position control

• 30-degree and 90-degree rules
• nearly striaght-in shots
• useful reference lines
• where the CB goes for different cases

for more information, see Chapter 5 in The Illustrated Principles of Pool and Billiards
and Disc I and Disc II of the Video Encyclopedia of Pool Shots

nearly striaght-in shots

How can I get position on the next shot if the current shot is nearly straight in?

See: NV B.30 - Cue ball position control with nearly straight-in shots.

useful reference lines

How can I know where the cue ball will go on every type of shot?

See:

• NV B.43 - Cue ball position control stun, roll, and draw reference lines
• NV B.44 - Dr. Dave 30-degree-rule peace-sign hand calibration
• NV B.45 - Cue ball path speed effects
• NV B.46 - Cue ball path scratch avoid, cluster break-out, and billiard (carom) examples
• NV B.60 - Mike Page's Cue Ball Control
• NV B.66 - The 30-degree rule, from VEPS I
• NV B.67 - The trisect system for draw shots, from VEPS I
• NV B.68 - Tweener cluster breaks, from VEPS I

For more info, see:

• where the CB goes for different cases
• my January '09 and February '09 BD articles on this topic

where the CB goes for different cases

Where will the cue ball go after it hits an object ball?

For a stun shot, most people know the right answer: in the tangent line direction, perpendicular to the OB direction. This is the 90-degree rule (see my Jan '04 article). If you want a more precise answer that accounts for various effects (e.g., friction and English), see my March-June '05 articles. FYI, here is a convenient one-page summary of the 90-degree rule.

For a rolling CB, the cue ball changes direction by about 30 degrees for a wide range of cut shots (1/4 to 3/4 ball hit). This is the 30 degree rule (see my April '04 article). If you want to be more precise, the angle is a little more (about 34 degrees) closer to a 1/2-ball hit and a little less (about 27 degrees) closer to a 1/4-ball or 3/4-ball hit. If you want to know how to account for speed effects, see my June '05 article. If you want an easy way to use your hand to accurately visualize the cue ball direction, use the Dr. Dave peace-sign technique. FYI, here is a convenient one-page summary of the 30-degree rule.

For a draw shot with good draw action, and for cut angles smaller than about 40 degrees (i.e., ball-hit fraction greater than about 3/8), the trisect system is your answer (see my March '06 article). You can use a modified version of the Dr. Dave peace-sign technique to predict the cue ball direction (see the article, NV B.43, and NV B.67 for illustrations and examples).

For shots "in between" all of these different cases, the cue ball will go somewhere in between the indicated directions. The only way to get a feel for how much "in between" the cue ball will go is to practice ... a lot!

To see the effects of speed, spin, and cue elevation, see:

HSV B.23 - cue ball path speed, spin, and cue elevation effects

For more info, see:

• NV B.43 - Cue ball position control stun, roll, and draw reference lines
• NV B.44 - Dr. Dave 30-degree-rule peace-sign hand calibration
• NV B.45 - Cue ball path speed effects
• NV B.46 - Cue ball path scratch avoid, cluster break-out, and billiard (carom) example
• NV B.60 - Mike Page's Cue Ball Control
• NV B.66 - The 30-degree rule, from VEPS I
• NV B.67 - The trisect system for draw shots, from VEPS I
• NV B.68 - Tweener cluster breaks, from VEPS I
• my January '09 and February '09 BD articles on these topics

What if the cut is very thin or hit very full?

For roll shots, there are good approximations for the CB deflection angles. The math and illustrations can be found in a 1988 technical article by George Onoda.

For a fairly full hit, with a ball-hit-fraction greater than 3/4, the CB will deflect about 2.5 times the cut angle (e.g., for a shot with a cut angle of 10 degrees, the CB will deflect about 25 degrees).

For a fairly thin hit, with a ball-hit-fraction less than 1/4, the CB will deflect about 70% of the angle between the aiming line and the tangent line.

See Figures 4 and 5 in the article for illustrations. As with the 30 degree rule and trisect system, the full-hit and thin-hit rules apply to the final direction of the CB. The actual final path of the CB is shifted down the tangent line with higher speed.

Video demonstrations of these types of shots can be found in the Video Encyclopedia of Pool Shots.

From Bob_Jewett:

While this is true for perfect elasticity and no ball-ball friction, I find that using 3 times in the first case (for a nearly full-ball hit) and 75% in the second case seems to work pretty well. In the case of 75%, it's easy to bisect and then bisect again.

Here is a system for calculating the follow angle that works pretty well for all angles but is easiest to apply for fairly thin cuts. Imagine the tangent line. Take the cue ball position and drop a perpendicular to the tangent line from the cue ball. Go from the the cue 3/4 of the way along that perpendicular to the tangent line. Put a coin there. Sight from that coin through the center of the ghost ball and that will give the direction of the cue ball after it follows off the object ball.

For nearly full follow shots, a simple rule of thumb is that if you cut the object ball one degree to the right, the cue ball will go three degrees to the left of its original path, or four degrees to the left of the object ball's path.