# Aerodynamics of a flying disc

by apollo100
Tags: aerodynamics, disc, flying
 P: 7 Why does a Frisbee delivered by a right handed thrower with a back hand release tend to roll to the left? or in general: Why does a flying disc tend to roll in the opposite direction that it is spinning? (see attached image)
 Sci Advisor P: 842 The edge of the Frisbee which is spinning in the direction of flight is moving through the air faster than the opposite edge. This results in slightly greater lift on that side, which causes it to lift upwards with respect to the opposite edge and the Frisbee tilts. Since the Frisbee also has a net upwards lift, it turns in the direction of the tilt.
 P: 7 That's what I would think, but the edge of the disc that is spinning in the direction of flight is the one that goes down. That is what I don't understand...
P: 4,780

## Aerodynamics of a flying disc

If you look at the equations of motion you will find a coupling term in the inertia tensor.
 HW Helper P: 6,925 The disc normally experiences a pitch down torque due to it's shape (cambered airfoil) and forward movement. The gyroscopic reaction to the pitch down torque is a roll reaction based on right hand rule (or left hand rule if you keep everything consistent). A flying ring would normally have a forwards center of lift, resutling in a pitch up torque, also resulting in a roll reaction. An "Aerobie" is a flying ring is designed to keep the center of lift close to the middle, minimize any pitch torque, and if properly "tuned" (before throwing it you flex it in the concave or convex direction), will fly straight without rolling. http://en.wikipedia.org/wiki/Aerobie http://www.aerobie.com/Products/Deta...tificPaper.htm
PF Gold
P: 619
 Quote by Jeff Reid The disc normally experiences a pitch down torque due to it's shape (cambered airfoil) and forward movement. The gyroscopic reaction to the pitch down torque is an inwards roll. A flying ring would normally have a forwards center of lift, resutling in a pitch up torque, resulting in a outwards roll. An "Aerobie" is a flying ring is designed to keep the center of lift close to the middle, minimize any pitch torque, and if properly "tuned" (before throwing it you flex it in the concave or convex direction), will fly straight without rolling. http://en.wikipedia.org/wiki/Aerobie http://www.aerobie.com/Products/Deta...tificPaper.htm
I would just like to rephrase this as since the torque is negative it experiences a left roll. Oppositely if the torque is positive it experiences a right roll.

(Just wording it in a more palatable language =] )
 P: 7 Thanks for the info!
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P: 6,925
 Quote by apollo100 Why does a Frisbee delivered by a right handed thrower with a back hand release tend to roll to the left?
It should roll to the right, which is what mine do. For a frisbees (cambered disk), the roll is such that the forwards moving edge moves upwards while the backwards moving edge moves downwards, but this is more related to pitch down torque related to a cambered airfoil and the gyroscopic roll reaction to pitch torque than any difference in lift. For a flat flying ring, the pitch torque is upwards, resulting in the opposite roll response. The Aerobie is a flying ring designed so that the airfoil and center of lift don't produce a pitching torque.

 Quote by djeitnstine I would just like to rephrase this as since the torque is negative it experiences a left roll. Oppositely if the torque is positive it experiences a right roll.
I corrected my previous post.

Depends if the disc was thrown with clockwise spin or counter-clockwise spin. Right hand (or left hand) rule applies. Clockwise spin occurs from a right handed inside toss (like a backhand stroke in tennis), or from a left handed outside toss (like a forehand stroke in tennis or a side arm throw in baseball), counter clockwise for the other combinations. For clockwise spin, pitch down torque results in right roll, for counter-clockwise spin, pitch down torque results in left roll. Pitch up torque would result in the opposite roll response of pitch down torque.

A typical right handed inside toss of a frisbee results in a right roll, so throwing with outside edge down helps a bit.

A "tuned" Aerobie doesn't roll, and requires very little angle of attack, and a nearly horizontal throw is best.
 P: 7 Just to make sure I understand. This effect is caused by the gyroscopic response to torque and not the aerodynamics? As another example: Olympic discus throwers experience a similar effect. Throws either land fairly flat or roll inwards. They never roll out, regardless of wind direction. Based on what I've read so far then: Because right handed discus throwers produce clockwise spin, when viewed from above, the downward pitch torque produces a gyroscopic reaction that causes a roll to the left. Please correct me if I'm wrong, and thanks again for the help.
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P: 6,925
 Quote by apollo100 Just to make sure I understand. This effect is caused by the gyroscopic response to torque and not the aerodynamics?
Pitch torque results in roll reaction and vice versa. The control inputs for a helicopter are set 90 degrees out of phase to compenstate for this.

