The Geometry of Snow Sports

Geometry is essential for snow sports. 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 snow sports? 
2. What spatial perspectives and/or mathematical planes are important for precision? 

The cover of The Geometry of Winter Olympic Sports, to the right above, features a cross-country skier 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 snow sports are available in the following book from Schottenbauer Publishing:

Geometry Workbooks

• The Geometry of Winter Olympic Sports

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Schottenbauer Publishing

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Laboratory Model of a Ski Jump

Ski jumps are impressive aerial displays of the laws of physics. Studying jumps in the laboratory, without the presence of wind, presents data which is easier to analyze. 

The following graph is excerpted from Volume 4 of The Science of Snow Sports from Schottenbauer Publishing.

Discussion Questions

1. Using a red pen, separate the graph into the following segments: (a) At Rest on Top of Slope, (b) Trajectory on Slope, (c) Trajectory in Air, (d) Trajectory on Ground, (e) At Rest on Ground.
2. Create a table with the above categories, including: (a) Initial Time, (b) Ending Time, (c) Highest x Value, (d) Lowest x Value, (e) Highest y Value, (f) Lowest y Value.
3. Using the above information, calculate the average velocity during the trajectory on the slope in terms of the speed in the x direction, the y direction, and overall.
4. Using the above information, calculate the average velocity in the air in terms of the speed in the x direction, the y direction, and overall.
5. What occurs after the model skier hits the ground?

Additional data on snow sports can be found in the following science lab manuals from Schottenbauer Publishing:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Snow Sports 
• Volume 1: Force, Acceleration, & Video Analysis (Outdoor Snow & Lab)
• Volume 2: Force & Video Analysis (Plastic Models in Lab)
• Volume 3: Force & Acceleration (Ice-Topped Snow)
• Volume 4: Video Analysis (Models on Curved Surfaces in Lab)

Anthologies of 28 Graphs

• The Science of Winter Olympic Sports 

Schottenbauer Publishing also features other books on sport science, including:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Athletic Training
• The Science of Exercise Equipment 
• The Science of Gymnastics 
• The Science of Yoga, Pilates, & Ballet

  Anthologies of 28 Graphs

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

Additional Information

Schottenbauer Publishing

Free Education Resources

Free YouTube Videos Demonstrate Snow Sport Science Models in Lab

Two new YouTube videos from Schottenbauer Publishing demonstrate the science of snow sports in laboratory conditions. Coordinated with graphs from Volume 4 of The Science of Snow Sports, these videos demonstrate the motion of various wood blocks, a cylinder, a rubber ball, and plastic skier models on a High Density Polyethylene (HDPE) plastic surface. Both natural inclines and curved surfaces are modeled.

Additional data on snow sports can be found in the following science lab manuals from Schottenbauer Publishing:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Snow Sports 
• Volume 1: Force, Acceleration, & Video Analysis (Outdoor Snow & Lab)
• Volume 2: Force & Video Analysis (Plastic Models in Lab)
• Volume 3: Force & Acceleration (Ice-Topped Snow)
• Volume 4: Video Analysis (Models on Curved Surfaces in Lab)

Anthologies of 28 Graphs

• The Science of Winter Olympic Sports 

Schottenbauer Publishing also features other books on sport science, including:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Athletic Training
• The Science of Exercise Equipment 
• The Science of Gymnastics 
• The Science of Yoga, Pilates, & Ballet

  Anthologies of 28 Graphs

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

Additional Information

Schottenbauer Publishing

Free Education Resources

New! The Science of Snow Sports: Volume 4

A new volume of The Science of Snow Sports has arrived! Volume 4 contains graphs from laboratory conditions. The volume compares motion of different objects on curved surfaces which are similar to ski slopes. The main surfaces incline a mildly-abraded piece of HDPE plastic, molded into sloping and U-shaped inclines, and a curved piece of metal sheeting molded into a ski jump. Graphs show the motion of a model skier on skis and a snowboard, plus a variety of shapes of wood blocks, a cylinder, and a rubber ball, as they travel down these slopes.

These data can be used for lesson plans by teachers and parents as supplements for traditional classes, as well as for special school projects, after-school enrichment activities, homeschool, and special science camps.

A sample graph from The Science of Snow Sports: Volume 4 is shown below:

Discussion Questions

1. How far does the skier travel in the vertical plane? 
2. How far does the skier travel in the horizontal plane?
3. Draw a sketch of the curved incline on which the skier travels.
4. Describe the forces on the skier.
5. Calculate the maximum velocity of the skier.
6. What event occurs towards the end of the trajectory? Why?
7. Describe the entire motion of the skier, using a full paragraph.
8. The mass of the skier is 35.93 g and the mass of the skis are 4.60 g. The dimensions of the skis in cm are 7.1 x 1.3 x 0.2.  What additional calculations can be made with these values?

