Science of Ice Skating Memorabilia

Celebrate the sport science of ice skating with memorabilia from Zazzle! Colorful graphs from Schottenbauer Publishing are featured on these mugs, magnets, keychains, & postcards. Direct links to each collection are included below:

     

A variety of other sport science collections are also available from Schottenbauer Publishing on Zazzle, which features regular sales on most items.  


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Schottenbauer Publishing 

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The Geometry of Ice Skating

Geometry is essential for ice skating. Take a moment to write down a few ways in which geometry affects the precision of the sport. 

Discussion Questions

1. What data is necessary to collect in order to understand the role of geometry in figure skating, hockey, and speed skating? 
2. What spatial perspectives and/or mathematical planes are important for precision? 

The cover of The Geometry of Figure Skating, to the right above, features a skater in action. 

Discussion Questions

1. What angles can be measured on the diagram, in order to understand the accuracy of technique?  
2. Is any essential information missing from the picture? What is necessary in order to measure that information?

Geometry diagrams featuring ice skating are available in the following books from Schottenbauer Publishing:

Geometry Workbooks

• The Geometry of Figure Skating
• The Geometry of Winter Olympic Sports

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Schottenbauer Publishing

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Comparing Ice Skating Equipment in the Lab

What types of measurements are ideal for understanding ice skating? Take a moment to write down a list of at least four types of data to collect and compare. What types of equipment are necessary to measure each type? What physics concepts are relevant?

Many types of interesting data are available for comparison in the book The Science of Ice Skating: Volume 1 (Extended Edition) from Schottenbauer Publishing. Data include position, velocity, acceleration, and force for the following equipment:

• Surface Types
• Ice
• Synthetic Ice
• Wet
• Dry
• Skate Types
• Bob Skates
• Child Double-Runner Skates
• Hockey Skates
• Youth
• Adult
• Figure Skates
• 2 Sizes
• 2 Types of Blades
• Blade Preparation
• Sharpened
• Unsharpened
• Skate Mass
• None
• Added 2.5 pounds of weight

Additional types of data include:

• Hockey Puck Motion
• Vertical Motions (Force)
• Stepping
• Jumping
• Skate Support for Ankles (Force)
• Ice Melting (Temperature)

Free sample graphs are available in a free pamphlet from the publisher's webpage.

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Schottenbauer Publishing

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Graphing Spins: A New Video

A new video from Schottenbauer Publishing analyzes four spins with graphs. These include three forward spins (centered, centered with step out, and traveling), and a back spin (centered). The video is available on YouTube.

Two graphs from the video are shown below:

Discussion Questions

1. What body part is most likely traced in the video?
2. Using a ruler, estimate the center of each spin on its graph.
3. How many times does the skater revolve in the first graph? In the second graph?
4. What would a traveling spin look like on a graph?

Additional free graphs are available in a free pamphlet from the publisher's webpage. 

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of ice skating, figure skating, and hockey:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Ice Skating 
• Volume 1: Translational Motion
• Volume 2: Rotational Motion (Curves)
• Volume 3: Rotational Motion (Spins)
• Volume 4: Jumps
• Volume 5: Ice Hockey
• Volume 6: Biophysics
• Volume 7: Video Analysis
• Volume 8: Reference Manual
• The Science of Hockey
• Volume 1: Force, Acceleration, & Video Analysis of Pucks & Balls
• Volume 2: Force & Acceleration of Sticks, plus Biophysics
• Volume 3: Video Analysis of Ice, Field, & Street Hockey Sticks

Anthologies of 28 Graphs

• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports

Additional Information

Schottenbauer Publishing

Free Education Resources

Video Analysis of "Cool Skating Move"

As with any sport, ice skating can be analysed in graphs. Consider the following graph below, excerpted from the upcoming Volume 9 of Glide, Spin, & Jump! The Science of Ice Skating by Schottenbauer Publishing. 

Discussion Questions

1. What body parts are moving in this example?
2. Which body part moves the most in the x direction? In the y direction?
3. What is the name of this move?

Now, consider the following pictures, excerpted from the video. (This move is shown in the YouTube Video Cool Skating Move.) 

Discussion Questions

1. Is this move in the first or second half of the graph?
2. What is the primary motion which occurs between these two pictures?
3. What concept(s) from physics are relevant for this move?
4. Is this move found in (a) figure skating, (b) ice hockey, or (c) both?

