Lessons on Friction & Collisions

Friction and collisions are concepts relevant to both ice hockey and figure skating. Consider the graph below, excerpted from a book by Schottenbauer Publishing:

Discussion Questions

1. How is air hockey similar to ice hockey? How is it different?
2. How is air hockey similar to ice skating? How is it different?
3. What happens when a hockey puck collides with a stick? 
4. How are the phenomena in this graph similar to collisions between an ice hockey puck and stick? How are they different?
5. What is the role of friction in ice skating? What does friction do to the motion of a hockey puck or a skater? 
6. How does this graph demonstrate friction?
7. How are the phenomena in this graph similar to friction experienced by an ice hockey puck? How are they different?
8. How are the phenomena in this graph similar to friction experienced by an ice skater? How are they different?

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

Additional Information

Schottenbauer Publishing

Free Education Resources

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.  


Additional Information

Schottenbauer Publishing 

Free Education Resources

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.

Additional Information

Schottenbauer Publishing

Free Education Resources

Affordable Synthetic Ice for Home Practice

The location and cost of ice rinks is often a limiting factor for families interested in recreational skating. Fortunately, several low-cost options are available for both ice hockey and figure skaters.

Shooting Boards
Starting at less than $100, it is possible to purchase various types of hockey shooting pads. These are plastic boards which can be used for practicing puck handling techniques, but not skating. These boards, approximately 2 to 4 feet wide and 4 to 8 feet long, are available from a variety of manufacturers and stores.

HDPE, US Plastic Corporation
High Density Polyethylene (HDPE) is an affordable plastic which can be purchased directly from a manufacturing company, starting at only $2 to $3 per square foot. As a low-glide surface, it is suitable for ice hockey practice and some basic figure skating. A demonstration video available on YouTube shows the use of two HDPE sheets, each 4 x 8 feet and 3/16 inches thick, from US Plastics Corporation. In February 2014, these two sheets cost only $140, plus a $140 freight shipping charge! Placed side by side, these two sheets make a rink 8 feet by 8 feet.

UHDPE, Direct Import from China
The next best surface is Ultra-High Density Polyethylene (UHDPE), which is commonly used at commercial synthetic ice rinks. These are available from various companies in the USA and abroad, but the best value can be imported direct from China. According to a February 2015 estimate, an Olympic-sized synthetic ice rink (100 ft x 200 ft UHDPE) with sideboards is available for only $22,000, including shipping to East Coast USA! (Import tax and transportation from seaport were not included in this estimate.)

Recycled Plastic, Budget Ice from Canada
One of the lowest-cost synthetic rinks in North America is a recycled plastic surface available from Canada. A small sample is available for only $208 plus tax and shipping, according to an estimate in October 2015.

Sinter-Pressed, SmartRink from Canada
One of the highest-quality synthetic ice consists of sinter-pressed materials, which are reported not to flake or scratch like other brands. This surface is available from Canada, as well as some US warehouse locations.

Buildings
Ice rinks can range from a recreation-room or basement model  (e.g., 8' x 8') to a full Olympic sized rink. Although outdoor rinks offer a lower cost and the ambiance of outdoors, indoor rinks have many additional benefits. For instance, indoor rinks allow for more flexibility of use, such as skating at night and during bad weather, as well as protection from leaves and organic matter. Some of the most common buildings used for ice rinks include tension fabric structures, steel structures, and pole barns. These options are available at ultra low-cost from China, with prices as low as $3 per square foot, compared to US models from $9 per square foot or more! Some companies also offer free installation options.


Additional Information

Schottenbauer Publishing

Free Education Resources

The Physics of Spins

Acceleration is an important feature of all ice skating. The same as with motion, acceleration can be translational (in a straight line), or rotational (in a circle). If acceleration is rotational, then it is in an axial direction, pointing inward to the center of the circle of motion. This form of acceleration is called centripetal acceleration.

Consider the following graph, excerpted from The Science of Ice Skating: Volume 3 from Schottenbauer Publishing. The graph shows acceleration during a figure skating spin.

Discussion Questions

1. Initially, which direction is vertical or nearly vertical?
2. At the end, which direction is vertical or nearly vertical?
3. Describe the relationship between the initial and final angles of the foot in relation to the floor.
4. Is it possible to identify how many revolutions are present? If so, how many? If not, why?
5. Is it possible to determine whether this is a slow or fast spin? If so, which is it?
6. What is the initial velocity? The final velocity?
7. What is most likely the cause of the spikes in the 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

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

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

Learning to Glide, Spin, and Jump!

The science and math of ice skating are topics of new books from Schottenbauer Publishing. Presenting data from real figure skating and hockey collected by the science writer and publisher M. Schottenbauer, Ph.D., these books bring the "high tech" end of skating to audiences everywhere!

In these books, students can enjoy learning about common moves from figure skating and hockey. One series of books, written for elementary school students, focuses on geometry. Two series of science books feature graphs and data; these illustrate common mathematical functions, plus a variety of concepts from physics and biophysics. The science books can be integrated into classes such as math, physical science, physics, physical education, and health, anywhere from 7th grade through high school, as well as some introductory college and university classes. 

The books directly pertaining to ice skating and hockey include the following:

Geometry Workbooks

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

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 

These books are complemented by a series of science books on other popular sports topics, including Olympic sports, athletic training, exercise equipment, gymnastics, yoga, ballet, and more. Topics related to ice skating include:

Geometry Workbooks

• The Geometry of Yoga
• The Geometry of Ballet
• The Geometry of Gymnastics

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Athletic Training
• Volume 1: Force & Acceleration
• Volume 2: Biophysics
• Volume 3: Video Analysis 
• The Science of Exercise Equipment 
• Volume 1: Force & Acceleration
• Volume 2: Biophysics
• Volume 3: Video Analysis
• The Science of Yoga, Pilates, & Ballet 
• Volume 1: Force & Acceleration
• Volume 2: Biophysics
• Volume 3: Video Analysis
• The Science of Gymnastics 
• Volume 1: Force & Acceleration
• Volume 2: Biophysics
• Volume 3: Video Analysis

Anthologies of 28 Graphs

• The Science of Physical Fitness
• The Science of Dance & Ballet
• The Science of Gymnastics
• The Science of Yoga

Most of the books above are available in both English and German translation. The books pertaining to the geometry of Olympic sports are also available in 15 world languages. 

The same publisher offers similar books on additional popular topics, including sports, transportation, construction, environment, music, entertainment, and general physics. All of these book series are available in several formats and languages, including the following:

Geometry Workbooks

• Print & E-Book Editions
• Available in English & German
• Olympics Books Available in 15 Languages

Graphs & Data for Science Lab: Multi-Volume Series

• Print Editions
• Available in English & German

Anthologies of 28 Graphs

• Print Editions
• English Only

Additional Information

Schottenbauer Publishing

Free Education Resources

Vendors

Amazon & Worldwide Affiliates

Barnes & Noble

Books-a-Million

CreateSpace

CreateSpace Wholesale

MusicaNeo Digial Sheet Music

Zazzle Art, Posters, & Memorabilia

Unbeatable Specials

With Kindle Unlimited ($9.99/month) at Amazon.com, you can read all e-books from Schottenbauer Publishing for no extra charge! Amazon offers Free 30 Day Trials of Kindle Unlimited. With this deal, trial members can read all Schottenbauer Publishing e-books free! This includes all the geometry workbooks, plus "The World in a Graph," "Alphabets of the World," textbooks on the science of music, all the e-book puzzles, and the educational novels by M. Schottenbauer, Ph.D.