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Mathematics in Hockey

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Josh Baltazar

on 1 August 2013

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Transcript of Mathematics in Hockey

Reaction Time
& Reflexes

Goalie Crease
Mathematics in Hockey
By: Joe Rodriguez, Emmelynn Rivera, Josh Baltazar
Hockey Overview
The game of ice hockey most likely evolved from the game of field hockey
The modern version of ice-hockey finds its origins in the rules laid down by a Canadian named J G Creighton.
His rules were implemented in the first game of ice hockey played in Montreal, Canada in the year 1875.

Initially there were as many as thirty players for each side and the goals were two stones frozen on one end of the ice.
The rules for the game of ice hockey were drafted at McGill University in Montreal, Canada in the year 1879.
Ice hockey found its way to the US in the year 1893.
By the early 1900s, the sport had become prevalent in parts of Europe including the UK.
Hockey Geometry
History of Hockey
Position:

the change in a player's speed and/or direction over a period of time.
Kinematics
Velocity:
Basic Info
Reaction Time
Grab a partner
Rest arm on edge of table
Hand hanging over the edge
Thumb and index finger an inch apart
Have partner hold a ruler so the bottom just between your fingers
Drop it and try to close your fingers on the stick
Count where you caught the ruler in the inches side and remember the number
So how fast are you?
1 official NHL puck = 5.8 oz
Average mph

85-95 mph (slapshot)

50-60 mph (wrist shot)

64 feet
Works Cited
http://www.exploratorium.edu/hockey/save1.html
http://science360.gov/obj/video/88e76593-7a56-4480-b0a3-449a92c8d553/reflexes-reaction-time

Hockey is a team sport with 12 players on the ice at any given time with usually one designated player on each team as the goalie.
-Offensive Players: 3 forwards on the ice, a center, left and right wing

-Defensive Players: 2 defensive players on the ice, left defenseman and right defenseman
-Played on large ice rink/surface.
-Gear: Ice skates, helmet/mask, mouth guard, gloves, protection pads over body, and hockey stick.
Goal: Getting the hockey puck past the goalie into the opposing teams net.
The puck that is used to play is a cylinder and a three diemsional object
The blade and the shaft are usually 135 degree angles, which are known as obtuse angles.
15 feet
30 foot diameter
180 degree angle
360 degrees in a circle
Faceoff Circles
One at center ice, two at each endzone
In order to begin the game, or resume play, a referee drops the puck into the center circle.

Because of the geometry of a circle, each player has an equal chance of getting to the puck.
Neutral Zone
Truncated Circle
Offsides
First, I build a function f(X) to get angle alpha from horizontal distance X.

Angle alpha is equal to the angle at the eyeball position for the whole triangle, minus the angle of the smaller triangle XY.

We need to find the maximum of this function. This is a calculus problem. We therefore find the derivative f’(x)

Setting this derivative to 0 to find the maximum, we get two roots:

Assuming only the first root is of interest, we can therefore evaluate f(X) at X.

This gives the maximum angle
Calculus Problem of the Week November 18, 2011 | Math Bootcamps - Online Bootcamps, Math Tips, and How-to Articles
What would be the most optimal angle for a player to shoot and make a goal?
Finding the Maximum
Velocity Vectors
the speed and direction the player is moving in.
The actual velocity the puck will travel to reach the teammate.
The resultant
Location of the player on the ice at a given moment.
Acceleration:
Calculus + Hockey =
A lower lie is best for skaters who lean forward closer to the ice or use a longer stick.
Higher lies keep the puck closer to the body and are preferred by more upright skaters or skaters with shorter sticks.
Reaction Time = Distance / Rate
48 feet
Slapshot 90 mph = 132 ft per sec
(48 feet)/(132 ft per sec.)
= .364 sec
32 feet
(32 feet)/(132 ft per sec)
= .242 sec
16 feet
(16 feet)/(132 ft per sec)
= .121 sec
Inches Fallen Reaction Time in Seconds

5.0 0.161
5.5 0.169
6.0 0.177
6.5 0.184
7.0 0.191
7.5 0.198
8.0 0.204
8.5 0.210
Meaning behind the #'s
So a profession NHL hockey goalie average reaction time is between .125 and
.175 seconds
http://science360.gov/series/science-nhl-hockey/41c74cc3-2d9a-40f6-95c1-76c04834afce
Reaction Time
and Reflexes
Full transcript