Why doesn’t a cushion reflect like a mirror?
On top of the geometric reference of equal angles in and out, spin, friction, restitution loss and cushion deformation come into play.
One thing to remember today
Even from the same incoming direction, the rebound direction and the path afterwards can change with the spin and speed at the moment of impact.
Written and edited by TTBoys · How we write and check sources · Report an error
Reading the motion in diagrams
- Incoming
- Ideal mirror reflection
- Example running farther along the cushion
- Example leaving the cushion more steeply
A concept diagram made by TTBoys for learning. It is not a measured graph or simulation result from a paper; arrow lengths and angles are there to explain the principle.
The mirror construction is a starting point for comparison
If you assume a point-sized ball rebounding perfectly elastically off a hard, frictionless wall, the angle in equals the angle out. The angles are measured from the cushion’s normal, the line perpendicular to the cushion.
A real ball has size, and the cushion is an elastic material. The rebound point of the ball’s center is not the cushion nose itself, and the diamonds on the frame are not the contact point either.
Spin changes the sliding at the contact surface
Running and reverse English describe how the spin relates to the direction the ball enters that cushion. The same right tip position plays a different role on a different cushion. Do not tie spin names to left or right tip positions.
Cushion friction acts on the relative motion at the contact surface and changes speed and spin together. Top or bottom spin and cloth friction after the impact also affect the path, so sidespin alone cannot settle the whole trajectory.
The numbers in papers also have conditions
The 2010 model by Mathavan and colleagues analyzes cushion impacts in 3D. What matters is that it includes the spin and friction a simple 2D mirror formula leaves out.
The model assumes the cushion deforms only a little, and it has limits at high impact speeds. Do not enter the coefficients from the paper as constants for every carom table, or generalize that new cloth always plays long or short.
An observation drill suggested by TTBoys
Compare the same first cushion with three kinds of spin
- Fix one cue ball and a first-cushion target, and repeat a reference shot with reduced sidespin 5 times.
- Aiming for the same speed, compare 5 shots each with a little running English and a little reverse English. Mark separately any shot whose actual first-cushion contact moved.
- Write down the first contact, the direction right after the rebound and the arrival at the next cushion separately. Do not change speed and spin by a lot at the same time within one set.
What to watch: Check whether a miss started with the first aim or appeared after the rebound.
When interpreting: Changing the side tip position can move the first contact point through squirt and swerve. Do not read differences between shots with different contact points as the effect of cushion spin alone.
Connect to Basics, Systems and Practice
Evidence from papers and where it applies
Sources reviewed: 2026-10-10 · The explanations and drills are TTBoys' editing.
Theoretical paper · S. Mathavan · M. R. Jackson · R. M. Parkin
A theoretical analysis of billiard ball dynamics under cushion impacts ↗
Proc. IMechE Part C 224, 1863–1873 (2010) · DOI 10.1243/09544062JMES1964
What this source explains: Uses a 3D impact model that includes spin and friction to calculate the speed and direction of a cushion rebound, and compares it with earlier experiments.
Limits: It assumes the cushion deforms only a little. The friction and restitution coefficients and the speed range it uses cannot be carried over unchanged to every carom table.
Experimental and theoretical paper · S. Mathavan · M. R. Jackson · R. M. Parkin
Application of high-speed imaging to determine the dynamics of billiards ↗
American Journal of Physics 77, 788–794 (2009) · DOI 10.1119/1.3157159
What this source explains: Tracks changes in position and velocity in high-speed video to study sliding and rolling, cushion impacts and separation angles.
Limits: The experiments used a snooker table and calibrated camera equipment. This does not mean a smartphone gives the same accuracy, and tracking spin needs separate observation.