mattman said:
This is really what I want to know. When someone says, "this shot requires 1 tip below center". Ok..follow me here. If a tip diameter is equal to a shaft diameter and it's a 13mm shaft, that means the tip is 13mm or roughly 1/2" (13 X .039 = .507"). Imagine a circle that is 2.25" in diameter. Place a 1/2" dot in the middle, that's center ball hit. Now, when they say "shoot one tip below center, would that mean bringing it down 1/4" or 1/2"?
This is actually a
semantic problem, and not a
mathematical problem. Once you define the meaning of the word "tip" you have your answer.
In fact, mathematical and logical decuction shows that you can strike the cue ball only (about) 1.25 "physcial" tips below the center point anyway.
For example:
As mentioned above, the tip and cue ball are curved surfaces.
When you aim extreme draw, you may think you are hitting the cue ball at the very bottom, but you cannot hit any lower than ~1/2"
above the point where the cue ball rests on the table. This would be close to the theoretical maximum contact point.
Using this physical constraint, and the characteristics of the tip, chalk, and smoothness of the cue ball (i.e., polished or not), the
maximum tip striking distance (for draw) is about 5/8" below the vertical center of the cue ball.
Using your conversion above, 5/8" is approximately 25% larger than a 13mm tip. Thus, if you talk about "tips above and below" you can only strike the cue ball at 1.25 tips below center...
As discussed, I believe that the concept of "tips off center" is an instruction tool to teach the effects of "off center hits," and should NOT be considered during play.
NB: contemplate this: you are viewing from a plane above the striking plane of the cue stick. I.e., you are looking at the top of the shaft and sighting over the top of the tip. This will affect how your brain "perceives" your draw contact point.
-td