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There is often a lot of discussion about why discs do what they do in flight. Why do they turn over, why are they over stable, why do they fade at the end of the flight?

This article is the best lay discourse I've ever read on the issue. Before reading it, Google precession and get a good feeling for that issue because it is key.

Putting it simply, Precession means that if you have lift on the back edge of your disc, by the time that lift comes into play, the disc will have turned 90 degrees (due to spin) and so the lift acts on the side of the disc. Over stable discs have lift in the front, and under stable discs have lift in the back.

Read away:

DO YOU ever stand in the local park wondering why your Frisbee will not fly without flopping over? Rest assured - the fault is not entirely yours. One of the last great challenges facing those who make the plastic discs, as well as the professional throwers of 'disc-sport', is to design a disc that does not turn over before it reaches the end of its flight. Decades of developments have increased the time and distances that discs will stay aloft but the one unsolved problem remains the 'turnover effect'.

Flying discs in one form or another have been around since the last century and yet its aerodynamics still baffle enthusiasts. It all began in 1871 when William Russell Frisbie opened a pie factory close to the college that, 16 years later, became Yale University. Hungry students were regular customers of what became the Frisbie Pie Company. Before long, the energetic lateral thinkers among them discovered that an empty pie tin, turned upside down, was great fun to throw. But the commercial potential of the flying tin remained unexploited until after the Second World War. Then Frederick Morrison, an enthusiastic pie tin thrower before the war, took advantage of evolving plastics technology. In 1948, he used butyl stearate to make the first modern disc and, within 10 years, he had sold the idea to the Wham-O Corporation, an American toy manufacturer based in California. Wham-O coined the name 'Frisbee' for its new plastic toy, a trademark that is now synonymous with flying discs.

As customers demanded discs that flew farther, that were lighter and easier to catch, that were more accurate or performed tricks better, other manufacturers began to produce them too. Wham-O's patent protected only the shape of the Frisbee; the company could not monopolise the notion that discs can fly. New types of discs, with different cross sections and made from other forms of plastic, appeared throughout the world, notably in the US and West Germany. In 1972, the American universities of Princeton and Rutgers staged the first intercollegiate Ultimate Frisbee match - 103 years to the day after they had competed in the first intercollegiate American football match. In Ultimate Frisbee, players of one team throw the disc among themselves, trying to keep possession of the disc as they move towards the opposition's end of the field. A player scores points for the team by catching the disc in the opposition's 'end zone'. Unlike American football, there are no goal posts and no physical tackles.

Disc manufacturers faced greater demands as the sport of throwing discs, or disc-sport, became more popular. National teams began to compete in several different disciplines, which included distance and accurate throwing, and making the disc perform like a boomerang. Manufacturers designed discs for these specific purposes. For instance, they soon discovered that small, heavy discs flew the farthest but that there was a natural limit to this approach. The heaviest discs now weigh around 200 grams, although the average weight of those used for throwing long distances is about 175 grams - the world record for the longest throw with one of them is 190 metres. Throwers use lighter discs, weighing about 100 grams, when they compete in a discipline known as 'self-caught flight' in which the disc should take as long as it can to return to the thrower - the world record for the 'maximum time aloft' in this discipline is 16.72 seconds.

A flying disc generates lift in the same way that an aerofoil does; it creates a difference in pressure between its top and bottom sides. The top side is slightly convex and the bottom side is flat. As the disc flies forward, these shapes force the air flowing over the top of the disc to move faster than the air flowing below it. According to Bernoulli's equation, which governs the conservation of energy within a moving fluid, the local pressure reduces in proportion to the square of the speed of the flow. This means that only a small increase in air speed is needed to create a significant decrease in pressure, and vice versa. The disc's modest speed and gentle convex line are all it needs to create the drop in pressure above, relative to that below, that gives it lift .

But that is where the similarity between a Frisbee and an aircraft wing ends. Aerodynamic engineers can design aerofoils so that the lift acts at a particular place on a wing, which is usually about one quarter of the width of the aerofoil from the leading edge. This is not possible with a Frisbee. A disc turns over during flight because the distribution of lift it generates is irregular and not easy to predict or compensate for. Discs with rims tend to produce more lift on their back halves than on their front halves. This is because air flows at a fairly constant speed across the top of the disc, which is streamlined, but at varying speeds below it, where the rim disrupts the flow. The turbulent airstreams that result tend to move more slowly at the back end of the disc than they do at the front. Relative to the top of the disc, this causes a greater difference in air speeds, and hence pressures, at the back than at the front of the disc.

But this is not always the case. Less frequently, depending on the shape of the rim, a disc will generate more lift on its front half. Cheaper discs tend to do this and also some of those with wedge-shaped rims, which manufacturers have developed in their search for discs that will fly farther than existing models. (A wedge-shaped rim tends to produce less drag than a blunt one.) Incidentally, sheets of cardboard or other types of makeshift discs without rims tend to generate more lift on their front halves; they are also very unstable.

