Graphing a Simple Gymnastics Move

What does a simple gymnastics move look like in a graph? A new video from Schottenbauer Publishing shows how a simple head roll can be graphed, using technology from Vernier.

The slides below, excerpted from the video, show the critical components of graphing. 

First, the video shows the motion of the head, with the corresponding graph:

Next, the video shows the motion of the hip, with the corresponding graph:

Finally, the video superimposes both graphs:

Discussion Questions

1. Which part is higher at the beginning? In the middle? At the end?
2. Which part moves the most during the video? Describe the motion in words.
3. Which part moves the most in the x axis? In the y axis? 
4. Does the graph capture the inversion of the head? If so, how?
5. Does the graph capture the rotation of the hip? If so, how?

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Examining Periodicity with a Goniometer

Gymnastic routines involve many types of repetitive motions. In graphs, repetitive motions tend to appear as sine wave functions. Sometimes, multiple sine wave functions must be added, in order to create more complex graphs. A form of advanced mathematics called Fourier analysis allows scientists to analyze oscillation which is more complicated than a simple sine wave.

The following graph is excerpted from The Science of Gymnastics: Volume 2 from Schottenbauer Publishing.

Discussion Questions

1. What is the smallest angle of contraction of the arm? What is the largest angle?
2. Counting from the bottom of the first trough, what is the amplitude of the first oscillation? What is the amplitude of the second oscillation?
3. Counting from the bottom of the first trough, what is the wavelength of the first oscillation? What is the wavelength of the second oscillation?
4. In the first two oscillations, what is the average frequency of oscillation?
5. What occurs at the end of the graph?

Additional graphs of oscillatory motion in gymnastics are available in the same volume, The Science of Gymnastics: 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 Yoga, Pilates, & Ballet, and more.

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Force & Acceleration in Gymnastics

Common gymnastics events can demonstrate the relationship between force and acceleration. Consider the following graphs, excerpted from The Science of Gymnastics: Volume 1 from Schottenbauer Publishing. Although both graphs demonstrate a similar phenomenon, these data were recorded on separate occasions.

Discussion Questions

1. What is the maximum force in the first graph? The second graph?
2. In the first graph, how long is the person in the air for each jump?
3. What is the maximum acceleration in the second graph (assuming that the x axis is vertical)?
4. In the first graph, where does the person begin? (a) On the floor, (b) On the force plate.
5. In the first graph, where does the person end? (a) On the floor, (b) On the force plate.
6. In theory, which requires more force? (a) Stretch Jump, (b) Bounding. 
7. In the first graph, which shows the most force? (a) Stretch Jump, (b) All Bounds, (c) Final Bound.
8. In the second graph, which shows the most force? (a) Stretch Jump, (b) All Bounds, (c) Final Bound.
9. In theory, which requires more acceleration? (a) Stretch Jump, (b) Bounding. 
10. In the second graph, which shows the most acceleration? (a) Stretch Jump, (b) All Bounds, (c) Final Bound.
11. In the second graph, what is the maximum height of the bounding?
12. Do these two graphs show similar technique? If not, describe the differences in words.

Additional graphs of force and acceleration, are available in the same volume, The Science of Gymnastics: Volume 1 from Schottenbauer Publishing. Similar physics data is also available in Volume 1 of several other lab manual series, including The Science of Athletic Training, The Science of Exercise Equipment, The Science of Yoga, Pilates, & Ballet, and more.

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Graphing Breathing Technique with a Spirometer

Breathing is essential for life, and proper breathing technique is essential for success in gymnastics. The following graph, excerpted from The Science of Gymnastics: Volume 2 from Schottenbauer Publishing, illustrates one of the most common breathing problems in gymnastics:

Discussion Questions

1. Describe the set of maximum values. 
2. Describe the set of minimum values.
3. What is the average maximum value?
4. What is the average minimum value?
5. Describe the set of times for the breathing cycle, beginning with inhale and ending with exhale.
6. What is the average length of the cycle in time?
7. What is the average length of time the breath is held?
8. Describe the breathing cycle in words, using a few sentences.