The diagram below highlights the move on the graph.

Discussion Questions

1. Which body part moves the most during this segment of the graph?
2. Which body part moves the most in the x direction? In the y direction?

Additional free graphs are available in a free pamphlet from the publisher's webpage. 

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of ice skating, figure skating, and hockey:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Ice Skating 
• Volume 1: Translational Motion
• Volume 2: Rotational Motion (Curves)
• Volume 3: Rotational Motion (Spins)
• Volume 4: Jumps
• Volume 5: Ice Hockey
• Volume 6: Biophysics
• Volume 7: Video Analysis
• Volume 8: Reference Manual
• The Science of Hockey
• Volume 1: Force, Acceleration, & Video Analysis of Pucks & Balls
• Volume 2: Force & Acceleration of Sticks, plus Biophysics
• Volume 3: Video Analysis of Ice, Field, & Street Hockey Sticks

Anthologies of 28 Graphs

• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports

Additional Information

Schottenbauer Publishing

Free Education Resources

Comparing Real & Synthetic Ice

Synthetic ice is a popular, low-cost alternative to real ice rinks. Available in several forms and quality levels, synthetic ice usually consists of a slippery plastic surface which mimics the performance of real ice. 

How good is synthetic ice? The following graphs, excerpted from Glide, Spin, & Jump: The Science of Ice Skating: Volume 1: Extended Edition, compare the performance of a sharpened figure skate on real ice and HDPE synthetic ice.

Discussion Questions

1. Compare the force line in each graph, using words. What is one major qualitative difference between the graphs? 
2. In the second graph, what is the minimum force? Is the real force ever less than 0? Why or why not? 
3. Why is force applied before the skate moves? Does this force contribute to velocity? At what point does force contribute to acceleration and velocity? 
4. In the first graph, what is the maximum force? The maximum position? Velocity? Acceleration? 
5. In the second graph, what is the maximum force? The maximum position? Velocity? Acceleration? 
6. In each graph, calculate the range of time in which skate movement occurs. Which is larger?
7. The second graph claims that the skate has been pulled 1 meter. What is the evidence for or against this assertion? (Hint: How long is the skate?) 
8. What force is required to pull the skate 1 meter on synthetic ice? On real ice? Which force is larger?

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of ice skating, figure skating, and hockey:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Ice Skating 
• Volume 1: Translational Motion
• Volume 2: Rotational Motion (Curves)
• Volume 3: Rotational Motion (Spins)
• Volume 4: Jumps
• Volume 5: Ice Hockey
• Volume 6: Biophysics
• Volume 7: Video Analysis
• Volume 8: Reference Manual
• The Science of Hockey
• Volume 1: Force, Acceleration, & Video Analysis of Pucks & Balls
• Volume 2: Force & Acceleration of Sticks, plus Biophysics
• Volume 3: Video Analysis of Ice, Field, & Street Hockey Sticks

Anthologies of 28 Graphs

• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports

In addition, the following books are suitable for younger children learning geometry:

Geometry Workbooks

• The Geometry of Figure Skating
• The Geometry of Winter Olympic Sports 

A simple demonstration of one type of synthetic ice is available below, in the YouTube video My First Ice Rink. This synthetic ice consists of High Density Polyethylene (HDPE), one of the least expensive surfaces manufactured in the USA. In fact, 3/16" x 48" x 96" HDPE sheets from US Plastics Corporation sold for approximately $2 per square foot in 2014. 

While high-quality synthetic ice may cost $16 per square foot or more, one variety of Ultra-High Density Polyethlene (UHDPE) is available low-cost from Dezhou Shengtong Rubber & Plastic Co., Ltd. in China. According to price estimates in February 2015, an Olympic-sized synthetic ice rink (100x200 ft, UHDPE with sideboards) is available from China to East Coast USA w/shipping (not including import tax) for only $22,000! 

Additional videos demonstrating HDPE synthetic ice are available on the Skating Science Playlist.

Additional Information

Schottenbauer Publishing

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Sliding on Ice: The Case of Two Hockey Pucks

The concept of friction is essential to all skating on ice, whether it is for hockey, speed, or figure skating. Ice provides a reduced-friction surface, which allows humans to glide, rather than stick to the floor. Synthetic ice, consisting of slippery plastic, also reduces friction. The friction of synthetic ice can be lowered further by applying soapwater, or other slippery liquids.

