How Physics Applies to Disc Golf
Doing Work!
Written by Team Disc Store Member Joseph Johnson
Doing work! In disc golf this could mean taking a commanding lead by getting several birdies in a row or making some long putts to stay in contention for a win. In physics, work has a more specific definition. Work equals the change in energy in a system. If no work is done to a system or by a system, then the total energy in that system doesn’t change. We say that the energy is conserved. We can calculate the amount of work done by finding something called a “dot product” of the force vector applied to an object and the displacement vector as the object moves through space.
For math minded folks out there, this is equal to the magnitude of the force vector times the magnitude of the displacement vector times the cosine of the angle between them. The cosine term picks out the parallel parts of the force and displacement. In other words, only the force in the same direction of the motion adds energy to the object and when we push or pull something to move it, we give it some of our energy. This is what happens when we pull the disc through the power pocket and release it. We give it some of our energy in the form of kinetic energy.
Kinetic energy, or the energy of motion, equals one-half times the mass of the object times the velocity of the object squared. The more kinetic energy we transfer to the disc, the faster it leaves our hand. To increase the work done on the disc and the kinetic energy transferred we can increase the force applied (pull harder) or the distance over which that force is applied (reach back and follow through).
In the interest of testing this and testing out a new Tech Disc™ that we purchased for my current disc golf biomechanics research project, I recorded a few throws and analyzed them using Logger Pro™ software.
The curved path indicates a variable acceleration, which means a variable force. Acceleration and force increase as the disc passes through the power pocket and approaches the release point. I found a final release velocity of 22.5 m/s (50.3 mph) for this throw, very close to the 51.7 mph indicated by the tech disc.
For ease of calculations, I will find the average acceleration for the throw and use that to find the average force. I will then use that average force in our work equation to figure out the work done. This should equal the kinetic energy of the disc (mass = 0.1779 kg) as it leaves my hand.
A quick check of my numbers using the kinetic energy equation from above shows that this is a conservative estimate for the work done:
It is also worth noting that some of the work done goes into rotational kinetic energy (something we will talk about in a future post), but it gives us a sense of how the variables I control in a throw can give me more power.
In physics, power is the work done divided by the time, so I am exerting power at a rate of:
This is pretty cool! By increasing the force or the distance over which I apply the force, I can increase the energy I transfer to the disc. If I decrease the time (move faster) I can increase the power of the throw.