Introduction. Physics of Sports.

Last updated on 19 May/98

Instructor: Kenneth K. Young. Office B213
Tel: 543 4186, email: URL ../

Teaching Assistant: Anton Ryzhov. Office B149. tel: 543 6669. email:

Class meetings in A118 Physics-Astronomy Building on MWF at 10:30.

Office hours: MWF at 11:30; and Tu,Th at 10:30 at the lab B143; or by appointment.


Test 1 on 13 April. You should premake an information sheet. One information sheet is permitted to be used during all exams. No books or notebooks or printed class notes are permitted.

The process of condensing your knowledge is a good discipline that will help you to learn and understand.

Qualifications for this class

The aspiring student should have at least have successfully completed college level science and math; or at least have been a whiz at high school science and math; especially in the "story-book" problems.

Mathematics is not just another language. Mathematics is a language plus reasoning; it is like a language plus logic. Mathematics is a tool for reasoning. It is in fact a big collection of the results of some person's careful thought and reasoning. By mathematics it is possible to connect one statment to another. From "Character of Physical Law by Richard Feynman.

FAQs about this class

Texts :

a) Web documents on this site.

b) Physics 208A notes and excercises , available from ASUW lecture notes at the HUB.

useful references:

c) Muscles, Reflexes, and Locomotion. Thomas A. McMahon. $25. This is a superb book on the fundamentals of locomotion which range from basic muscle mechanics and thermodynamics to coordinated motion. There is a thought provoking section on the effects of scale. What if any is there any advantage to a particular size for a particular sport?

d) The Biomechanics of Sports Techniques, James G. Hay. This text covers major sports. Baseball, Basketball, Football, Golf, Gymnastics, Softball, Swimming, Track and Field.

e) Sport Science, Peter J. Brancazio. This is a highly readable book by a sports fanatic physicist.

f) The Physics of Baseball, Robert K. Adair. Professor Adair is the Physicist of the National League. Professor Adair's evocation of insects sitting on baseballs to give you some idea of how flow of fluids work is masterful.

g) World-in-Motion. CD for Physics Analysis Software with examples. Physics Curriculum and instruction. 22585 Woodhill Dr., Lakeville, MN 55044. Tel: 612 6461 3470

h) Physics of Sports, Ed. Angelo Armetnti, Jr, American Institute of Physics (1992). This is a collection of articles on the physics of sports that have been published by AIP and has been a starting point for many of the developments in physics of sports.

i) Bicycling Science, F. Rowland and D.G. Wilson, MIT Press (1985). There has been a lot of developments on training since this book was published but you'll find it to be a very useful guide on the limiting factors for producing speed for various durations from sprints to long distance.

Here's a sample of the type of questions that we will address and study.

How does Sam Perkins optimize his stroke to get a season average of 41% in the 3-point basketball shot? Does the apparently upright posture of Michael Johnson, the Olympic Champ in 200 and 400 meter go against conventional wisdom? How does a modern larger head tennis racket make us better players? What's the basis for the sculling type stroke used by successful free style swim racers? Why does "thinking" hard while shooting the basketball usually make things worse? Why does a curve ball curve? and why does it appear to "break"? Why do some thicker keels and rudders make a boat go faster than a knife edge, thin keels and rudders? Why does the optimal golf shot off the tee take off at about 20 degrees while the optimal shot put is launched at 45 degrees? Why do big runners and swimmers in distance events go no faster than small athletes? Are there some sports where big is best? or small is best? .. and why All this and more!

Each student will be expected to carry out a sports measurement as part of the course.


There is considerable scientific evidence that the healthy personality is one who not only plays, but who takes his play seriously. -Dr. William Menninger

You are motivated by curiosity about high level of sports performance and have the desire to improve your own level of physical performance. This is the premise for this course. There are many elements in optimum sports performance which includes physiology, psychology as well as the science of motion. In this course, we will touch on all of the elements but we will concentrate on the PHYSICS of sports which is concerned with the MECHANICS of motion. This includes kinematics, dynamics, and the ideas of momentum, energy and power and the efficient use of the human body and of sports equipment to achieve high levels of performance.

Our historical development has left us with a mish-mash of ways of measuring physical quantities (e.g. foot, mile, meter, pound, Newtons, horsepower, watts). In this course, we will use the STANDARD INTERNATIONAL UNITS (METRIC). There is great virtue to the use of these (as well as some disadvantages) as you will see during this course. I will expect you to develop facility at using the SI units and at converting other units into SI units. The lectures will consist of the uncovering some of the subjects from your reading and exploring them in greater depths. We will have many physical demonstrations and video slow-motion demonstrations of the physics points. There will be ample opportunities for questions. I quite believe that the classroom time is well used if my presentations and your reading raises lots of questions.

