The Physics in Hockey

For those who know me, you will not be surprised to learn that my two main interests in life are hockey and science. Therefore it was only a matter of time before I used this blog to combine the two and show everyone the physics behind the sport I’ve played since I was 5 years old.

If you have never played or even seen hockey before – and I’m talking about actually hockey and not ice hockey – it is a sport played with 11 players per team, played for 70 minutes and the only equipment you are allowed to use to strike the ball is a hockey stick. Nice and simple yes?

However when you consider the forces and energy involved in hockey then it becomes a lot more complicated. The main skill in hockey is to hit the ball, where the stick is swung up and back down before connecting with the ball, sending it away from the player. If we consider this movement to be similar to a swinging pendulum, then we find that energy is always conserved in the swing, but different forces appear.

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A hit in hockey usually starts just about waist height at position 1. At this point the potential energy of the stick is at a maximum, and the kinetic energy is zero, since for a split second the stick has ‘paused’ in the air. This means that the overall energy is m.g.h, the mass of the stick x the gravitational constant x the height from the ground. Similarly the only force acting on the stick is gravity, which means the overall force is m.g, the mass of the stick x the gravitational constant.

However, when the player lowers the stick towards the ball, the potential energy is gradually converted into kinetic energy (energy is conserved), and the overall energy becoming m.g.h + ½ m.v2, with the value of m.g.h decreasing and the value of ½ m.v2 increasing.

Similarly, a radial force (m.g.sinθ) is introduced, which gradually increases as the stick heads towards the ball until it reaches position 2 where it becomes a maximum. The energy at position 2 is now all kinetic energy with no potential energy for the split second the stick reaches the bottom of its swing.

However, when the stick strikes the ball, then we have a collision and the Physics slightly changes. In any collision the momentum P is always conservered, that is the momentum before the collision equals the momentum after the collision, Pb = Pa . Momentum is defined as mass x velocity, and we will split the action of the stick striking the ball into the before and after parts.

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Say we have a stationary ball to begin with, the overall momentum before the collision is the momentum of the swinging stick plus the momentum of the stationary ball, msvs +mbvb.  However since the ball is stationary then it has no momentum so our overall momentum before the collision is msvs.

After our collision, our stick is still moving, but our ball is now moving in the same direction as a result of the collision. So our momentum after the collision is now  msvs + mbvb.

Since overall momentum is conserved then our equation become (msvs)befiore = (msvs + mbvb)after

Another skill in hockey is known as the drag flick, which is a specialist skill and if done correctly generally results in goals being scored. The clue is in the name, as the ball is dragged a yard before being flicked (either high or low) at the goal. This technique has the potential to fling the ball at speeds of 70- 80 mph.

The basic technique is to spin the ball along the length of the stick before flicking it toward the goal like a slingshot.  This is ably demonstrated, in an overly dramatic way, by Taeke Taekema in the video below.

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Since the ball is spinning as it moves along the stick then we now have to consider angular momentum in our equations (L).

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The equation for angular momentum is L = I Ɯ, where I is the moment of inertia and Ɯ is the angular velocity. As the ball moves along the stick the momentum is increased before eventually being released at the end of the stick before the goal.

If we move away from stick skills and focus on the equipment itself we find that resistance is important in hockey, or rather how to reduce it. Hockey used to be played on grass but has now evolved to sand based astroturf and finally the modern day water based astroturf. The result of having water on the pitch reduces friction on the ball, making it move faster and in turn making the game quicker.

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The ball itself has been modified to have dimples all around it. This is so that tiny air pockets are produced on the surface of the ball, which minimises the surface area in contact in the ground and once again reduces the friction between the ball and the surface.

So that’s a general description of some of the physics, as no doubt there are many more factors and forces involved that would complicate the equations to a ridiculous degree. You may be wondering if all this information has helped me be successful on the pitch, so I’ll answer that with the picture below……. Inverleith Nomads Double winners 2012/13!!!

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