Comparing Ball Performance: Basketball & Soccer

Ball sports require many different types of balls, each with various characteristics. These properties can be examined by the scientific method. Consider the following table, excerpted and edited from Volume 4 of Bounce, Roll, & Fly: The Science of Balls from Schottenbauer Publishing. 

Discussion Questions

1. How many times does the ball bounce?
2. For what length of time does the ball bounce?
3. From what initial height is the ball dropped?
4. How high does the ball bounce each time? Make a table listing the values, in order.
5. What is the difference between sequential heights? Add these to the table.
6. How far does the ball drift in the x direction?

Discussion Questions

1. How many times does the ball bounce?
2. For what length of time does the ball bounce?
3. From what initial height is the ball dropped?
4. How high does the ball bounce each time? Make a table listing the values, in order.
5. What is the difference between sequential heights? Add these to the table.
6. How far does the ball drift in the x direction?

Comparison Questions

1. Which ball is larger?
2. Which ball has more mass?
3. Which ball bounces more times?
4. Which ball bounces longer in time?
5. Which ball is dropped from the higher point?
6. Which ball drifts further in the x direction?

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Bouncy & Sticky Balls

Although most sports balls will bounce when hitting hard surfaces, not all balls have such properties. Clay balls, for example, may either bounce or stick, depending on the consistency of clay. Some clay balls may even shatter upon contact, due to fragility.

In order to compare bouncing and sticking properties of various types of balls, consider the following graph, excerpted from Bounce, Roll, & Fly: The Science of Balls, Volume 8 from Schottenbauer Publishing.

Discussion Questions

1. What is the initial position of each ball? Write the coordinates in terms of (x, y) pairs.
2. Which ball is initially higher?
3. Which ball falls faster? Why is this the case?
4. What is the time difference between points of contact with the wood?
5. Do both balls bounce? Cite data from the graph to answer the question. What is the height of bounce?

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Natural vs. Sport Action of Swinging Clubs

Many sports involve a swinging action. Depending on the sport, it may be clubs, bats, rackets, arms, and/or feet which are swung. 

Variations in swinging technique lead to massive differences in results. Take a moment to consider the natural swinging motion of a golf club. The following graph is excerpted from Golf Science, Volume 1 from Schottenbauer Publishing.

Discussion Questions:

1. What are the maximum and minimum x positions of the club? The y positions? Write these as coordinate pairs (x, y).
2. Sketch the real positions of the club, during the first swing back and forth. Does the club begin at the right or left?
3. How many times does the club swing in the graph?
4. How does an athletic swing of the club differ from the natural swing of the club?

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Does Follow-Through Really Matter?

One of the most important techniques for children to learn in physical education class is the concept of follow-through. Hitting a ball effectively requires prolonged contact between the bat/club/racket/foot and the ball. This means that the bat/club/racket/foot must continue through the point of initial contact, following the ball and pushing it as far as possible as it travels away from the player.

The concept of follow-through can be examined using graphs. Consider the graphs below, excerpted from the book Golf Science from Schottenbauer Publishing:

Discussion Questions:

1. Which graph above shows backwards rebound of the golf club from the ball?
2. Which graph above shows follow-through in the swing?
3. Compare the graphs, and describe the difference in the highest pre-swing position of the golf club, including both vertical & horizontal coordinates. Is the highest pre-swing position of the club approximately the same in both graphs?
4. Compare the graphs, and describe the difference in velocity (speed and direction) of the golf club at the moment it hits the ball. Is the velocity approximately the same in both graphs?
5. Compare the graphs, and describe any differences in the trajectory of the ball.
6. Using these graphs, describe the importance of follow-through.
7. Are these graphs suitable for assessing the importance of follow-through?

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Relating Ball Specifications to Performance

Take a moment to think: How many ball sports exist? Each one requires a ball of a specific size and construction. Within each sport, certain manufacturers may offer a set of uniquely performing balls, each varying slightly from the others in materials. Some sports also offer multiple sizes of balls, to accommodate the needs of children, youth, and adults.

Consider the following table, excerpted and edited from the Sampler Edition of Bounce, Roll, & Fly: The Science of Balls. This table contains a selection of balls found both in the Sampler Edition and a set of accompanying YouTube videos:

Discussion Questions:

1. How many sports are represented in the table above? 
2. What is the largest ball? The smallest?
3. Which ball has the largest mass? The smallest?
4. Write out the ball names in order from smallest to largest size. 
5. Write out the ball names in order from smallest to largest mass. 
6. Is the order of balls in #4 and #5 the same? Why of why not?
7. For this set of data, how should the average size be calculated?
8. What is the average size of ball? 
9. What is the average mass of ball?
10. Describe the differences between the three types of baseballs. Why is one smaller than the others?
11. Is the information above sufficient for manufacturing a ball? Why or why not?
12. Use the Internet to find out which balls from the table above are solid and which are hollow. Among those which are hollow, which are inflatable and which are not? What is the normal air pressure for each inflatable ball?

Lab manuals from Schottenbauer Publishing can be used to supplement traditional curricula in math, physical science, physics, and physical education. They can also be integrated into summer camp and other summer academic enrichment activities, from approximately age 10 and onward. Ideas for lesson plans can be found in the blog Graphs in Education. 

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The Art & Science of Baseball

As the summer arrives, the warm weather beckons children outdoors. In-between ball games and sporting events, do they have time to learn about the math and science of sports? Lab manuals from Schottenbauer Publishing make it easier than ever to learn about sport science.