Additional graphs of breathing techniques, plus other biophysics variables, are available in the same volume, The Science of Gymnastics: Volume 2 from Schottenbauer Publishing. Similar biophysics 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 Yoga, Pilates, & Ballet, and more.

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Science of Gymnastics: Volume 4

A new volume of The Science of Gymnastics: Data & Graphs for Science Lab has arrived! Volume 4 features 24 brightly colored graphs depicting a variety of moves on pommel horse, parallel bars, and rings, plus handstands. Many of the moves are available for viewing in a series of free videos on the publisher's YouTube site under the playlist Gymnastics.

The graph below is excerpted from the Volume 4:

Discussion Questions

1. Describe the minimum and the maximum value for each variable.
2. How high do the feet travel? Are the feet ever higher than the hips? Than the head?
3. During this sequence of moves, are the legs straight? Is the body straight? 
4. Describe the initial and final positions of the legs.
5. Can the height of the parallel bars be determined from this graph? If so, what is it?
6. If this graph shows the swings slowed by 2x, what is the timing of the actual swings?

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The Physics of Gymnastics: Pendulum Motion and Circles

Physics divides motion into two general types: translational (straight) motion and rotational (curved) motion. Two types of rotational motion are prevalent in gymnastics: pendulum motion (swinging) and rotation (circles). 

The graphs below, excerpted from the science lab manuals Gravity, Springs, & Collisions: Graphs of Classical Physics Experiments from Schottenbauer Publishing, show patterns of motion from pendulum motion and circular motion.

Discussion Questions

1. What variables are present in Graphs 1? In Graph 2? Is it possible to compare motion using these variables?
2. In which dimensions is there motion in the top graph? In the lower graph?
3. Qualitatively describe the motion contained in these two graphs. What are the similarities? What are the differences?
4. Which types of gymnastics moves involve pendulum motion? How are these moves different from the motion described in Graph 1? 
5. Which types of gymnastics moves involve circular motion? How are these moves different from the motion described in Graph 2?

Data such as those above can be obtained in several series of science and math books by M. Schottenbauer, Ph.D. The first set of books are multi-volume series of graphs. Selections from these lab manuals have also been collected into anthologies: 

Graphs & Data for Science Lab: Multi-Volume Series

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

Anthologies of 28 Graphs

• The Science of Gymnastics
• The Science of Summer Olympic Sports
• The Science of Physical Fitness
• The Science of Dance & Ballet
• The Science of Yoga

Young audiences may be interested in the following series of geometry workbooks on gymnastics and related topics:

Geometry Workbooks

• The Geometry of Gymnastics
• The Geometry of Summer Olympic Sports 
• The Geometry of Yoga
• The Geometry of Ballet

Additional Information

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Free Education Resources

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.

Graphs Shed Light on the Science of Gymnastics

Gymnastics is an amazing sport, which can be studied scientifically in several different ways. First of all, there is a simple physics perspective on the sport: trajectory of movement, velocity, acceleration, and force. But gymnastics is much more complicated, and must include multiple aspects of the human body in order to develop a more comprehensive understanding of its movements. Biophysics data, including joint angles, electrical activity of the muscles (EMG) and heart (EKG), heart rate, blood pressure, breathing, and lung capacity add additional perspective to the sport of gymnastics.

Real scientific data on gymnastics is now available to the public in a set of science lab books, The Science of Gymnastics, from Schottenbauer Publishing. These books, which are suitable for science classes from 7th grade through 12th grade, plus some college and university, offer a variety of samples of data from the above categories. The books can be integrated into math and science classes, plus physical education, health, and coaching sessions in extracurricular sports.

Several samples from the lab manuals (Copyright 2014; All Rights Reserved) are included below. 

