Reference position: half ball, rollingBall fraction: 1/2Cue ball at contact: Natural roll (30° rule)Deflection angle (°): 33.7Half ball, natural roll → the cue ball deflects 33.7° from the aiming line. Ball 2 goes 30° to the other side.
Natural angle: the 30° and 90° rules · Drill cards
Sliding ball: Deflection = 90° − cut angle · Rolling ball: tan(Deflection) = sin θ · cos θ ÷ (sin² θ + 0.4)
1/4 ball, rollingBall fraction: 1/4Cue ball at contact: Natural roll (30° rule)Deflection angle (°): 27.31/4 ball → deflection 27.3°. Even though the fraction drops from half to a quarter, the direction changes by only 6.4°.
3/4 ball, rollingBall fraction: 3/4Cue ball at contact: Natural roll (30° rule)Deflection angle (°): 27.63/4 ball → deflection 27.6°. Between 1/4 and 3/4 ball, a rolling ball deflects about 30°.
Half ball, sliding (90° rule)Ball fraction: 1/2Deflection angle (°): 60Half ball, no rotation at contact → the cue ball travels along the tangent line, perpendicular to the path of ball 2: deflection 90° − 30° = 60°.
1/4 ball, sliding (90° rule)Ball fraction: 1/4Deflection angle (°): 41.41/4 ball, cut angle 48.6° → deflection 90° − 48.6° = 41.4°.
7/8 ball, rollingBall fraction: 7/8Cue ball at contact: Natural roll (30° rule)Deflection angle (°): 16.6Very full hit → deflection only 16.6°. The 30° rule does not hold at this fraction.