For instance, consider the new series The Science of Baseball. The following graphs teach children about several aspects of baseball science. What can be learned from each graph?

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Does a Ball Fall Like This? Free Video Tests of Motion

Teachers and homeschool parents can quiz their students on the motion of balls with a new series of free YouTube videos from Schottenbauer Publishing. 

• Motion Test 1: Does a Ball Fall Like This? 
• Motion Test 2: Does a Ball Bounce Like This?
• Motion Test 3: Does a Ball Fly Like This?

These videos can be watched before and after three tutorial videos, showing 24 real sport balls bouncing, rolling, and flying through the air in projectile motion.

• Sport Balls Bouncing
• Sport Balls Rolling
• Sport Balls Flying

The latter three videos correspond to the Sampler Edition of Bounce, Roll, & Fly: The Science of Balls. This and other books by M. Schottenbauer, Ph.D. are available in both English and German from Amazon, Barnes & Noble, Books-a-Million, Powell's, and other internet retailers. Wholesale is available directly from CreateSpace online.

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The Science of Baseball: A New Book Series

A new book series, The Science of Baseball, Volumes 1 & 2, has arrived from Schottenbauer Publishing! This book series is available from CreateSpace, Amazon, and other internet retailers.

This book series contains graphs relevant to baseball and softball. The first two volumes focus on video analysis of balls and bats under common conditions. Graphs show trajectories from various points of origin, with time plotted against x and y variables. Topics for Volumes 1 and 2 include the following:

Volume 1 Topics

• Trajectories of Plastic Balls from Pitching Machine
• Hardball
• Softball
• Pop Fly
• Grounder
• Lateral Drift Due to Wind

Volume 2 Topics

• Comparison and Contrast of Balls & Bats
• Bats
• Wood
• Plastic
• Aluminum
• Balls
• Official Baseball
• Safety Baseballs
• Plastic Baseballs
• Softball
• Wiffle Ball
• Balls falling and rebounding from bats & concrete
• Balls rebounding from plywood set at angles
• Bats hitting balls on a stationary tee

These books are suitable as a supplement for class projects in math, physical science, physics, and physical education. Ideas for lesson plans can be found in the blog Graphs in Education. 

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Comparing Graphs of 24 Sport Balls Bouncing, Rolling, & Flying

A new edition of Bounce, Roll, & Fly: The Science of Balls has arrived! The Sampler Edition contains graphs of 24 sport balls as they bounce, roll, and fly through the air, including three baseballs (official, safety, plastic), a basketball, a cricket ball, a dodge ball, a football, three golf balls (official, foam, plastic), a hackeysack, three hockey balls (field, low-density street, high-density street), a kickball, a lacrosse ball, a ping pong ball, a racquetball, a rugby ball, a soccer ball, a softball, a tennis ball, a toy ball, and a volleyball. This is undoubtedly the best book in the series, because it is coordinated with three YouTube videos showing the balls in motion, bouncing, rolling and flying!

The graph below is excerpted from Bounce, Roll, & Fly: The Science of Balls: Sampler Edition.

Discussion Questions

1. How many times does the baseball bounce?
2. From what height is the baseball dropped?
3. Write one or more equations describing the motion of the ball.
4. What is the potential energy of the baseball in the beginning? At the peak of each bounce? In the end of the graph?
5. What is the maximum velocity of the ball? The maximum momentum?

Understanding graphs such as the one found above can be enhanced by viewing free YouTube videos on the publisher's site. These videos allow students to compare the motion of the balls visually as they travel in space. Students might be asked to watch the videos first, and estimate the performance of the balls visually before examining the graphs. For instance, which ball bounced highest?


Books related to ball sports from Schottenbauer Publishing include: 

Graphs & Data for Science Lab: Multi-Volume Series

• Bounce, Roll, & Fly! The Science of Ball Sports
• The Science of Hockey (Field, Street, & Ice)

Anthologies of 28 Graphs

• The Science of Ball Sports
• The Science of Summer Olympic Sports 
• The World in a Graph

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Free Video Shows 23 Sport Balls Bouncing!

Corresponding to the theme of the science lab manual series, Bounce, Roll, & Fly: The Science of Balls, a new, free YouTube video from Schottenbauer Publishing contains footage of 23 balls bouncing. 

The balls, in order shown in the video, include: Dodgeball, Kickball, Soccer, Volleyball, Basketball, Softball, Official Baseball, Safety Baseball, Plastic Baseball, Tennis, Cricket, Racquetball, Lacrosse, Field Hockey, High Density Street Hockey, Low Density Street Hockey, Official Golf, Foam Golf, Plastic Golf, Ping Pong, Football, Rugby, and Hackeysack.


Discussion Questions for the Video

1. From how high, approximately, are the balls dropped?
2. From a visual estimate, which is the largest ball? How large is the ball, approximately?
3. Use a stopwatch to time the length of bouncing for each ball. Which ball bounces the longest amount of time? The shortest amount of time?
4. How far do the balls rebound each time? Is there a ratio to describe the decrease in ball height for each bounce?
5. What features of the ball determine the ball's performance during bouncing? How do these features relate to the sport?

This video is part of a 3-part series, consisting of individual videos with balls bouncing, rolling and flying. Students can view these videos in conjunction with science lab manuals from Schottenbauer Publishing.

Update (2/26/2015)! The Science of Balls: Sampler Edition and its German translation, are now available! Corresponding directly to the three YouTube videos listed above, this book contains graphs of 24 sport balls as they bounce, roll, and fly through the air.

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