Motion of a frisbee

To date, our physics class has discussed the mechanics of motion in two dimensions. I started thinking about the motion of other objects that could be simplified into two dimensions, such as the motion of a frisbee. So a logical question would be: At what angle would a frisbee be thrown to maximize distance?

With most objects that we have analyzed so far, such as the baseball in the group problem, the maximum distance has come from placing the maximum force on the object at approximately 45 degrees, with some adjustment based on the object's starting height. This allows a large amount of force to be put in the x-direction, while also putting enough force in the y-direction to allow some time before gravity brings it back down.



However, if one throws a frisbee at 45 degrees without spinning it, it will not travel very far at all. Through 5 trials of throwing a frisbee at approximately 45 degrees without spinning it and measuring the time it took to hit the ground, I came up with an average flight time of 1.59 seconds. Assuming standard projectile conditions (negating air resistance), and ignoring the height I added by throwing it, this means that it rose for ~.8 seconds, and therefore had an initial velocity of (9.8 m/s2) * .8 seconds, or the acceleration of gravity times the time it took gravity to make it change direction, or 7.8 m/s. Assuming that it was thrown at a 45 degree angle, this means that the horizontal velocity is the same, and 7.8 (m/s) * 1.59 s = ~ 12 meters. How far did really fly? We didn't measure it, but merely eyeballing it, I can safely say it was less than half that.



It travels up along the expected projectile path for a few seconds, and then falls almost straight down. What accounts for this difference? Video of this motion

The main factors are air resistance and the shape of the frisbee. In most projectile equations, air resistance is ignored since its effects are negligible and really hard to calculate. However, with the frisbee, the large, flat surface generates a lot more air resistance than the typical bullet or baseball. This causes the air resistance to slow motion in the x-direction as fast as motion is slowed in the y-direction by gravity, bringing the frisbee to a screeching halt and a quick fall.

So how does one increase the distance? One would have to learn how a frisbee really flew. The key component of a frisbee's motion is its spin. By putting spin on the frisbee, the disc both stabilizes itself (due to its rotational inertia), and is less likely to be affected by outside forces. This aspect of a frisbee's motion is similar to a gyroscope.

Keeping with the projectile idea that 45 degrees is the ideal angle, I tried throwing the frisbee at 45 degrees with spin. It did indeed go slightly higher and slightly further. It averaged a flight time of 2.02 seconds across 5 trials. However, this was still much shorter than the typical, and far more ideal throw angle, which, by personal experience, is only slightly above horizontal. Therefore there must be other forces acting upon it when it is closer to level.

Video #2, spin at upward angle

The shape and motion of a frisbee has a huge effect on it's flight. These attributes are similar to those of an airplane wing. To understand this one must analyze the path of the air over the frisbee. Since the path of the air over the top of the frisbee is longer than over the bottom, the air flying over the top has to accelerate. Thus the air on the top is of lower pressure, and the higher pressure air on the bottom pushes the frisbee up. This force is referred to as lift. Lift allows the frisbee to fly much farther than a typical projectile would if thrown at the same angle. The frisbee will eventually slow down and fall, once the drag slows the frisbee down and force of lift is less than the force of gravity.



So how does one increase the distance of one's frisbee throw? Put more spin on it so it both stays stable longer and flies faster. I hope to find some equations to go with this type of motion later in the year, but currently it is too complicated to calculate an ideal path, spin, and force to find the maximum distance a frisbee can be thrown.

Decent throw

Additional info: http://www.ultimatehandbook.com/Webpages/Beginner/physics.html
http://www.afda.com/skills/physics.htm

Thanks to my roommate Gary Doran for timing my throws for data and videoing the throws shown here.

spin keeping it stable would be similar to the gyroscopic forces we dealt with.

Really good research Martha! I'm happy to be enlightened.

However, while I'm sure everything you've presented is perfectly applicable to airplanes, in the case of frisbees I think spin is probably a greater factor than angle of attack. After all, if one merely tosses the frisbee at an angle of 15 degrees (the ideal angle according to one of the websites you presented), it will not go nearly as far as if one throws it properly (x velocity and spin) it at zero degrees.

There's definitely something very interesting going on with the spin. I wish I understood how it effects the flight of the frisbee.