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sappo
01-08-2006, 02:34 PM
if im shooting a straight-in shot with the object ball at midtable and the cueball 2 diamonds back and assume the my stroke is void of any spin and that im aiming to the exact middle of the corner pocket, what variance on the hit on the object ball will allow it to still be pocketed. i realize there could be many variables but assume a 5" pocket opening and moderate speed. im looking for and answer like 1/16" to either side of a perfect hit. thanks for your help.

Jal
01-09-2006, 02:09 AM
Without taking throw into account, the maximum sideways offset of the center of the cueball to the center of the object ball is .0718" on a 9' table, or about 4.6/64", which is very close to your estimate. The offset of the actual contact point is half of this. The corresponding maximum cut angle is 1.83 degrees. Note that these figures are all for the case when the cueball is two diamonds away.

Adjusting for throw, which helps here, and would be just about 0.31 degrees at the slightly greater cut angle allowed by it (and is independent of how hard or soft the ball is hit), the maximum angle increases to about 2.17 degrees. The corresponding center to center offset is .0852", or about 5.5/64". So I think the answer you're looking for is 11/128".

There is a slight correction which is dependent on ball speed, and is a result of the finite contact time (it being greater than zero). My estimate is that this would decrease the maximum allowed cut angle by about .04 degree for a very hard shot, say 15 mph, and by .02 degree for a shot half this speed. In other words, we can ignore it for the most part.

Dr. Dave has worked out the pocket tolerances at various approach angles, which is here in his technical proof section:

http://www.engr.colostate.edu/~dga/pool/

From this and from a little crude testing of my own, I used a figure of 5.5" for the effective pocket size, or a target size of 3.25". It would be a little smaller for fast shots.

Jim

sappo
01-10-2006, 05:45 PM
thanks for your imput, i appreciate your time.

SpiderMan
01-10-2006, 08:53 PM
Sappo,

Here's an approximate rule of thumb you can use for shots that are close to straight in:

(aiming error) x (distance OB travels) x 0.9 = OB deviation from expected path

In other words, if your cueball misses your perfect aim point by 1/16 of an inch, and the object ball travels 3 feet, the OB will be "off" the intended path by about two inches. (0.9)x(1/16)x(36) = 2.025

SpiderMan