# Rotational speed of a discus

I was wondering whether the rotational speed of a discus has any influence on the flight of the discus. Would slowing the rotation or speeding it up change the trajectory in any way or would the flight simply become unstable when slowing down?

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## 3 Answers

Allegedly the rotation has two effects. I say "allegedly" because although I was told this in physics lectures at university I'm not sure if anyone has ever rigorously proved it.

Anyhow, with the disclaimer behind me, the first effect is that the angular momentum stabilises the angle of the discus as it travels through the air. That allows the angle of attack to be maintained at the optimum value and hence increases the lift and therefore the range. The second effect is that a high rotational speed makes the boundary layer turbulent, and this decreases aerodynamic drag and once again increases the range.

Given this I guess higher rotational speed is better, though presumably an athlete is limited to how high a rotational speed they can generate without compromising the speed they can throw at.

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+ This reminds me of a related issue - how does a frisbee work - but in that case there's more of an airfoil effect, I would think. – Mike Dunlavey May 31 '12 at 20:21
I take it then that accelerating the angular moment influences only the distance and stability of the flight, but I cannot "steer" the discus to the left or the right by accelerating or slowing down the angular moment, right? – cdecker May 31 '12 at 20:46
@cdecker: don't forget, it's a gyroscope, and gyroscopes precess. So if there is a force to cause it to "pitch up", that will make it roll right or left, and vice versa. Which way it goes depends on the direction and rate of spin. – Mike Dunlavey Jun 1 '12 at 0:36

The faster it spins, the greater the aerodynamic side force on it; see Magnus effect.

Also, higher rotation increases the $\mu$ (ratio of edge speed relative to body to airspeed of the body) of the disc; the higher airspeed of the advancing edge relative to the retreating edge creates asymmetric lift & drag. The former would impart a rolling moment, while the latter would impart a moment opposing the in-plane rotation of the discus.

All that said, I doubt either are particularly significant effects.

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Simply on one side the airspeed is higher than the other side, affecting the lift and drag on each side. This causes the discus to drift or slice. – ja72 Jun 1 '12 at 1:55

Given the physical conditions, this seems like an appropriate explanation: The faster the discus rotates, the more violently and quickly it displaces the air around it. Now the absence or scarcity of air causes a reduction in air friction or viscosity around the discus and this allows it to move onward in the direction of propulsion; now that depends on what angle the athlete projects it. After a certain distance there begins a constant deceleration of rotational speed because at some point, the air friction starts overpowering the rotation and this results in the discus entering the second half of its trajectory, i.e., moves downward along a curved path. I hope that answers your question.

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Maybe I'm not used to the lingo, but "violently and quickly it displaces the air" and "absence or scarcity of air" doesn't sound like the kind of aerodynamics I'm used to. Want to give it another shot? – Mike Dunlavey May 31 '12 at 20:25
What I was trying to convey by the use of the quoted phrases was that Bernoulli's Principle comes into play in this situation. – Graviton Jun 1 '12 at 6:53
Let me suggest alternate wording, then you do what you want: The disk is an airfoil whose orientation is gyroscopically stabilized. As it follows its (nominally parabolic) arc, as it goes into the descending portion of the arc, its angle of attack increases. The rotational speed could have an effect of delaying the onset of aerodynamic stall, thus lengthening the trajectory. It also could have increased lift on the forward-moving side, causing precession that could also affect the angle of attack. – Mike Dunlavey Jun 1 '12 at 13:22
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