The effect of the uneven distribution of lift between the two halves is not as you might expect; it does not cause the back of the disc to rise and the front to fall. (A tilting forward of this sort, which changes the angle a disc makes with the oncoming air, the 'angle of attack', can occur but other influences during a flight are responsible.) Instead, the disc tilts sideways rather than forwards - it begins to turn over. This is an inevitable result of trying to make the disc stable during flight. Discs must be light to fly, but this leaves them with little inertia that would help to keep them stable. With this in mind, manufacturers provide a rim and throwers impart a spin that together aim to give the disc enough rotational momentum to resist and reduce changes in its orientation during flight.

The rim and the spin are the two most important stabilising features; they also encourage designers to experiment with the way that they distribute the mass of the disc. The rotational momentum depends on the mass of the disc, its speed of rotation and the square of the distance of the individual particles of mass to the axis of rotation. By concentrating the mass around the circumference and providing a good spin, the disc has enough rotational momentum to compensate for its lack of mass overall. When a disc leaves the hand of the average thrower, it is spinning at about 8 revolutions per second. Professional throwers might give the disc a spin of up to 16 revolutions per second though it would depend on the ambient flying conditions and on what they wanted the disc to do during its flight. A freestyle thrower, who performs tricks with the disc, needs to impart a high spin; a distance thrower is more interested in the orientation and forward speed of the disc. Someone throwing a disc in the park to a friend may not want to give the disc a high spin because this would make it difficult to catch; on the other hand, a high spin would be useful in blustery conditions to give the disc more stability.

The drawbacks of these stabilising features are that the spin is responsible for the turnover effect and the rim produces drag that rapidly slows down the disc.
Revolutions in the air

A spinning disc behaves like a gyroscope. An attempt to tilt its axis of rotation in one plane causes it to turn in a plane that is mutually perpendicular to the spinning plane and to the plane of the tilting force. For example, assume you have a disc spinning clockwise on the tip of a pencil; now imagine the dial of an analogue watch over it. If you apply a downward force at the 3 o'clock position, the spinning disc will react by tilting down at the 6 o'clock position. This phenomenon is known as gyroscopic precession and it is characteristic of all spinning objects, from flying discs to toy tops.

In the case of the flying disc, the effect of the unequal distribution of lift only becomes evident a quarter of a revolution later. If the centre of lift is somewhere on the trailing half of the disc's longitudinal axis, you would think that the leading edge should want to nose dive. Instead, because of gyroscopic precession, the disc dips and veers to the right (from the thrower's perspective) if it is spinning clockwise (looking from above), and to the left if it is spinning anticlockwise.

Aerodynamic engineers have not yet found a way of eliminating this natural tendency of discs to turn about their flight axis. To some extent, throwers can compensate for the effect by taking more care over how they release the disc. Inexperienced ones, who expect the disc to remain horizontal during its flight, tend to throw the disc so that it is horizontal at release as well. This is not a good idea, even though many people keep doing it. Thrown this way the disc quickly starts to tilt sideways, often reaching a vertical position and continuing its motion rolling along the ground. All these throwers need to do is to release the disc with a compensating tilt in the other direction; this is called adjusting the hyzer angle, which measures the sideways inclination of the disc to the horizontal. In broad terms, if you are going to give the disc a clockwise spin, release it with its left side tilted down, and vice versa. That way, you should at least throw discs farther. Professional throwers must take several other influences into account.

In the early 1980s, while I was still at school, I wrote a paper on the aerodynamics of flying discs for a national science competition for young people. One of the things that concerned me was the turnover effect; the solution seemed obvious. Designers had only to make the centre of gravity and the centre of lift of a disc coincide and there would be no gyroscopic precession. When I qualified for the final of the competition, one of the judges offered me the chance to spend a few afternoons at the Swiss Federal Institute of Technology in Zurich. In the laboratories there, I suspended a spinning disc in a channel of moving water and then used blue dye to highlight the patterns of flow around the disc. These experiments made me realise the difficult problems that aerodynamics engineers face. Frisbee throwers would have to live with the turnover effect - the patterns of flow around a spinning disc were far more complex than I had ever imagined. K K One of the surprises was that although a spinning disc has an axisymmetric, rigid body, most of the phenomena associated with its motion are asymmetric. For a start, the rotation increases the difference in air speeds above and below the disc on the side where the direction of spin matches that of the oncoming air; it reduces the difference on the other side. This results in an upwards force acting on the side of matching directions of motion. The force tries to turn the disc about its flight axis but, because of gyroscopic precession and irrespective of whether the disc is spinning clockwise or anticlockwise, it causes the disc's leading edge to dip. The rate of change of the angle of attack depends mainly on the disc's flight and rotational speeds. The wind's strength and variability may also affect it.

