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 Collections: Engineering