For gliding motion to occur, two types of friction must be overcome: initial non-moving (static) friction, and moving (kinetic) friction.

The following graphs, excerpted from Volume 1 of The Science of Hockey, show the effect of force on motion of an official hockey puck.

Discussion Questions

1. Describe the magnitude of each force in Graph 1. For what amount of time is each force applied?
2. Describe the motion of the puck in Graph 2, using words.
3. How far does the puck travel? In what direction?
4. Are the graphs coordinated in the time dimension?

The following graphs, excerpted from Volume 1 of The Science of Hockey, compare the force required to move two types of pucks on synthetic ice (HDPE plastic).

Discussion Questions

1. Is the total force different in these two graphs? If so, why?
2. Is the initial force different in these two graphs? If so, why?
3. What is the average force is applied to each puck?
4. Calculate the work involved for each puck.
5. Why does the practice hockey puck perform differently on synthetic ice than an official puck? (Hint: The practice hockey puck is normally used on concrete floors.)

Additional free graphs on the science of ice skating are available in a free pamphlet from the publisher's webpage. 

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of ice skating, figure skating, and hockey:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Ice Skating 
• Volume 1: Translational Motion
• Volume 2: Rotational Motion (Curves)
• Volume 3: Rotational Motion (Spins)
• Volume 4: Jumps
• Volume 5: Ice Hockey
• Volume 6: Biophysics
• Volume 7: Video Analysis
• Volume 8: Reference Manual
• The Science of Hockey
• Volume 1: Force, Acceleration, & Video Analysis of Pucks & Balls
• Volume 2: Force & Acceleration of Sticks, plus Biophysics
• Volume 3: Video Analysis of Ice, Field, & Street Hockey Sticks

Anthologies of 28 Graphs

• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports

In addition, the following books are suitable for younger children learning geometry:

Geometry Workbooks

• The Geometry of Figure Skating
• The Geometry of Winter Olympic Sports 

Additional Information

Schottenbauer Publishing

Free Education Resources

The Science of Jumping

What happens when an ice skater jumps? The answer can be modeled in various levels of difficulty. One the simplest level, assume that the skater is simply a point mass object, without movement within the body. In this analysis, acceleration occurs in three planes, leading to changes in altitude and rotation. 

On the most complex level, the skater's body must be analysed as separate components moving in relation to the center of mass, which for most humans is approximately in the center of the abdomen or hips.

Discussion Questions

1. What everyday motions are related to skating? 
2. If skater motion were to be studied by making comparisons between graphs, which types of motions should be compared?

Volume 4 of Glide, Spin, & Jump: The Science of Ice Skating contains graphs of acceleration, force, and vertical distance in a series of motions completed by the author. 

Graphs of Motion

• Standing to Squatting Position
• Jumping with No Rotation
• Rotation with No Jumping
• Skating Jumps on Land
• Skating Jump on Synthetic Ice

Jumps on Land

• Half Jumps
• Stag
• Waltz
• Ballet 
• Mazurka
• Half Axel
• Single & Double Jumps
• Salchow
• Loop
• Toe Loop
• Flip
• Lutz
• Axel

The following two graphs are excerpted from Volume 4 of Glide, Spin, & Jump: The Science of Ice Skating. Notice that these jumps, completed in a purely vertical direction on land, are simpler to analyze, because they lack the horizontal translational motion across the ice. 

Discussion Questions

1. What are the major differences between these graphs?
2. In these graphs, how can direction be determined? What direction is up?
3. In each graph, what occurs in the vertical direction? 
4. In the lower graph, what is the pattern of acceleration in the horizontal plane during the rotations?
5. In each graph, what sort of tilt (side to side) occurs?
6. Is it better to locate the wireless device on the stomach or chest? Why?
7. Describe the role of knee motions during each of the above jumps, and their effects on acceleration.
8. What is the role of non-relevant movements (such as the motion of breathing) in these graphs, if any?
9. What is the role of error or random motion in these graphs, if any? 
10. Are these clean (technically correct) jumps? If not, what would the acceleration pattern be during a clean jump?
11. What would a fall look like in a graph of acceleration?
12. What would the graphs look like if the jumps were completed on the ice?

Additional free graphs of ice skating are available in a free pamphlet from the publisher's webpage. A humorous cartoon animation of an ice skater, showing approximate force vectors, is available from the publisher's YouTube channel.

