Breathing Patterns

Breathing is an essential component of all forms of physical exercise. 

How can breathing be measured? Take a moment to write a list of variables relevant to breathing. 

Respiration rate (number of breaths per unit time), lung capacity, depth of respiration, and rate of airflow are all ways to measure breathing. 

A spirometer measures the rate of flow of air from breathing. Consider the graphs of spirometer readings below, excerpted from a book series by Schottenbauer Publishing.

Discussion Questions

1. In each graph above, what are the maximum and minimum flow rates?
2. In each graph above, what is the period of breath cycle? 
3. In each graph above, what is the frequency of breath cycle? 
4. Why is the first graph not a perfect sine wave?
5. Why is the second graph not showing the same shape as the first graph?

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Science of Yoga & Ballet Memorabilia

Celebrate the sport science of ballet and yoga 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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The Geometry of Ballet & Yoga

Geometry is essential for physical activities such as ballet and yoga. Take a moment to write down a few ways in which geometry affects the precision of these activities. 

Discussion Questions

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

The cover of The Geometry of Ballet, to the right above, features a dancer 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?

The cover of The Geometry of Yoga, to the right below, features a yoga pose. 

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 ballet and yoga are available in the following books from Schottenbauer Publishing:

Geometry Workbooks

• The Geometry of Ballet
• Paperback
• Kindle E-Book
• The Geometry of Yoga
• Paperback
• Kindle E-Book

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The Mathematics of Goniometer Readings

A goniometer is a device which measures joint angles, such as those made repetitively in ballet, dance, PIlates, and yoga. Goniometer readings often appear as sine waves, and can be analyzed as such.

Consider the following graph, excerpted from The Science of Yoga, Pilates, & Ballet: Volume 2 from Schottenbauer Publishing:

Discussion Questions

1. What is the initial position of the knee? Is the leg entirely straight?
2. What is the deepest angle of bending at the knee?
3. What is the range of angles contained in the graph?
4. Counting from the bottom of the first trough, what is the amplitude of the oscillation? 
5. Counting from the bottom of the first trough, what is the wavelength of the oscillation? 
6. What is the frequency of the oscillation?
7. How many knee bends are included in the graph?

Additional graphs of goniometer readings are available in the same volume, The Science of Yoga, Pilates, & Ballet: Volume 2 from Schottenbauer Publishing. Similar physics data is also available in Volume 2 of several other lab manual series, including The Science of Athletic Training, The Science of Exercise Equipment, The Science of Gymnastics, and more.


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How Is Acceleration Relevant to Yoga?

As one of the slowest sports, yoga may not seem to contain much acceleration. The phenomena of acceleration, however, is essential to understanding the benefits of yoga, due to the effects of gravity. Gravity is the force which pulls all matter towards the center of the earth. On the earth's surface, the pull of gravity is associated with acceleration downwards. Yoga includes poses in various positions, including full and partial inversions. Therefore, various yoga poses engage the acceleration of earth's gravity in different ways.

Consider the following graph of a sun salutation sequence, excerpted from The Science of Yoga, Pilates, & Ballet: Volume 1 from Schottenbauer Publishing:

Discussion Questions

1. Which direction is initially in the vertical position: x, y, or z? Why? (Hint: What is the acceleration due to gravity at the earth's surface?)
2. Separate the graph into four sections, based on position. Label each section with one of the following: (a) Bow at Waist with Hands in Front or Behind Legs, (b) Hands Up and Around to Backbend, (c) Hands Up and Around to Standing Prayer Position, (d) Standing Prayer Position.
3. What are the effects of gravity on fluids in the body (blood, lymph, etc.) during these motions?
4. How might these differences in acceleration affect the health benefits and/or risks of yoga?

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Science of Yoga, Pilates, & Ballet: Volume 4

A new volume of The Science of Yoga, Pilates, & Ballet: Data & Graphs for Science Lab has arrived! Volume 4 features brightly colored graphs depicting a variety of complex moves. Examples include a yoga sun salutation, Pilates splits, backbend, and inverted bicycle, and a series of ballet leaps (Glissade, Sauté, Soubresaut, Pas Assemblé, Pas de Chat, Sissonne Fermée, Royale, Grand Jeté, and Cabriole). The book also contains graphs showing ballet jumps with a variety of axes options, as well as comparison data from the motion of a ball flying through the air, falling, and bouncing on a carpet.

The two sample graphs below are excerpted from Volume 4:

Discussion Questions

1. What is the minimum and the maximum for each variable in these graphs?
2. Which leg rises into the air first?
3. How high is the jump?
4. How long is the person in the air?
5. Does either ankle ever rise higher than either knee?
6. Is this correct technique for glissade?
7. Draw a sketch of the person's movement at five (5) points during the move, to show what the move looks like to an audience. Use a stick figure.
8. Where should the arms be for the glissade? Draw the ideal position of the arms on each of your sketches from #7. Then, draw a graph showing the ideal movement of the arms. Use a separate graph for the right and left arms. Include Shoulder, elbow, and wrist in your graphs.

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The Science of Yoga, Pilates, & Ballet: Suggested Activities

The science book series Stretch, Hold, Move, & Leap! The Science of Yoga, Pilates, & Ballet Volumes 1, 2, & 3 by M. Schottenbauer, Ph.D., contain a treasure-chest of graphs filled with physics and biophysics variables. The following are a small sample of the many questions which can be explored in this series of books!

Activity Questions for Volume 1: Force & Acceleration!

• What does a flat step on a force plate look like? (Find the answer on page 27!) What about stepping on toe? (Answer on page 30!) What is the difference between these two motions?
• During Pilates arm circles, does anything happen to the feet? (Find the answer on page 22!)
• Describe the forces and reactions involved in toe lifts, first from the perspective of the mover, then from the perspective of a force plate underneath the feet. (Find the answer in the graph above!)

Activity Questions for Volume 2: Biophysics!

• What are the effects of spinal twists on blood pressure and pulse? (Find the answer on page 88!) 
• In order to lower blood pressure immediately, is it better to do a partial inversion with legs raised, or 15 minutes of aerobic exercise? (Answer on pages 88-90!)
• Compare the flow rate and volume of normal breathing with slow and fast yoga breathing (pranayama), respectively. (Answers on pages 80-83!)

Activity Questions for Volume 3: Plots of Motion!

• Do Pilates arm circles look different in an x-y plot when graphed from the front view, when compared to arm circles graphed from the side view? (Answer on page 10-11!)

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Yoga, Pilates, & Ballet
• Volume 1: Force & Acceleration
• Volume 2: Biophysics
• Volume 3: Video Analysis

Anthologies of 28 Graphs

• The Science of Yoga
• The Science of Dance & Ballet

Related books, appropriate for younger students, include the following:

Geometry Workbooks

• The Geometry of Yoga
• The Geometry of Ballet 

Additional information on these and related book series is available on the author's blog on Sport Science Education.


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