Summary: Billiards Digest November, 2011
"Rolling Cue Ball Deflection Angle Approximations" ILLUSTRATED PRINCIPLES
David Alciatore, PhD ("Dr. Dave")
Supporting narrated video (NV) demonstrations, high-speed video (HSV) clips, and technical proofs (TP),
and all of my past articles, can be accessed and viewed online at billiards.colostate.edu. The reference
numbers used in my articles will help you locate the resources on the website. If you have a slow or
inconvenient Internet connection, you might want to view the resources from a CD-ROM or DVD. Details
can be found online at: dr-dave-billiards.com.
This article summarizes some useful techniques for approximating the path a rolling cue ball (CB) will
take after striking an object ball (OB) when the hit is fairly thin or fairly thick.
I have covered the topic of CB control in many past articles, all of which are available at
billiards.colostate.edu. In my April '04 article, I presented the 30º degree rule, which predicts that a rolling
CB will deflect by about 30º degrees (the "natural angle") for the wide range of cut shots between a ¼-ball
and ¾-ball hit. The rule is illustrated in Diagram 1. The clear message of the diagram is that even though
the OB is being cut by very different amounts in the three shots, the CB still heads in nearly the same
direction after impact. This "natural angle" can be easily visualized at the table using your hand, as
demonstrated in NV B.66 and NV B.75. For more information, see "Dr. Dave peace-sign technique" under
"30º rule" in the FAQ section of my website.
b) 1/2-ball hit c) 3/4-ball hita) 1/4-ball hit