Schottenbauer Publishing

Showing posts with label mathematics. Show all posts
Showing posts with label mathematics. Show all posts

Friday, June 12, 2015

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 SkatingNotice 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:

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

    Sunday, April 5, 2015

    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. 


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

    Thursday, October 2, 2014

    Pucks & Balls: The Physics of Motion

    How does a ice hockey puck compare to a field hockey ball? This question is highly relevant for ice hockey players, who are eager to keep in shape over the warm summer months. According to physics, balls do not act like pucks. The graphs below (Copyright 2014, All Rights Reserved), excerpted from the book series The Science of Hockey from Schottenbauer Publishing, show an official field hockey ball and an official ice hockey puck in 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. Use the information from the graph to draw the trajectory of the ball and the puck on separate pieces of paper. Include beginning and ending time points in your drawing.
    3. Using the information from Questions 1 and 2, compare the graphs. What is different about the motion of the ball and the puck?
    4. Approximately how much energy from the ball is lost due to friction? 
    5. Approximately how much energy from the puck is lost due to friction? 

    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

      Spinning on Ice

      Physics divides motion into two general types: translational (straight) motion and rotational (curved) motion. Whether it is a figure skater, hockey skater, or puck rotating on the ice, the same laws of physics apply. 

      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 a rod rotating around a central axis.




      Discussion Questions
      1. Describe the four variables contained in the graph. What is the range of each variable?
      2. How is position measured in the graph? What is the unit of measurement?
      3. How many times is force applied to the rod? 
      4. When force is applied, what happens to the rod?
      5. Why does the rod slow down, and motion stop?
      6. What is the definition of acceleration? 
      7. Why does acceleration change so much, when the velocity and position do not?


      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


        Thursday, July 31, 2014

        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:

        • 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




        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.