The asymmetric flow around a spinning disc also causes the disc to drift sideways slightly during flight as the rim is subjected to forces of different magnitude. It is easier to appreciate these forces if you think of the disc as a short section of a rotating cylinder. On one side of the cylinder, the spin augments the speed of the passing flow of air; on the other side, it reduces the air speed. According to the Bernoulli equation, the difference in speed between the two sides generates a difference in pressure. This causes a force to act from the region of high pressure, or low speed, to the region of low pressure, or high speed. The phenomenon is known as the Magnus effect, after its discoverer in 1852, Heinrich Gustav Magnus, a German physicist. It is responsible for the way that golfers, footballers and tennis players swerve balls with a slice. For Frisbees, the magnitude of the Magnus force depends on the disc's width and the speed of its rotation relative to that of the flow. For thin discs, it hardly affects the stability and flight path of the disc; for others, it causes a noticeable effect.

Taking advantage of the turnover

Disc manufacturers and professional throwers must consider all these forces when they set about trying to design a disc that does not turn over so quickly in a wide range of flying conditions. What makes the task doubly difficult is that the parameters of a flying disc, such as its spin and orientation, are continuously changing in flight.

But the turnover effect also has its positive sides. It is responsible for one of the most intriguing aspects of disc-sport competitions, the so-called 'self-caught flight'. As the name implies, the object of this discipline is to throw the disc up against the wind in such a way that it slowly floats back into the thrower's hand, much as a boomerang is supposed to do.

The type of disc a competitor chooses and the way it is thrown will depend on the wind conditions, which will also help to determine the flight path.

One of the two most frequent flight paths looks a bit like an upside down V; the other, which is just a prolonged version of the first, looks more like a capital N.

On the way up, the disc precesses on a curving flight path until it reaches the highest point of its trajectory, then it precesses on descent back to the thrower. During the extended version, a disc changes its direction twice. If it is spinning clockwise, the disc first flies in a curve to the right and then in one to the left. Sometimes the disc will continue this left curve into a spiralling flight path, which is very spectacular to watch but depends, to some extent, on remarkably obliging wind conditions. Gyroscopic precession enables the discs to follow two different curves. On the ascent, a clockwise spinning disc will dip and veer to the right as it confronts the head wind; on the descent, with the head wind becoming a tail wind, the disc tilts to the other side. With this flight path, the slightest change in wind direction and speed will quickly alter the disc's behaviour. Throwers competing for world records need considerable knowledge and experience of flying discs and of wind conditions, as well as some luck, to stand a chance of breaking them.

Throwing discs long distances means doing without a thick rim, which generates drag. In the late 1970s, Alan Adler, a lecturer in engineering at Stanford University in California and a disc-sport enthusiast, began to investigate the possibilities. Nearly a decade later, he had abandoned the disc for a ring, which he calls the Aerobie ring.

With the help of a computer simulation, Adler designed a flying ring that remains perfectly balanced at all speeds. Although the ring is axisymmetric, a cross section reveals that its outer edge is different from its inner edge. The outer edge has a short inclined rim that extends above and below the ring's main body; the inner edge is streamlined. The centre of the section is made from polycarbonate to give the ring a tough, flexible backbone; the edges come in soft rubber to make the ring comfortable to catch.

The Aerobie ring has flown much farther than the Frisbee. In early 1985, when the first rings were on sale, it covered 1046 feet. Within 18 months, Scott Zimmerman, a former world champion in disc-sport, threw the ring 1256 feet, which is more than double the distance travelled by a flying disc.

If you want to impress your friends in the park, perhaps you should go for a flying ring - but remember that you will have to walk a long way to recover it. Alternatively, you could stick with that old Frisbee and learn to have much more fun simply by adjusting your hyzer angle.

Mace Schuurmans studies medicine at the University of Basle. He is a former Swiss disc-throwing champion and has competed in individual disc-sport as a member of the national team. engineers.
From issue 1727 of New Scientist magazine, 28 July 1990, page

BTW - here's the link! http://www.newscientist.com/article.ns?id=mg12717274.800&print=...

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Replies to This Discussion

Thanks, Lyle!

I'm gonna have to read it a few more times, but it's very interesting.
Thanks for the information. When you combine the variables in flight dynamics, all external forces - gravity, body mechanics and forces, wind, materials and physical design etc, it all seems very complex. Somehow the human body adjusts quickly to this and is able to do a decent job of controlling the discs after only a few throws. I am a retired engineer and used to do a lot of computer programming (fortran etc) and am now getting interested in Java programming. I am now looking for freeware to do some simulations.
I guarantee that took some typing. I started reading and it just kept going and going and going.
Thanks Lyle.
A little lengthly but a great read, it really gets your head spinning.
Great information to keep in the back of our mind, thanks! Good job citing the article and including the link. Gotta give credit where it is due, and it is definately due.
I do believe a little thought went into this...
Wow! I had to study during my studying just to understand half of this. Who was saying something about homeless people and hippies playing this sport? That is an amazing piece of information to wrap my head around. I want to go throw just to see it in motion and think about it again. Thank you!
GREEAAAAAAAAAAT now I have to think about PRECESSION as I'm teeing off. BUT, its a good thing I read this. I was thinking this exact same thing, just didn't know how to put it into words.
What a great read. Though i have understood it for quite some time putting into words has always been an unbeatable foe. Thanks Lyle.

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