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of ice skating, figure skating, and hockey:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Ice Skating 
• Volume 1: Translational Motion
• Volume 2: Rotational Motion (Curves)
• Volume 3: Rotational Motion (Spins)
• Volume 4: Jumps
• Volume 5: Ice Hockey
• Volume 6: Biophysics
• Volume 7: Video Analysis
• Volume 8: Reference Manual
• The Science of Hockey
• Volume 1: Force, Acceleration, & Video Analysis of Pucks & Balls
• Volume 2: Force & Acceleration of Sticks, plus Biophysics
• Volume 3: Video Analysis of Ice, Field, & Street Hockey Sticks

Anthologies of 28 Graphs

• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports

In addition, the following books are suitable for younger children learning geometry:

Geometry Workbooks

• The Geometry of Figure Skating
• The Geometry of Winter Olympic Sports 

Additional Information

Schottenbauer Publishing

Free Education Resources

How Does Geometry Affect Ice Skating?

On the surface level, both the technique and beauty of ice skating can be described by geometry, in terms of the angles of knee bends and arm positions. On a technical level, geometry is essential for understanding the science of ice skating, including the physics of force and motion.

The books The Geometry of Winter Olympic Sports and The Geometry of Figure Skating contain diagrams which introduce children and teens to the task of identifying angles in ice skating. Consider the diagram below, excerpted from page 25 of The Geometry of Winter Olympic Sports (Copyright 2014, All Rights Reserved).

Discussion Questions

1. How many angles are formed in this diagram?
2. From a casual analysis, what types of angles (Acute/Obtuse/Right) are located in the diagram? Indicate the location of each angle.
3. In order to analyze the angles in this diagram, where should the coordinate axis be placed? Why? Is it necessary to identify more than one coordinate axis? Why or why not? If so, where should the axes be placed?
4. Using a protractor, measure all the angles in the diagram that are relevant to the art or physics of skating.
5. Is it possible to identify the direction of motion from this diagram? Why or why not?
6. Is this a figure skater or a hockey player? Justify your answer.

Assistance answering some of these questions may be found by watching the video How to Use Geometry Workbooks on the publisher's YouTube channel.

The following books from Schottenbauer Publishing contain geometry diagrams relevant to ice skating, figure skating, and hockey. 

Geometry Workbooks

• The Geometry of Figure Skating
• The Geometry of Winter Olympic Sports 

Additional Information

Schottenbauer Publishing

Free Education Resources

Skater in Motion: x-y Plots of Movement

In elementary school, math students learn the graph-reading skills. How often do these same students enjoy applying math to real-life data? In books from Schottenbauer Publishing, students have the opportunity to decode graphs showing movement during popular sports.

The graph below (Copyright 2014, All Rights Reserved), excerpted from the book series Glide, Spin, & Jump: The Science of Ice Skating from Schottenbauer Publishing, shows an ice skater in forward motion.

Discussion Questions

1. What is the range of each variable in each graph? Include x, y, and t as variables in your analysis.
2. In this sample, which leg is used for pushing off? Which leg moves forward first? 
3. Use the information from the graph to draw the body in physical space, at a minimum of 4 time points.
4. Is the right knee ever in front of the right hip? Is the right ankle ever in front of the right knee or right hip? Describe the sequence of motion.
5. Is the left knee ever in front of the left hip? Is the left ankle ever in front of the left knee or left hip? Describe the sequence of motion.

Additional free graphs are available in a free pamphlet from the publisher's webpage. 

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of ice skating, figure skating, and hockey:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Ice Skating 
• Volume 1: Translational Motion
• Volume 2: Rotational Motion (Curves)
• Volume 3: Rotational Motion (Spins)
• Volume 4: Jumps
• Volume 5: Ice Hockey
• Volume 6: Biophysics
• Volume 7: Video Analysis
• Volume 8: Reference Manual
• The Science of Hockey
• Volume 1: Force, Acceleration, & Video Analysis of Pucks & Balls
• Volume 2: Force & Acceleration of Sticks, plus Biophysics
• Volume 3: Video Analysis of Ice, Field, & Street Hockey Sticks

Anthologies of 28 Graphs

• The Science of Figure Skating
• The Science of Ice Hockey
• The Science of Winter Olympic Sports

In addition, the following books are suitable for younger children learning geometry:

Geometry Workbooks

• The Geometry of Figure Skating
• The Geometry of Winter Olympic Sports 

Additional Information

Schottenbauer Publishing

Free Education Resources