Class Notes

Many of the class notes and problem solutions etc will be available on the website for this class. This will be hyperlinked from the study schedule section of this document.

It would be best if you were to access these notes from your own web browser or from one of the browsers available from the University. Click here for a list of sites for the web browsers on campus and for how to convert your home computer to a web browser.

How to Study Physics. Notes from the University of Texas.

Click here. for Some Frequently Asked Questions (FAQs) about Muscles , Tendons and Bones.


The out-of-towner on 5th Ave in NYC asks "How do I get to Carnegie Hall?". The answer " Practice, Practice". While you would not expect to learn how to play the piano or bat a baseball by reading about the subject, many students have the mistaken belief that Physics can be learnt by reading about the subject only. It would be best to practice, practice, practice with the actual phenomena.. unfortunately, this is not practical for this lecture class. I offer you practice with the formal theoretical parts. I leave the physical practice to your own spare-time activity. I will assign weekly problem sets. At the end of the weekly period, I will give you solutions to the problems and a discussion session. I will not collect the problems for grading. However, to encourage you to carry out the problem practicing assiduously, I will give tests rather often.....every two weeks. The tests will consist mostly of variations of the homework problems. To do well on the tests, you must practice, practice. You should expect to at least study for two hours for each hour of class. Expect that this class will take at least 9 hours per week.

Tell me and I will forget. Show me and I might remember. But let me do it, and I will both understand and Remember.

Chinese Proverb.

Study in groups.

You'll find that you learn immense amounts when you verbalize the ideas. During the business hours, the physics TA's in the study Center [mezzanine of PAB A wing] will offer help tutoring you in physics. There will also be tutoring sessions in B143 at 11:30 on M W F; and 10:30 on Tu and Th.


I expect that you will learn to be able to characterize a sports activity in the framework of physics. I will also expect interpret data in tabular or graphical form to use this to evaluate physics performance in some standard physical parameters. TESTS. There will be 4 tests during the term and the final during finals week. The tests will consist of questions which are similar to the weekly problem sets. Each of the 4 tests will count for 1 unit. The final will count for 2 units. Your grade will be figured from the 4 best of the 6 units. Each exam will be weighted according to the average and standard deviation for the particular exam. The dropping of the worst unit is meant to take care of your "off-day" or "illness-day" or "---?". You can choose (with permission) to retake the unit tests during the period for the final exam. However, these exams will only count up to the 2.0 for that exam. You may bring a help page with constants, formulae, etc. which you have made to the exam. Calculators are permitted but I would prefer that you leave your solutions in unrationalized form.

PROJECTS . Project opportunities in place of tests are not available in 1998. You may wish to carry out some projects under supervision but without grade.

A student may find the pace in class too slow and might choose to carry out a sports-physics project in order to study some particular sports area in greater depth. A typical project may be a measurement of a sports activity with analysis in physics terms. The project may count for 2 units and may be used in lieu of 2 units of the TESTS. A student carrying out a project for evaluation would then be graded on the best 4 of his possible 8 units. Usually, only those students who are deeply involved with athletics and have access to team equipment find this to be a viable alternative. I would expect the project to be reported formally in the style of a normal scientific report with:

  1. INTRODUCTION. theory and motivation for the study.
  2. METHOD. Method used to make evaluation and analysis.
  3. APPARATUS. What is used to make the measurement.
  4. DATA. Data collected
  5. ANALYSIS. Analysis of the data set
  6. RESULTS. The results of your investigations
  7. DISCUSSION. Discuss results and compare with other investigators and subjective impressions.
  8. CONCLUSION. summary of your scientific conclusions.

Form of the project

The project could be submitted in hard-copy paper form or it could be in multimedia form. For example, each student at UW has the resources to make their own web page. [This uses the computer named "WEBER".] In this form, you could have text, pictures, videos as well as sound. Outstanding projects would be transferred to a permanent file where this could be a library resource for future generations as well as a resource for the sportspersons around the world. What would also be welcomed could be projects on video tape. Since we are studying motion, videos of various kinds of motion would be welcomed in tape form. I have facilities for using 8mm as we as VHS tapes. [No BETA max, please.] Of course a video presentation should be accompanied by text... probably in hard copy form for legibility. A brief description of how to make your own web page is described here.

