# Physics of Pool and Billiards

## ... resources to help learn pool physics.

Coriolis

Where can I find information on the billiards and pool physics work of the great mathematician and physicist Coriolis?

The following instructional articles summarize and illustrate many of Coriolis' original contributions from his 1835 book (which was written in French):

An English translation of his famous book became available in 2005.

The following technical article also summarizes and illustrates many of the pool physics principles discovered by Coriolis and others: Pool and Billiards Physics Principles by Coriolis and Others.

knowledge can be useful, but you still need skill

What is the difference between "knowledge" and "skill" and do they go hand in hand?

physical properties

What are approximate values for pool equipment physical properties?

ball diameter: 2.25 in

ball mass: 6 oz

ball mass moment of inertia: 2/5 mR2

ball-ball coefficient of friction (μ): 0.03-0.08

ball-ball coefficient of restitution (e): 0.92-0.98

ball-cloth coefficient of rolling resistance (μ): 0.005 - 0.015

ball-cloth coefficient of sliding friction (μ): 0.15-0.4 (typical value: 0.2)

ball-cloth spin deceleration rate: 5-15 rad/sec2

ball-rail coefficient of restitution (e): 0.6-0.9

ball-table coefficient of restitution (e): 0.5

cue-tip-ball coefficient of friction (μ): 0.6

cue-tip-ball coefficient of restitution (e): 0.71-0.75 (leather tip), 0.81-0.87 (phenolic tip)

Here are some typical values for various shot "speeds" in miles per hour (mph) and feet per second (fps):

touch: 1.5 mph = 2.2 fps
slow: 3 mph = 4.4 fps
medium-soft: 5 mph = 7.3 fps
medium: 7 mph = 10 fps
medium-fast: 8 mph = 12 fps
fast: 12 mph = 18 fps
power: 15-20 mph = 22-29 fps
powerful break: 25-30 mph = 36-44 fps

physics "understanding" sometimes provides useful insight

How can physics analysis and understanding help my pool game?

pool-in-school teaching and learning resources

Where can I find ideas for how to teach pool-related math, geometry, trigonometry, and physics in the classroom?

Good examples of how math and physics can be demonstrated at a pool table are the 90-degree and 30-degree rules described and demonstrated here:

Other good examples are the draw-shot trisect system, back-hand english, basic kick and bank shot diamond systems, and the Corner-5 and Plus Systems for aiming kick shots. For more info and demonstrations, see:

Others can be found here:

The following articles provide a good introduction to many interesting pool physics principles:

Lots of examples of how algebra, geometry, trigonometry, calculus, and physics can be applied to pool can be found here:

Many of these analyses are beyond the K-12 level, but some could be presented in a way that is appropriate. The billiards and pool physics resources page also provides a list of references and links to many general interest and technical articles, books, and websites providing excellent general resources related to pool physics.

It is also fun and interesting to teach kids the basic fundamentals of how to play pool. Many resources available to help do this are available here:

And all people (especially young people) seem to enjoy seeing and being involved with trick and proposition shots. Classic examples are described, illustrated, and demonstrated here:

And any time a student or teacher comes across a terms or phrases they do not understand, definitions can be found here:

Here's a video interview with Dr. Dave showing how he incorporates his passion for pool into the engineering classroom.

resources

Where can I find information and resources on pool and billiards physics?

The billiards and pool physics resources page has lists of references and links to many general interest and technical articles, books, and websites providing excellent resources on this topic.

simulator

How does one go about creating a pool simulator?

The physics complexities are dealt with in many good resources. An open-source graphics simulator project called FooBilliard, with source code, is available here: http://foobillard.sourceforge.net.

Virtual Pool is a good commercially available pool simulator. A free demo version can be downloaded here: http://download.cnet.com/Virtual-Pool-3-demo/3000-7427_4-10049870.html

from John Novak:

Virtual Pool 3 DL is as close to the real thing as you can get.. When I first heard about it over 10 years ago I looked at it as just a computer game. But, it is not. Everything you can do on a real table can be simulated in this game. Cue butt angle, squirt, swerve, etc. Check it out the graphics are amazing... You can even adjust the table cloth speed, rail speed, pocket size and pocket cut... www.celeris.com use the promo code vp3pc1104 and you can purchase it for about 10 bucks, best money you ever spent...This can also be played on line against people all over the world...Give it a try.

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