * Sref

where CD is the drag coefficient (choose CD = 0.5 for a tennis ball----a quick-and-dirty estimate) and Sref is a reference area, use Sref = pi * radius * radius for a spherical ball.

drag force acts in the direction of U and should be added to lift force to estimate the complete aerodynamic force.

As always, make sure your units are consistent!

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

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Good stuff man, good stuff. I knew this forum would be kewl.

"We are the music makers, and we are the dreamers of the dreams."
- Willy Wonka

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I think it would be better to just use simple parabolas. Very few players would actually notice....

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Yeah, but still for the sake of realism, you want all of your playerbase to have a good experience with your game. So having one group notice isn't a good thing because even though you are losing a small amount of your playerbase, it's too large to risk. So I'd opt to use a bit more technology and make your game stand out from the rest that "just use simple parabolas".

Edited by - Erlog on June 21, 2001 2:47:57 AM

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quote:
Original post by gph-gw
I think it would be better to just use simple parabolas. Very few players would actually notice....

Perhaps you are right, for some games such as a tennis game. And most casual players of ball games might not notice or care. I would think that hardcore baseball fans (for example) would definitely notice and appreciate the inclusion of the effects of ball spinning, given that pitchers use spinning as a strategy for pitching strikes. I know my brother, who is a hardcore baseball fan and player of baseball video games, would. Hardcore players include many of the 12-13 year old kids who play these games---they notice all the details, as I''ve observed while talking to the teenage son of a co-worker, and his son''s friends.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

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