Understanding Ball-Hit Fractions and Cut Angles

This diagram is about cue ball-object ball collisions and how different amounts of overlap (called ball-hit fractions) affect:

1. The cut angle – how sharply the object ball moves off the aiming line.

2. The cue ball deflection angle – how much the cue ball deviates after impact.

🔶 Top View (Bird’s-Eye View of the Table)

This shows three scenarios:

a) ¼-Ball Hit (Large Cut Angle)

• The cue ball hits just the edge of the object ball.

• Only ¼ of the cue ball contacts the object ball.

• This causes a large cut angle — the object ball moves sharply sideways.

• The cue ball deflects ~30° off the original path.

b) ½-Ball Hit (Medium Cut Angle)

• The cue ball hits the centerline of the object ball.

• The collision splits the angle between cue ball and object ball movement.

• The cut angle is moderate.

• The cue ball still deflects about 30° off the original path.

c) ¾-Ball Hit (Small Cut Angle)

• The cue ball hits most of the object ball.

• Only ¼ of the object ball is missed.

• This results in a small cut angle, barely moving the object ball off the straight line.

• Cue ball deflection remains ~30°.

🔷 Side View (Looking Down the Aiming Line)

This shows how much of the object ball is struck:

• a) ¼-Ball Hit – Small overlap, nearly a glancing blow.

• b) ½-Ball Hit – Direct, central hit.

• c) ¾-Ball Hit – Strong hit, most of the object ball is covered.

This side view complements the top view by clarifying the impact zone.

📐 Important Insights

• Cue Ball Deflection ≈ 30°
  Surprisingly, the cue ball path is deflected by around 30° regardless of the hit fraction. This is a known concept in pool physics and helps players judge where the cue ball will go after contact.

• Cut Angle = Object Ball Direction
  The more glancing the hit (¼-ball), the wider the object ball angle. The more direct the hit (¾-ball), the narrower the angle.

• Predictability
  Understanding these hit fractions allows players to predict both object ball paths and cue ball motion — a critical skill for positioning in the next shot.