Aerodynamics in Sports Equipment, Recreation and Machines - Discus

Aerodynamics of the Discus

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The discus has a long tradition in sports, first appearing in the ancient games in 708 B.C. In those days, stone and bronze disks were used. The size and weight of the disk varied. In 1896, the discus was an event in the first modern Olympic games. At the same time the sport was enjoyed in Scandinavia and the United States. It wasn't until 1907, however, that the event was standardized. Today, the men's discus weighs 2kg (4.4lbs) and measures 22cm (8.66in) in diameter. The women's discus weighs 1kg (2.2lbs) and has a diameter of 18.2cm (7.2in). The discus is thrown from a circle which is 2.5 meters (8.2 feet) in diameter.

The throwing style has also changed. Originally, the thrower stood in one place, only moving his arms. Later, the nordic swinging style of throwing was used. In 1926, the current throwing style was introduced. This style involves the turning and skipping before release. This style was first used by Clarence Houser of the United States.

Aerodynamic forces

While the discus and the sport of discus throwing has evolved over the years, one fact remains constant: The discus is greatly influenced by aerodynamic forces. In fact, greater distances can be achieved by throwing the discus into a moderate headwind. This is due to the importance of the aerodynamic lift produced by the discus in flight. In order to completely understand this phenomena, we must look at the shape of the discus.

By examining the cross section, as shown in the figure, we notice that both the upper and lower surface have the same shape. Therefore, we can consider the discus cross section as a symmetric airfoil. If given a small angle of attack the discus will produce lift, just like a symmetric airfoil. Again, we just need to look at the Bernoulli Principle to see how this works. Given an angle of attack, the stagnation point will move from the centerline of the discus to the lower surface. Therefore the air traveling over the upper surface has to travel faster than the air on the lower surface. This translates to a higher pressure on the lower surface than on the upper surface. Hence, the production of lift. However, as is the case with any airfoil, if the angle of attack is too large, the flow will separate. This separation represents the sudden loss of lift. For a discus this occurs at approximately 26 degrees angle of attack.

So, how does a moderate headwind translate to greater distance for a discus thrower? The velocity of the wind increases the speed of the air traveling over the the discus. This implies an increase in the lift force experienced by the discus. The increased lift translates to longer flight time and, hence, greater lift. Of coarse, this increase in performance doesn't come without a price. The discus thrower must be more precise with his throwing technique to take advantage of the headwind. However, for an experienced athlete, throwing into a headwind of 10 m/s can mean an increase of 5 or more meters in distance.

Gyroscopic stability

The lift imparted on the discus is similar to the lift felt by your hand when you hold it outside the window of a moving car. Your flattened hand experiences very strong forces acting either up or down depending on which way it is angled (giving it a positive or negative angle of attack). The other force you feel, the one pushing your hand back, is the drag or frictional force. Another phenomena you will notice is the tendency of your hand to want to twist towards a broadside orientation (open palm facing the wind). This twisting motion is caused by a torque being applied to your hand. Most all surfaces which generate lift also experience this torque.

The torque you experience is also felt by the discus. The torque will cause a pitch up moment which will eventually cause the discus to stall. However, we never see this happen at a track meet. This is because the discus is thrown with a spin. This spin gives the discus angular momentum. The angular momentum of an object remains constant in time (both the spin rate and the orientation of the spin axis) unless acted on by an external torque.

A simple way to experience this phenomena for yourself is to perform a simple experiment with a gyroscope. While holding a spinning gyroscope in your hand, try to change the orientation of the spin axis. You should notice the gyroscope resisting the movement.

The angular momentum plays an important role in the stability of several projectiles. The angular momentum is proportional to the mass of the object, and its rotational velocity. Therefore, a heavy object (like the discus) doesn't require as high a spin rate as a lighter object (like a frisbee) for stability.

Summary

The discus is greatly influenced by the forces of aerodynamics. While its drag plays a minor role in the flight, the lift dictates the distance of the discus flight.

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