- About a vertical axis - will not affect the ball's trajectory along the alley but may come into play on collision with pins.
- About a horizontal axis across the alley (ω2 radians/s) - this affects the transition from skidding to pure rolling and the ball's speed down the alley but has no direct impact on swerve.
- About a horizontal axis along the alley (ω1 radians/s) - this is the component that creates swerve. Ceteri paribus, the greater the speed of delivery, the longer the length of time over which swerve can occur.
x = ½ (µg sinθ) T2
where: tanθ = ω1r / (V - ω2r)
T = 2U / 7μg
and U2 = (V - ω2r)2 + (ω2r)2
As an example of the magnitude of the swerve which can be achieved, consider a 4½ inch diameter ball, delivered at 8 m/s along a 10 m alley, spinning at 1 revolution per second about an axis along the alley with a coefficient of friction of 0.3. Skidding will cease after about 5½ m where the transverse movement will be about 4 cm, increasing to 12 cm when the pins are reached. The overall swerve is only 1° but the potential impact of spin can mean the difference between hitting a pin and missing all.
Lessons from evaluating realistic ranges of speed of delivery and spin:
- Late swerve may be a reality but it is most likely to be due to a bias in the ball or an imperfectly level alley as the pins are approached. A vertical mismatch between boards is likely to have a significant effect.
- Attempting to spin a slow delivery causes swerve in the early stages of travel down the alley making control of the trajectory more difficult. For a given spin the transverse movement is inversely proportional to the speed of delivery, i.e. is disproportionately greater for slower deliveries. If the spin is proportional to the speed of delivery then transverse movement is approximately independent of delivery speed.
- If you have a natural tendency to spin the ball clockwise along the length of the alley don't stand on the right side to launch it! Likewise avoid the left side if you have a tendency to anti-clockwise spin. Otherwise the ball will tend to straighten on its way down the alley and impacting the pins at an angle will not be facilitated.
- In view of these conclusions, avoid deliberate spin in matches until your delivery is well practised!