How do cue ball and object ball speeds and travel distances vary with cut angle?
For stun shots, see the graph and summary statements on page 2 of:
For roll shots, see the graph and summary statements on page 3 of:
Here are some useful conclusion statements from the analyses:
- With a stun shot, the cue ball and object ball speeds and travel distances are the same for a 45° cut angle. The post-impact speeds are equal and about 70% of the initial cue ball speed. The distances are also equal and 50% of the distance the stunned cue ball would travel if there were no collision.
- With a rolling cue ball, the ball speeds and distances traveled are the same at a little less than a 1/2-ball hit,
which is slightly more than a 30° cut angle.
- If a rolling cue ball hits an object ball squarely, the object ball will travel about 7 times farther than the cue ball after impact. This number can vary quite a bit with ball and cloth conditions.
- Distance vs. cut angle and ball-hit fraction plots, and approximate ball-distance proportions for various common angles can be found on pages 10 and 11 of TP A.16.
“Fundamentals – Part VII: speed control” (BD, March, 2009) also provides some good illustrations and examples.