Angles guide

The wall: why angle in is not angle out

A real ball loses speed off the wall and is gripped by it. The two pull the exit angle in opposite directions.

The ideal: angle in equals angle out

Picture a perfectly smooth ball that bounces perfectly. It meets the wall, its speed straight into the wall is turned round in full, and its speed along the wall is untouched. It leaves at the mirror angle: the exit angle equals the arrival angle. This is the picture most of us carry, and it is a good first guess.

A real ball is neither perfectly bouncy nor perfectly smooth, so two things change, and they pull in opposite directions.

The ball loses push-out speed

Every real ball squashes against the wall and does not spring all the way back. It keeps only a share of its speed straight out of the wall, its bounce factor. Its speed along the wall is not cut by this. So, on its own, a lost bounce makes the ball come off flatter than the mirror angle, closer to running along the wall.

The wall grips the ball

The wall also pushes along its surface, against the way the ball's surface is sliding across it (friction). That slows the ball's run along the wall and sets it turning. On its own, the grip makes the ball come off squarer than the mirror angle.

How far the grip gets depends on the arrival. A ball that arrives fairly square presses hard into the wall, so the grip can stop the sliding altogether: the ball leaves rolling along the wall. A glancing ball presses only lightly and slides all the way through, so the grip takes off only a little. For the middle ball in Figure 2, that switch happens at an arrival angle of about 23°.

Which one wins

One arrival, three exitsSeen from above. A ball arrives at the front wall at 45 degrees. A dashed line shows the mirror exit, also 45 degrees. A lively ball at a gentle speed leaves squarer, at about 53 degrees. A dead ball, or one hit very hard, leaves flatter, at about 40 degrees.Front wall45°ArrivalMirror exit: 45°Lively ball: about 53°Dead ball or hard hit: about 40°
Figure 1. Seen from above. The same 45° arrival, worked out for a lively ball at a gentle speed and for a dead ball (or a very hard hit). The mirror line is dashed.

Figure 1 shows one arrival at 45°. A lively ball hit gently keeps most of its push-out speed, the grip wins and it leaves squarer, about 53°. A dead ball, or any ball hit very hard, loses so much push-out speed that the bounce factor wins and it leaves flatter, about 40°. A ball in between leaves at about 47°.

Exit angle against arrival angleA chart. Across: the arrival angle to the wall, from 0 to 90 degrees. Up: the exit angle. The mirror is a dashed diagonal. The lively ball's line runs close to the mirror for glancing arrivals and above it (squarer) from about 10 degrees on. The middle ball is a little below the mirror for glancing arrivals and a little above it from about 20 degrees on. The dead ball's line is below the mirror (flatter) the whole way.0°0°30°30°60°60°90°90°Arrival angle to the wallExit angleMirrorLively ball, gentle hitIn betweenDead ball or hard hit
Figure 2. Exit angle for each arrival angle, no spin, for three balls on the same wall. Above the dashed mirror line means squarer than the mirror; below means flatter.

Figure 2 runs the same sum for every arrival angle. Three things are worth keeping:

The differences are a few degrees, not tens. Over a long court a few degrees is still a few feet.

Faster and slower arrivals, and the squash

The harder a rubber ball hits the wall, the more it squashes and, typically, the smaller the share of its push-out speed it gets back. So the same ball can be lively on a soft touch shot and fairly dead on a full-power drive: hard-hit balls tend to come off flatter and die sooner, soft ones tend to come off squarer and stay lively. The ball is also always slower after the wall than before it.

Liveliness also depends on the ball's temperature (the American rulebook gives a temperature for its bounce test for that reason) and on its age. A warm ball is typically livelier than a cold one. A dusty, damp or very smooth wall grips less; a rough one grips more.

The balls compared

Each ball's rules give a drop test: drop it from a set height and measure the rebound. The bounce factor is the square root of rebound over drop. These are slow impacts, so in play every ball is deader than these figures, but they rank the balls.

The one-wall rulebook does not give the big ball's size, weight or bounce; the figures above are those of a standard racquetball, which it matches in size. The small ball's figures are from the USHA rulebook, and the Irish balls' from the GAA's.

Next: spin, which changes the exit angle more than anything on this page.

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