Additional graphs similar to those above can be found in the following science lab manuals from Schottenbauer Publishing:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Snow Sports 
• Volume 1: Force, Acceleration, & Video Analysis (Outdoor Snow & Lab)
• Volume 2: Force & Video Analysis (Plastic Models in Lab)
• Volume 3: Force & Acceleration (Ice-Topped Snow)
• Volume 4: Video Analysis (Models on Curved Surfaces in Lab)

Anthologies of 28 Graphs

• The Science of Winter Olympic Sports 

Additional Information

Schottenbauer Publishing

Free Education Resources

New! The Science of Snow Sports: Volume 3

A new volume of The Science of Snow Sports has arrived! Volume 3 contains 40 graphs made from a wireless dynamics sensor system on a small sled, traveling on inclines of ice-topped snow. Similar to many snow sports, during the experiments the sled is either released freely or pushed, with a variety of motions laterally, uphill, and downhill. Comparison graphs include turns, drops, lifts, and flips. 

These data can be used for lesson plans by teachers and parents as supplements for traditional classes, as well as for special school projects, after-school enrichment activities, homeschool, and special science camps.

A sample graph from The Science of Snow Sports: Volume 3 is shown below:

Discussion Questions

1. How far does the sled travel in the vertical plane? 
2. How far does the sled travel in the horizontal plane?
3. What occurs between 9 and 10 seconds?
4. Describe the forces on the sled. 
5. What is the maximum force on the sled? The minimum force?
6. Calculate the final velocity of the sled.
7. Describe the motion of the sled, using a full paragraph.

Additional graphs similar to those above can be found in the following science lab manuals from Schottenbauer Publishing:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Snow Sports 
• Volume 1: Force, Acceleration, & Video Analysis (Outdoor Snow & Lab)
• Volume 2: Force & Video Analysis (Plastic Models)
• Volume 3: Force & Acceleration (Ice-Topped Snow)

Anthologies of 28 Graphs

• The Science of Winter Olympic Sports 

Additional Information

Schottenbauer Publishing

Free Education Resources

Using Laboratory Models to Study Snow Sports

Laboratory models have the possibility of simplifying the science of snow sports. The following graphs excerpted from The Science of Snow Sports: Volume 2 provide samples of straight and curved motion of a model skier on plastic slopes. The flat slope is HDPE Plastic, and the curved slope is Pinypon Ski.

Discussion Questions for Graph 1

1. How high is the model skier at the beginning of the trajectory? At the end?
2. What is the length of the slope? Draw a model of the slope.
3. What is the velocity of the skier at the end of the trajectory?
4. Approximately how much mass does the model (skier plus skis) contain? Is it possible to obtain a precise estimate?
5. Is it possible to estimate the size of the skis? How large might the skis be?

 Discussion Questions for Graph 2

1. Describe the motion of the skier.
2. Is this slope different than the slope from the first graph? If so, how?
3. Describe the forces on the skier. How do the forces affect the motion?

 Discussion Questions for Graphs 3 & 4

1. One of these graphs shows the front view of the turn, and one shows the side view. Which graph corresponds to each view?
2. Compare these two graphs to Graphs 1 and 2. What are the main differences?
3. Why are these graphs not smooth? What happens to the skier in the region of irregularity?
4. What is the effect of the curve on the skier’s motion?

Additional graphs similar to those above can be found in the following science lab manuals from Schottenbauer Publishing:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Snow Sports 
• Volume 1: Force, Acceleration, & Video Analysis 
• Volume 2: Force & Video Analysis 

Anthologies of 28 Graphs

• The Science of Winter Olympic Sports 

Additional Information

Schottenbauer Publishing

Free Education Resources

Applying the Science of Blocks & Marbles to Snow Sports!

Individuals seeking to understand the science of snow sports now have an unusual source of information to apply to their sport, from the science of toys! Quite to the surprise of many winter athletes, their motion can be approximated by blocks and marbles as they slide or roll down inclines.

The three graphs below (Copyright 2013, 2014; All Rights Reserved) illustrate some of the forces and motions similar to many snow sports.

Discussion Questions for Graph 1 (Above)

1. From what height does the cube fall?
2. What is the energy of the cube prior to falling?
3. What is the speed of the cube at the end of the trajectory?
4. What type of winter sports contain free fall, similar to the cube?

Discussion Questions for Graph 2 (Above)

1. From what height does the cube slide? 
2. What is the energy of the cube prior to its descent?
3. What is the speed of the cube at the end of the trajectory?
4. How much energy of the cube is converted to heat due to friction with the wood incline?
5. Do you think the coefficient of friction of snow is less than the coefficient of friction of a wood incline?

Discussion Questions for Graph 3 (Above)

1. From what height does the marble roll?
2. What is the energy of the marble prior to its descent?
3. What is the speed of the marble at the end of the trajectory?
4. How does the path of the marble compare to the cube from Graph 2? 
5. What type of snow sport motion is similar to a marble rolling?

Additional graphs similar to those above can be found in the following science lab manuals from Schottenbauer Publishing:

• The Science of Toys
• Volume 1: Blocks & Dominoes Pushed on Flat & Inclined Surfaces (Force)
• Volume 2: Block & Dominoes in Free-Fall, Sliding Down Inclined Surfaces (Force, Video Analysis)

• The Science of Marbles
• Volume 1: Marbles Rolling on Flat Surfaces with & without Friction (Force, Video Analysis)
• Volume 2: Marbles Rolling on Curved Surfaces (Video Analysis) 

• The Science of Play: An Anthology

Additional Information

Schottenbauer Publishing

Free Education Resources