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David Alciatore, PhD ("Dr. Dave") ILLUSTRATED PRINCIPLES "Just How Big are the Pockets, Anyway? Part III"
 

Summary: David Alciatore, PhD ("Dr. Dave") ILLUSTRATED PRINCIPLES
"Just How Big are the Pockets, Anyway? Part III"
Note: Supporting narrated video (NV) demonstrations, high-speed video (HSV) clips, and
technical proofs (TP) can be accessed and viewed online at billiards.colostate.edu. The
reference numbers used in the article (e.g., TP 3.10) help you locate the resources on the
website. You might also want to view the resources from a CD-ROM. See the website for more
details.
In my last two articles, I presented several principles concerning factors that make some
shots tougher than others. I covered the effects of speed, angle to the pocket, and aim point.
The purpose of this month's article is to take things a little further by including the effects of
distance between the cue ball, object ball, and pocket. Everybody knows that the further away a
ball is from a pocket, the more difficult the shot. This month's article quantifies this and shows
how the results vary with side and corner pockets.
In Technical Proofs TP 3.10 and TP 3.11, I derive the allowable margin of error for different
distances from a pocket. As I point out on my website, if you don't have a strong background in
mathematics and physics, the technical proofs may not be of interest to you and you should
proceed at your own risk (... just kidding). However, the results, which I present in graphical form,
should be of interest to most people. Diagrams 1 through 4 are plots of the results for side and
corner pockets at slow and fast speeds. The curves in the diagrams show allowable object ball
angle errors at different positions on the table. The allowable error is a measure of the required

  

Source: Alciatore, David G. - Department of Mechanical Engineering, Colorado State University

 

Collections: Engineering