 As another example: Olympic discus throwers experience a similar effect. Throws either land fairly flat or roll inwards. Based on what I've read so far then: Because right handed discus throwers produce clockwise spin, when viewed from above, the downward pitch torque produces a gyroscopic reaction that causes a roll to the left.
A discus is a symmetrical airfoil, so I wouldn't expect a pitch down torque. If you look at the video below, the discus mostly maintains it's angle of attack with respect to the ground, although the camera angle make some of them appear to pitch up. You probably want to turn off the sound.

http://www.youtube.com/watch?v=XoT5Dv0JO2k&fmt=18

If there was a pitch down torque, the reaction would be a right roll, not a left. This is how right hand back hand throws of frisbees react, so most throws are done with a bit of left roll, knowing that the frisbee will roll righ, to level out before continuning to roll right and veer off to the right.

Some toy boomerangs are thrown overhand at an angle, so counter-clockwise when viewed from above, have pitch up torque, so it's again a right roll. Thrown with just enough initial left side down, the boomerang will roll right (outwards) to horizontal on it's return path, and continue to roll right (now inwards) enough to do a figure 8 pattern.
 P: 7 Ok. Sorry, I'm a little slow. So a discus rolls inward because the leading edge is being pushed up?
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P: 6,925
 Quote by apollo100 So a discus rolls inward because the leading edge is being pushed up?
A discus probably doesn't roll, or at least not significantly. Looking at the video, the discus seems to maintain it's attitude until it impacts with the ground.

Use right hand (or left hand, but right hand rule is the convention) to figure this out. A clockwise spinning disk has a large angular momentum vector pointed downwards. The mathematics for precession is the cross product of the angular momentum and torque vectors, but it's easier to visualize this using vector addition. A pitch down torque is a small torque vector to the left. If you add the small left vector to the large down vector, the new vector points down and to the left, the equivalent of a right roll. This isn't a proper mathematical model, but it can help to understand pitch torque to roll coupling or vice versa.

Here's a wiki link with a diagram, note the circular arrow above the top is a view from above the circular arrow (the top is precessing counter-clockwise as viewed from above). The top precesses in the same direction as it spins (ωprecession has the same sign as ωspin)

http://en.wikipedia.org/wiki/Precess...28Newtonian.29
 P: 7 Actually, being very familiar with discus throwing, they very often roll in to some degree. In fact, with a little help from a quartering head wind, record throws almost always land vertically, frequently rolling inwards 45 degrees.
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P: 6,925
 Quote by apollo100 Actually, being very familiar with discus throwing, they very often roll in to some degree. In fact, with a little help from a quartering head wind, record throws almost always land vertically, frequently rolling inwards 45 degrees.
Olympic style discus? In the video above, the top throws didn't appear to have much roll at all. It's possible that a right handed thrower initiates a left roll in addition to clockwise spin at release. I'm not sure how much affect areodynamic pitch related torque would have on a 2kg discus.

For clockwise rotation, a pitch up torque results in a left roll response, the opposite of a frisbee, where the cambered airfoil causes a pitch down torque. By flexing an aerobie upwards or downwards, you can get either response.
 HW Helper P: 2,156 Getting back to the original question, tilt is actually the most important factor. Most frisbee throws are tilted slightly and the disc will curve toward whichever edge is tilted down, almost as if it's "sliding" on an invisible ramp of air. Most people let the loose edge (the one they're not holding) hang a little when they throw a frisbee, and that's the reason a typical backhand throw by a right-handed thrower curves left - the loose/low edge is the left edge. But if you're careful to keep the loose edge elevated as you release, you can easily get the disc to curve the other way. The Wikipedia article http://en.wikipedia.org/wiki/Physics_of_flying_discs has some interesting (and hopefully correct, though I can't personally vouch for it) info. (BTW my last paragraph comes from many years of experience throwing frisbees, not from Wikipedia)
 P: 7 As a college thrower I personally experienced the flight characteristics of the 2k disc. I just never understood the physics of it until now :-) I've often wondered why so many throws (at all levels) roll inwards. I'm still not sure I completely understand it, but I really appreciate all the help.
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 Quote by apollo100 I've often wondered why so many throws (at all levels) roll inwards.
If you look at any videos of a discus thrower, they hold the discus so the outside edge is down and the inside edge is up, in order to keep the discus from falling downwards out of the hand of the thrower. A bit before release, the thrower lowers the inside edge and/or raises the outside edge of the discus, imparting an inwards roll before any significant spin is imparted to the discus. The momentum of the inwards roll will be conserved during the toss. The 2kg mass of the discus is enough that aerodynamic torque / roll coupling is probably very low.

A frisbee and aerobie are affected by pitch torques, responding with roll reactions. The Aerobie case is covered here:

Early experiments concentrated on thin flying discs, but most airfoils have their center of lift at the quarter chord which is too far forward of the center of gravity (at the half-chord). This produces a pitch-up moment which gyroscopic precession converts to sideways roll. (The point of the article is to describe how the pitching moment was reduced so a small amount):

http://www.aerobie.com/Products/Deta...tificPaper.htm

For conventional cambered airfoils such as the Frisbee:

Conventional cambered airfoils supported at the aerodynamic center pitch nose-down so the pitching moment coefficient of these airfoils is negative

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

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