# 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

**Figure 1. One arrival, three exits.** 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 in words: Seen 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.

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°.

**Figure 2. Exit angle against arrival angle.** 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 in words: A 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.

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

- A dead ball, or a very hard hit, comes off **flatter than the mirror at every angle**.
- A lively ball hit gently comes off **close to the mirror when it arrives glancing**, and a little **squarer** when it arrives more square.
- At the same arrival, a **livelier ball always comes off squarer** than a deader one.

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.

- **One-wall big ball (racquetball size)**: 2¼ in, about 40 g. Its test: dropped 100 in, rebounds 68 to 72 in, a bounce factor of about 0.82 to 0.85 at that slow speed.
- **Small handball (American four-wall and one-wall)**: 1⅞ in, 61 g. Its test: dropped 70 in onto hardwood, rebounds 48 to 52 in, a bounce factor of about 0.83 to 0.86 at that slow speed.
- **Irish softball (60×30)**: 2.2 to 2.25 in, 58 to 60 g. Its test: dropped 118 in onto steel, rebounds 106.3 to 110.2 in, a bounce factor of about 0.95 to 0.97 at that slow speed.
- **Irish hardball (60×30)**: 1.8 to 1.95 in, 42.5 to 49.6 g. Its test: dropped 8 ft, rebounds 2.5 to 3.5 ft, a bounce factor of about 0.56 to 0.66 at that slow speed.

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.

- **The Irish softball** is by far the liveliest in its test (though its test is onto steel, not a wooden floor, so its figure is not directly comparable). Expect it to come off squarer and faster than the others and to carry deep.
- **The Irish hardball** is by far the deadest. Expect it to come off flatter than the mirror on almost every shot and to lose a lot of pace at each wall.
- **The one-wall big ball and the small handball** test about the same at slow speed. The big ball is bigger and much lighter, so the air slows it more and spin bends it more in flight; the small ball holds its pace through the air.
- A solid ball (the hardball) turns more easily than a hollow one of the same size and weight, so the same grip changes its spin a little more. The direction of every effect in this guide is the same for all four balls.

Next: [spin](https://handball.theperfectship.com/guide/angles/spin.md), which changes the exit angle more than anything on this page.

Part of the angles guide: https://handball.theperfectship.com/guide/angles.md