Before you start a project, you must present me with an outline and have my approval. The project must meet minimum levels of breadth and depth. While some library research is always necessary, the project should contain some measurements made by the student.

A valid project must undergo several stages, each with its deadline. The stages are:

1. submission and approval of an outline for the project. 5th week 28 April
2. submission and approval of a first draft of the project. 8th week 19 May
3. submission of the final draft of the project [by the date of the final exam.] 9 June.

In the matter of physics, the first lessons should contain nothing but what is experimental and interesting to see. A pretty experiment is in itself often more valuable than twenty formulas extracted from our minds; it is particularly important that a young mind that has yet to find its way about the world of phenomena should be spared the formulae altogether.

Albert Einstein.

Study Schedule.

The ones listed here are for 1998.

date test Subject test units
13 April Test 1 volumes 1,2 1
29 April test 2 volumes 3,4 1
13 May test 3 volume 5 1
27 May test 4 volumes 6, 9 1
8 June. 8:30-10:20 Final Exam volumes 1 to 10. 2

There will be NO make-up exams. There are 6 possible units that you can obtain and only the top 4 will be used for your grade.


item test1 test2 test3 test4 final
max possible 130 120 180 130  
max obtained 125 120 175 115  
average obtained 86.5 94 129 70  
min obtained 35 34 20 10  
standard deviation 23.1 22 37 30  
a 87 85 125 70  
b 24 22 37 30  
c 2.65 2.70 2.70 2.70  
gp = [your grade - a]/b + c
eg.  If your test1 grade is 100, the the gp = (100-87)/24 + 2.65 = 3.2
The constants will be unique to each test based on the tested performance of the class.
Your gp may go as high as 4.3 for an individual test.

I will choose averge the best 4 units for your final grade.

Test solutions.

Questions from Students on email and replies..



Things ought to be made as simple as possible, but no simpler.

wind tunnel test of bike
US Olympic Team test of aerodynamics of bike and rider.

Technology in Sports

1. materials
2. design principles
Physics of the Tennis Raquet. Brody, p 139, p 147 PoS.
3. How to make a sailboat go faster. Speed of sailboat. forces in equilibrium. drag force increases with v^2 so need propulsive force to increase with v^2. 4. The bobsled
5. Rowing Shells
6. Pole vault
7. Bike racing.

Probability and Statistics in Sports.

1. Outcome of World Series. Read Krane, p. 274 PoS.
2. What's the chance of winning a match in tennis if the chance of winning a game is known. Read:Fischer, page 275, PoS.

Effects of Wind and altitude on performance.

Frohlich, p120 PoS.

Puzzles and Anomalies in Physics of Sports.

1. Pretty fast for someone so small. Moves pretty well for a big guy
2. He's quick but slow. [said about Steve Largent]
3. Sailing upwind. The wind pushes in direction of motion only??
Rye, p 254 PoS.
4. sailing faster than the wind. Once you're travelling downwind with the wind speed, the relative wind is zero!
5. The stability of bicycles. [At first it seemed simple... angular momentum of wheels... but then Jones proved it wrong.]
Jones, p 169 PoS.
Reverse Steering. of a bike.
6. Scaling.

  • geometric
  • elastic
  • constant stress

    Measurements favor elastic scaling. McMahon, Muscles, Reflexes and Locomotion.

  • Intrinsic Limits to Human Perormance

    Intrinsic Limits to Performance

    Larger Size Illustration of Muscles

    Names of the Muscles

    Quick Conversion factors for physics units

    Quick scientific notation review

    deduce: to infer from general reasoning

    induce: to draw from particular facts.

    Newtons Rules of Reasoning.

  • "Nature does nothing ... in vain, and more is in vain when less will serve." Nature is essenially simple. Therefore, scientists ought not to introduce more hypotheses than are needed to explain observed facts.
  • Therefore to the same natural effects we must, as far as possible, assign the same causes. As to respiration in a man and in a beast; the descent of stones in Europe and in America;... the reflection of light in the earth, and in the planets."
  • Properties common to all bodies within reach of experiments are assumed (until proved otherwise) to apply to all bodies in general. For example, all physical objects known to experimenters had always been found to have mass. So by this rule, Newton proposed that every object has mass, even those beyond our reach in the celestial region.
  • In experimental philosophy, hypotheses or generalizations based on experience should be accpeted as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined. Scientists must accept such hypotheses until they have additional evidence by which the hypotheses may be made more accurate or revised.

    Review Questions.

    Links to other physics of sports sites.

  • Return to Ken Young's Home page.