MadSci Network: Physics Query:

### Re: what are the physics behind discus throwing?

Date: Wed May 26 09:59:52 1999
Posted By: Tom Cull, Staff, Clinical Sciences MR Division, Picker International
Area of science: Physics
ID: 926744675.Ph
Message:

Many people learn about the physics of ideal projectiles under ideal conditions.  In these cases the projectile motion is simply the result of gravity, initial velocity (magnitude and direction), and possibly the layout of the surroundings.  A flight of a discus is
greatly affected by the aerodynamic forces acting upon it.

An absolutely wonderful sports physics site http://wings.ucdavis.edu/Book/Sports/instructor has a very good summary on
the Aerodynamics of the Discus.   I highly recommend this site -- heck they may even put me out of business :).

The Physics of Sports edited by Angelo Armenti, Jr. has an article by Cliff Frohlich entitled Aerodymanic effects on discus flight that orignally was printed in American Journal of Physics 49, 1125-1132 (1981).

I site this reference in case you wish to look up the formulas for yourself, but I will proceed without equations.

The aerodynamic forces come from the movement of the discus through the air (a fluid).   When in flight, a discus is affected by the forces of gravity, aerodynamic lift, and aerodynamic drag.  The most fascinating effect about discus aerodynamics is discus throwers can throw significantly farther if the wind blows against the direction of the throw than if there is no wind or if the wind blows in the direction of the throw [Frohlich].

An important concept is relative velocity.  The observed velocity of the discus is the vector sum of the velocity of the wind and velocity of the discus relative to the air.   If there is no wind then the relative velocity will be the same as the observed velocity.   One way to imagine this is as a swimmer swimming a calm pool -- her velocity relative to the water is determined by her swimming ability and directional control.  Now suppose we put the same swimmer in a stream of moving water.  If she swims into the oncoming current (upstream) her velocity relative to the water is pretty much the same as in the calm pool, but to those of us watching from dry ground she doesn't seem to be moving nearly as fast because the water is moving in the opposite direction -- cancelling some of her effort.   If she were to turn around and swim with the current (downstream) we on the banks would see her moving much faster because the velocity of the water would be complimenting her efforts.

Lift is defined as the force that opposes the force of gravity.  Generating lift depends on the speed (usually speed squared) relative to the air, the cross sectional area of the object, the density of air, and a dimensionless parameter that depends on the shape of the object, orientation, and the angle of orientation (angle of attack) relative to the direction of motion.   Note that lift depends on speed and not velocity.

Drag is defined as the force that tends to oppose motion.  If there is wind present then the drag force will not act along a direction opposing the motion but along the direction of relative velocity.   Drag depends on speed relative (again usually squared) relative to the air, the cross sectional area of the object, the density of air, and a dimensionless paramter that depends on the shape of the object, orientation, and the angle of attack.  The parameter for drag is not the same in general as the parameter for lift.

The stability of the discus flight comes from the spin of the discus.  The spin gives the discus angular momentum.  If the angular momentum is large enough than the discus flight is stabilized much like a gyroscope.  The higher angular momentum the more torque it takes to knock the discus off its flight line.

The interaction of lift, drag, and gravity upon the discus change the ideal angle of release for maximum range from the 45 degrees value of ideal projectiles to a value of somewhere between 30 and 40 degrees according to Frohlich.   The lower angle produces an angle of attack that produces the most lift.

Throwing a discus successfully takes a great deal of coordination and a fair amount of strength.  The speed of the throw is generated from the stronger muscles of the legs and back not the arms.   Basically the thrower tries to generate as much speed for his hand as possible.   The maximum speed of the hand (or maybe better the point of release) is achieved by spinning the whole body around an axis throw the torso.  This spinning helps impact spin to the discus which is required for stable flight and is also necessary because of the small throwing region permitted by rule.

A typical discus throw involves spinning around at least 1.5 times before release.  During the approach to the throw the speed of revolution is produced by the legs with a final thrust provided by torque produced by the back and shoulder.   The arm is held close to the body to help the thrower generate as much spin as possible.  The arm closer to the body reduces the moment of inertia of the thrower which means he/she can generate a greater rate of rotation.  However, greater tangential speed is produced by having a greater radial distance from the point of rotation so the arm is extended as much as possible just before release to produce the greatest launching speed.

Keeping all this in mind is essential to a good release and distance.
The athlete must gauge the wind and use proper form to produce the greatest release speed at the best possible angle of release in order to maximize distance.  This a feat that requires strength, agility, and lots of practice.

Sincerely,

Tom "Give Me a Frisbee" Cull

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