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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Science of Gymnastics Memorabilia

Celebrate sport science with memorabilia from Zazzle! Colorful graphs from Schottenbauer Publishing are featured on these mugs, magnets, keychains, & postcards. Direct links 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 Gymnastics

Geometry is essential for gymnastics. 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 gymnastic events? 
2. What spatial perspectives and/or mathematical planes are important for precision? 

The cover of The Geometry of Gymnastics, to the right above, features a gymnast 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 gymnastics are available in the following books from Schottenbauer Publishing:

Geometry Workbooks

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

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Parallel Bars: Coordinated Video and Graph

What do gymnastic moves look like in a graph? Consider the following sample, excerpted from The Science of Gymnastics, Volume 4 from Schottenbauer Publishing:

The corresponding video, which includes moves on pommel horse, parallel bars, and rings, is included below:

Discussion Questions

1. How many swings are completed?
2. Describe the minimum and the maximum positions of the feet, knees, and hips.
3. What body part reaches the highest point in the graph?
4. Redraw the graph in real time (2x).

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Affordable Gymnastics Equipment

Due to the popularity of home gyms and the availability of low-cost imports, the price of exercise equipment has decreased substantially in the past 30 years. Despite these improvements, most formal gymnastics equipment is still above the reach of many consumers. Several options are available, however, for improving access to quality experiences.

Homemade Equipment
Beginners who are learning the most basic moves may be able to use simple homemade equipment. A variety of YouTube videos show how to make equipment suitable for simple exercises, although not for intermediate or advanced moves. Individuals using homemade equipment should beware the risk, which may cause injury or death. 

Direct Imports
Formal gymnastics equipment is available low-cost through the formal supplier to the 2008 Beijing Olympics, Tiashan Sports, as an import direct from China. For instance, an Olympic pommel horse, parallel  bars, and rings with support frame, plus 3 landing mats, shipping to an Eastern USA seaport, and import tax (approximately 5.5% in the USA), were quoted in February 2015 as only $13,000. Equipment must be picked up at seaport, or shipped within the USA at additional expense. Other foreign suppliers can of equipment can be located on the Made-in-China website, and other foreign trade websites.

Online Discount Vendors
A variety of online discount vendors, including Amazon.com, provide surprisingly low prices on formal gymnastics equipment. Some equipment is delivered with free shipping directly from Amazon, while other equipment is delivered at additional cost directly from vendors. Amazon.com offers Olympic gymnastics equipment, as well as preparatory equipment for children and traditional exercise equipment. The latter, including bicycles and weights from low-cost vendors such as Sunny Health & Fitness, may be the most convenient for facilitating gymnastics training at home.

For serious gymnasts, equipment will require a special building with a high ceiling. Several low-cost options 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.


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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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