Discussion Questions
1) For each graph, describe the range of x and y variables.
2) Which graph above provides the data most self-evident to observers of gymnastics?
3) On Graph 1, how many times does the gymnast bound? Is the force of bounding greater than the stretch jump? If so, why?
4) On Graph 2, what is greater, the electrical activity associated with dipping down or pushing up? What occurs after the dip has been completed?
5) On Graph 3, how high is the ankle during the V-Sit, in comparison to the ankle during the L-Sit? How long is the leg? What is the angle of the V-Sit?

Data such as those above can be obtained in several series of science and math books by M. Schottenbauer, Ph.D. The first set of books are multi-volume series of graphs. Selections from these lab manuals have also been collected into anthologies: 

Graphs & Data for Science Lab: Multi-Volume Series

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

     Each of these series contains multiple volumes, with the following content:

• Volume 1: Force & Acceleration
• Volume 2: Biophysics (Joint Angles, EKG/EMG, Heart Rate/BP, & Breathing)
• Volume 3: Video Analysis

Anthologies of 28 Graphs

• The Science of Gymnastics
• The Science of Summer Olympic Sports
• The Science of Physical Fitness
• The Science of Dance & Ballet
• The Science of Yoga

Additional Information

Schottenbauer Publishing

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The Science of Gymnastics: An Anthology of 28 Graphs

The Science of Gymnastics: An Anthologyof 28 Graphs for Kids, Teens, & Curious Adults by M. Schottenbauer, Ph.D., provides a unique set of data for students of math, science, and gymnastics. Containing a selection of graphs from a longer series by the same author, the book provides students with various types of data for comparison and contrast. Graphs represent a variety of motions typical of elementary gymnastics moves, including:

• Floor
• Vault
• Parallel Bars (Parallettes)
• Pommel Horse (Trainer & Pod)
• Rings
• High Bar

The 28 graphs include the following types of data, from the following positions:

Force Plate

• Plank Position
• Floor Hurdle
• Chassé

Acceleration

• Arm Motions
• Crab Walk
• Tuck Jump
• Vault
• Handstand
• Salto and Handstand on Rings
• Side Swings on Pommel Trainer

Video Analysis

• Quarter Circle on Pommel Pod
• Half Circle with Flare on Pommel Pod
• Side Swings on Pommel Trainer
• Swing to L-Sit on Parallettes
• Salto
• Rings Sequence (Upper Body & Lower Body on Separate Graphs)

Goniometer

• Dip on Large Parallettes
• Simulated Pushup in Handstand Position
• Standing to Deep Squat on Floor
• Standing to Tuck on Large Parallettes

Electromyogram

• Forward Support
• Dip on Large Parallettes
• Pull-Up on Large Parallettes, Neutral Grip
• Pull-Up on Rings, Neutral Grip
• Side Swings on Pommel Trainer

Spirometer

• Normal Breathing
• Breathing with Inappropriate Holding of Breath after Inhale

As with the main series of graphs, this book provides material for a flexible combination of lesson plans. The most basic skills include graph-reading, while more complex skills include comparison and contrast, critical thinking skills, and mathematical modeling.

The Science of Gymnastics: An Anthologyof 28 Graphs for Kids, Teens, & Curious Adults by M. Schottenbauer, Ph.D. is for sale from CreateSpace wholesale and major internet retailers, including Amazon, Barnes & Noble, Books-a-Million, and more!

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The Science of Gymnastics: Exploring the Possibilities!

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

In these books, students can enjoy learning about common moves from gymnastics, including floor, vault, high bar, rings, parallel bars, and pommel horse. 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 which include gymnastics include the following:

Geometry Workbooks

• The Geometry of Gymnastics
• The Geometry of Summer Olympic Sports 

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Gymnastics
• Volume 1: Force & Acceleration
• Volume 2: Biophysics
• Volume 3: Video Analysis

Anthologies of 28 Graphs

• The Science of Gymnastics
• The Science of Summer Olympic Sports

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

Geometry Workbooks

• The Geometry of Yoga
• The Geometry of Ballet

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

Anthologies of 28 Graphs

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

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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.