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A physicist's take on disc golf

Enrich your Physics

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Many of you have probably tried your hand at the sport of golf, but have you ever played disc golf? Well, like all ballistic sports, the physics of this aesthetically pleasing and addictive activity is definitely worth investigating.

Disc golf, which essentially originated with American college students throwing empty pie tins, involves getting a plastic disc into a series of baskets (with looped chains) in as few throws as possible. And whilst the method of playing is obviously radically different, the rules of this sport are not unlike those of its "royal and ancient" cousin.

Just as the flight of a modern golf ball is largely determined by the speed and angle of the club face at the point of impact, the behaviour of a disc is very much characterised by its specific mold. Of course, whilst a single golf ball is propelled down the fairway towards the hole using a variety of clubs, in disc golf, the drivers and putters are themselves the projectiles. A delightfully technical world of so-called hyzer flips and anhyzer curves, relating to a suitably skilful player's ability to shape their discs' trajectories, awaits a novice participant. But what is the magical force which keeps a disc, or frisbee, floating, seemingly effortlessly, through the air?

Mechanically speaking the dominant factors determining the success of a good throw are lift and spin. A disc which is propelled with sufficient initial velocity will experience aerodynamic lift in accordance with Bernoulli's Principle. This broadly states that an increase in the speed of a moving fluid will be accompanied by a commensurate decrease in pressure. Simply put, it helps explain how planes stay in the air, why umbrellas get pulled inside-out on windy days, and conversely, what keeps formula-one racing cars on the track!

We can think of a flying disc as a circular 'wing' whereby the deflection of oncoming air, over its body, produces a drop in pressure which contributes to the necessary lift force. Of course, if the disc wasn't spinning, it would immediately flip out of control and fall to the ground, so we need to invoke the law of conservation of angular momentum in order to maintain stability throughout its flight. Manufacturers often try to distribute the mass of their discs so that the vast bulk of the plastic is in the rim, approximating a hollow ring, thereby increasing the moment of inertia, upon which its angular momentum is strongly dependent.

Nowadays, plastic disc golf discs are invariably designated with a series of four numbers, each of which categorises a specific attribute of the expected trajectory, according to its mould. These relate to a disc's speed, glide, turn and fade. The speed number indicates how fast a disc needs to be thrown in order to achieve its optimum distance; higher numbers for drivers with wide aerodynamic rims, and lower numbers for midrange discs and putters with deeper, blunter profiles. The glide number represents a disc's capacity to 'hang' in the air, relative to its speed, which is a useful attribute to anticipate where, for example, a trade-off between distance and accuracy is needed. Discs with higher glide numbers often present a more rounded or domed profile, in order to maximise lift.

Finally, the turn and fade values indicate a disc's propensity to 'roll' right or left, respectively, from the point of view of a right-handed backhand thrower. These latter phenomena are very different to that of a draw or a slice in golf, or a curling shot in a soccer match. Turn may occur early in a sufficiently energetic throw, where a slight nose-down angle of attack, relative to the airflow, enables extra tail lift. Fade usually happens when a slowing, dropping disc starts to pitch nose-up. Both of these traits, which an experienced thrower may, in certain circumstances, use to their advantage, can be explained by understanding that a disc's angular momentum, besides having magnitude, is a vector pointing along the rotational axis. As the centre of pressure moves aft or fore of the centre of gravity, due to dynamic forces of lift and drag, the resulting external torque will cause the disc to precess like the flywheel of a gyroscope, or a spinning top.

So, whether you are simply enjoying a game of frisbee in the park with your friends, or you're intent on chasing a low score in a professional disc golf tournament, always remember… You can never blame the laws of physics for a lousy throw!

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