In the game of hockey, speed is everything. If you’re not at the right place at the right time, you’re not going to make it to the next level. Luckily, there is a formula for figuring out how fast a hockey puck travels.
When a player is shooting the puck, there is a point in the trajectory of the puck’s travel where it’s going to be at its maximum speed. This is called the puck’s peak speed. From this point on, the puck’s speed will gradually decline until it either comes to rest or is interfered with by an opposing player or element. (For more information, check out this interesting blog post by the San Francisco Hockey Club – the same team that brought you the Golden State Warriors.)
To best determine a hockey puck’s speed, one needs to consider several factors. These include, but are not limited to:
- The angle of the shot
- The arc of the shot
- The type of ice
- The quality of the ice
- Wind speed and direction
- Whether or not the puck is slick
- The temperature of the air and surface of the puck
- The quality of the light
- Whether or not there is an opposing team in the vicinity
- Snow conditions
To figure out the peak speed of a hockey puck, one first needs to define the arc of the puck’s flight. While there are several methods to doing this, you can use the Pythagorean Theorem to calculate the arc of any circular motion.
This theorem states that the length of a diameter (the distance between two points on the circle) squared plus the length of a third point of the diameter (the distance between the circle’s center and a point on the circle) squared equals the square of the length of the whole diameter. (For more information, see this Google search.)
If you know the length of two of the three sides of a triangle (in this case, the diameter of the circle and the length of the third side which is the hypotenuse), you can use the Pythagorean Theorem to calculate the third side.
In the game of hockey, the angle of a shot is typically from 45 to 90 degrees. Therefore, we can use the Pythagorean Theorem to find the arc of this type of shot. Let’s assume that we shoot the puck perpendicular to the goal line, as shown in the figure below.
Since the angle of the shot is 90 degrees (looked down the barrel of a gun at 45 degrees), we could use the Pythagorean Theorem to find the arc of this type of shot.
(1) The length of the whole diameter (from the top of the circle to the bottom of the circle) squared = (2) The length of the hypotenuse (the horizontal arm of the triangle) squared = (3) The length of the altitude (a vertical arm from one point of the diameter to the other) squared.
This is exactly the same formula the SFHC used in their blog post to find the arc of a 90 degree shot. If we plug in the numbers, we get an arc of 72 meters (just over 73 yards). (You can also use the Pythagorean Theorem to find the arc of any type of shot. Just remember to use the values from your particular situation.)
Once you have found the arc of the shot, you can use this information to determine the peak speed of the puck. Simply plug the numbers into the formula below and you’ll have your answer.
Where T is time in seconds (from the instant of shooting to the time the puck reaches its peak speed) and v is the instantaneous velocity in meters per second (one meter per second is equal to one meter in one second which is equal to 0.9 mph in the US and 1.8 km/h in Germany).
(T) squared + (v) squared = (2vT)/(3)
So, if we assume that we are shooting the puck at 90 degrees with an initial speed of v = 20 m/s, we can use the formula above to find that the peak speed of the puck will be 22.4 m/s. (Note: These are extremely rough numbers. They are meant to give one an idea of what to look for and how to use this information.)
How Do I Measure The Arc Of A Shot?
The angle of a shot can vary from 45 to 90 degrees, as mentioned previously. To find the arc of a shot, one needs to determine the angle of the shot and then use the Pythagorean Theorem. (For a step-by-step tutorial on measuring the angle of a shot, check out this tutorial video from the SFHC blog.)
To find the arc of a shot, one must measure the horizontal and vertical angles. To do this, one needs to mark two points on the field, one at each end of the goal line. The horizontal angle is measured from the top of the circle to the point on the field where you measure the vertical angle. (For a visual aid, check out figure below.)
Using these two points as reference points, one can use a protractor to measure the angle of the puck’s trajectory to the top of the circle. A standard hockey puck will make a complete circular rotation in approximately 75 ft (22.9 meters). Therefore, the ball will be at its highest point in the air at approximately 22.9 meters from the position where you shoot it. Subtracting this height from the height of the circle (9 meters) will give you the arc of the shot, as shown in figure below.
To determine the height of the puck at which it will peak, one would use the formula below. The height of the arc is equal to vT divided by g where vT is the velocity in meters per second of the puck at its highest point, g is the acceleration due to gravity (which is 9.81 meters per second squared).
(vT) / g = h
In our exercise, we will assume that vT = 22.4 meters per second, which is the puck’s peak speed. This gives us a height of 7.24 meters (just over 7 yards). The formula above can also be used to find the acceleration due to gravity provided that one knows the height at which the puck peaks. (For more information, see this SFHC blog post.)
Is The Puck’s Peak Speed Constant?
An interesting question to consider is whether or not the puck’s peak speed is constant. The answer is no. (For a detailed explanation, check out this SFHC blog post. But, to give you a basic idea, here’s the deal.
When a player is shooting the puck at 90 degrees (perpendicular to the goal line), the peak speed of the puck is maximum. However, when a player is shooting the puck at an angle less than 90 degrees, the max speed of the puck will be less than it is when shot perpendicular to the goal line. In the diagram below, we see a 45 degree angle. As you can see, the instantaneous velocity (the blue line touching the peak of the red line) is less than when the puck is shot at 90 degrees. (You can also use this information to find the speed of a puck shot at other angles.)
As the angle of the shot decreases, so does the speed of the puck. When the angle becomes close to 0 degrees (point-blank shot, like a goalie is blocking the puck), the speed of the puck will become zero. (For more information, check out this SFHC blog post.)