**Introduction**

One of the most fundamental aspects of engineering mechanics is the study of moving objects. Referred to as dynamics, this area of study aims to determine and predict the behaviour of various bodies as they move, accelerate, collide, and deform. This applies directly to hockey in many ways including the physics behind shots, passes, hits, and blocks. It’s often said that hockey players are the toughest athletes due to the intense stress placed on their bodies from the physicality and speed of the sport. From playing through sprains, fractures, and collapsed lungs, hockey players are definitely tough. Blocking shots, one of the easiest ways for players to get injured, has come under the microscope over the last few years. The debate among hockey opinionists over the value placed on blocking shots is one that still rages on social media and NHL head offices today. Some argue that blocks are an unnecessary danger and can actually prevent goaltenders from making saves. Some are of the opinion that blocks are a valuable metric that help indicated when you don’t have the puck and leave shooting lanes open. Some teams take it to the next level and use blocks as their sole indicator in evaluating defensemen. The topic is nicely summed up by Kent Wilson:

Generally, players who intentionally block shots do so from just inside the blueline, and place their bodies in front of point shots. The NHL is a game of power, and when hulking defensemen like Zdeno Chara and Shea Weber are winding up for a slapper, it can be intimidating to say the least. Looking at the slapshot specifically, it is one of the most lethal ways to score in today’s game solely because of the velocity and power it generates. The current record for hardest slapshot is held by none other than Chara, the 6’ 9” monster who currently serves as the captain for the Boston Bruins. There is a short list of hockey players who have blocked a Chara slapshot and lived to tell the tale. In the 2012 All Star Skills Competition, Chara wired the puck 30 ft into an open net in approximately 0.1 seconds. Officially clocking in at 108.8 miles per hour, he set a record that has stood the test of time. In this evaluation, we look at the force exerted by a slapshot when it impacts a defensemen making a block.

**Methodology**

The main physics behind blocking a shot is taking a moving object (the puck), and slowing it down to zero velocity (with your body) over a defined time period. There are several principles involved with this analysis.

**1. Kinetic Energy**

The two main forms of energy are potential and kinetic. Potential energy, as it sounds, is energy that is stored in a body. This includes gravitational potential energy that is associated with increasing the vertical height of an object, and also elastic potential energy that occurs when an object is stretched or compressed like a spring or elastic band. Kinetic energy is associated with the movement of a body. When the puck is flying through the air, it holds kinetic energy. When potential energy is “used”, it is converted to kinetic energy. At all times, the total energy of a system (potential + kinetic) is the same. This is the conservation of energy principle. Energy is defined in units of Joules in the metric system and foot-pounds in the imperial system. Kinetic energy is calculated using a formula which includes the mass of the object and its velocity.

**2. Deformation**

All bodies have elastic properties. This means that even the hardest of objects, take a rock for example, does deform when under stress. This deformation is the key reason why the puck slows to zero velocity after it makes contact with a defender. Its velocity slows to zero over the deformation distance where the puck is compressed. This compression converts the original kinetic energy of the puck into stored elastic potential energy. When the energy has been totally converted and the puck reaches zero velocity, the potential energy is then converted back into kinetic energy as it rebounds off the defender. Deformation distance is simply defined in terms of length, meters in the metric system and feet in the imperial

**3. Work and Energy**

Work refers to the energy transfer when a force moves an object over a defined distance. Both being represented in terms of Joules, work and energy are linked. The work and energy principle states that the difference in kinetic energy of an object is equal to the work done on that object. This principle allows us to evaluate the impact force as the puck is slowed to zero velocity by the defender. Work is calculated by simply multiplying the external force by the distance.

**4. Impact Force**

Impact force is the key metric of this analysis, and is calculated by equating the difference in kinetic energy to the work done on the puck by the defender. By knowing the deformation distance, the force can be easily calculated. Force is expressed in terms of Newtons in the metric system and pounds in the imperial system.

## Key Assumptions

In this analysis, several key assumptions were made to reduce the complexity of the study. However, overestimations were made wherever appropriate to keep with a conservative design approach. Assumptions made are as follows:

1. The collision between puck and defender is completely elastic, meaning we neglect the energy lost to sound, etc.

2. The impact is straight and not oblique, meaning the puck hits the defender and deflects back along the same line

3. The defender is a rigid body, meaning the only deforming object in this analysis is the hockey puck itself

4. The energy lost to air resistance is negligible

5. The puck maintains a constant elevation throughout, meaning no gravitational potential energy is converted to kinetic energy

6. The puck deformation distance is no greater than 10% of the puck’s diameter, though this figure is likely much larger than it is in real life

**Important Data**

The puck dimensions are according to the image below.

The puck speed is 100 mph, or 44.704 m/s

The mass of the puck is 170 g

## Evaluation

The initial kinetic energy of the puck before it contacts the defender is equal to 170 J:

The final kinetic energy of the puck is equal to zero, as the puck has slowed to zero velocity.

The deformation distance of the puck is equal to 7.62 mm:

Therefore, the impact force exerted on the defender is:

*Note: the puck likely deforms by less than 10% of the diameter due to the low temperature and stiffness of the puck. This means the force would be even higher than it is in this calculation.

## Analysis

What does 22310 N really mean? One way to rationalize this figure is to consider that a single 224 pound person exerts a force of 1000 N when they stand on a surface. So, when a brave defender slides in front of a 100 mph slapshot, they can experience a force equal to 22 people standing on top of them. Thankfully, hockey players are insulated by many layers of padding and protective equipment but even with the best shin guards, a force of that magnitude would surely sting at the very least.

Putting this into further perspective, the following chart shows the velocity at which various objects would need to travel in order to exert the same force. The deformation distance changes between objects, and this distance contributes greatly to the force calculation as indicated above. The dashed line indicates 100 mph, the speed of the hockey puck to achieve this impact force.

It’s crazy to think that getting hit by a 100 mph hockey puck is the same as being hit by a 300 mph squash ball.

## Conclusion

Blocking a slapshot is no joke. With pucks reaching speeds in excess of 100 mph, blocking a shot can be quite dangerous and has the potential to seriously injure defending players. It makes sense why so many players opt to duck and hide as opposed to diving in the lane when the Charas and Webers of the league wind up for a shot. Keep in mind that the analysis was conservative, and in all likeliness, the puck will have a higher impact force. Player safety is paramount and proper gear goes a long way. That being said, you can safely say that hockey players are incredibly tough.

Want to see more analyses like this? Let us know @wincolumnblog!

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