David Alciatore, PhD ("Dr. Dave") ILLUSTRATED PRINCIPLES "90 and 30 Rule Follow-up Part IV: English effects" Summary: David Alciatore, PhD ("Dr. Dave") ILLUSTRATED PRINCIPLES "90° and 30° Rule Follow-up ­ Part IV: English effects" 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., NV 3.4) 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 previous three articles, I answered a few questions that have come up concerning my series of articles on the 90° and 30° rules (see my January '04 through July '04 articles at billiards.colostate.edu). If you are getting tired of reading about these important rules, don't despair ... this is the last article in the series. In last month's article, we looked at the effects of ball inelasticity and friction. In this article, I conclude the series by looking at the effects of side English. As with the inelasticity and friction effects, the effects of side English are not very significant for most shots (more on this later). Honestly, the knowledge presented in these two most recent articles is probably not that useful in your game. I am presenting these effects mostly just to satisfy some people's curiosity and to maybe clear up some misconceptions that some people might have. If you don't remember what the 90° and 30° rules are and when they apply, see NV 3.4-3.5 and NV 3.7-3.10. Readers with engineering or physics backgrounds might also find TP 3.1 and TP 3.3 interesting. Remember, the 90° rule states that for a stun shot, where the cue ball is sliding at object ball impact, the cue ball and object ball paths separate at 90° (i.e., the separating Collections: Engineering