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Description of the game
The features of the game played by The Geordies in various divisions of the Thornbury & District Skittles League (TDSL) in South Gloucestershire vary from one alley to the next but in general are as follows:
Alley: About 30 feet long; 5 feet wide; ideally level and polished but usually exhibiting some vice, such as variation of camber or slope with tide in the River Severn.
Balls: Three in number, smooth and spherical (allegedly) when new, developing pits and chips with maturity, between 4½ and 5 inches in diameter, made of lignum vitae (self-lubricating) or composition (simulated wood).
Pins: Nine in number, about 10 inches high, between 4 and 5 inches in diameter, made of hardwood (traditionally beech or sycamore) in a variety of shapes. Our home alley's pins are Bristol style as shown here.
Layout of pins: 3x3 diamond although towards the end of a particularly draining match the nine pins may look more like a truncated tenpin formation (shown left) with inevitable difficulties for front first matches.
Objective: With each 'hand' of three balls to score as close to the maximum of 27 as possible. In practice, and in matches, the score tends to be somewhat lower, typically between 2 and 7 for each hand! So what's so difficult?
Collision cross-section for first ball
Since the collision cross-section for any individual pin is not significantly influenced by position and angle of delivery, there is no benefit to be gained from such considerations in front first games. There is also limited potential for influence in some other leagues where, for example, rules require players to have their leading foot in line with centreline of pins.
However, in other circumstances, there is some advantage to be gained from a combination of position on the alley and angle of delivery which maximises the chance of hitting wood.
Effective pin diameter is governed by size of ball and size & shape of pins (illustrated here for the Bristol pin shape). Use of an effective diameter reduces the ball to an infinitesimal point. The length and width of the alley may also be expressed in units of effective pin diameter, with the origin of a co-ordinate system for the alley at mid point of the bowling line, with the y-axis oriented along the alley through the centreline of the pins.
The distance from bowler to front pin is about 30 feet and width of alley is about 5 feet so the best achievable angle to front pin is arctan 2.5/30, i.e. arctan 0.08 or about 5 degrees to centreline of pins.
This illustration approximates the situation at The Geordies home alley. It applies to someone like The Geordies Hon. Sec. who lobs balls in the general direction of the pins and is lucky to keep them out of the gutter. There is about 1 in 2 chance of hitting wood if the ball runs parallel to the centreline, increasing to about 3 in 5 for a right hander bowling from the extreme right hand side of the alley.
Once pins fall, precision is crucial (unless all nine have fallen), and the chance of hitting any given pin for the Hon. Sec. on the Knot alley is about 1 in 10.
What about spin I hear you say. More of that later.
Stance, grip, swing & release
I don't yet know where I stand on this complex set of topics. As soon as I get into the swing of it and my analyses are complete I will post them to the site. Amongst the questions to be answered is whether it is best to adopt a tenpin style, running up to the baseline to release the ball? Or does a stationary stance minimise the margin for error introduced by a run up? See Top tips for my best advice on these matters.
Skidding & rolling
For pure rolling, the velocity of that part of the ball which is in instantaneous contact with the alley must be zero. This requires that the velocity of the ball along the alley should be perfectly balanced by the rotational velocity of the ball's surface at the contact point. Any imbalance will give rise to skidding, in which case a frictional force will operate, the ball's linear speed will decrease and its rotation will increase until the velocity of the contact point is zero and pure rolling is occurring.
The speed of delivery and initial spin are major factors in both time from release and distance down the alley before pure rolling is established. It is therefore also a dominant inluence on the ability to swerve the ball.
Assuming that the ball is not rotating on release, the time taken (T) and distance travelled (S) before pure rolling are given by C.B. Daish (Chapter 14 of The Physics of Ball Games) as follows:
T
= 2V / 7µg ; S = 12V2 / 49µg
where V is the speed of delivery (m/s),
µ is the coefficient of sliding friction,
and g is gravitational acceleration (m/s2).
The coefficient of sliding friction (µ) for wood on wood is between 0.2 and 0.5 depending on the conditions of the ball and alley surfaces. The lower value is appropriate to pristine balls on a newly laid and polished alley. A value towards the upper end of the range is more likely to apply to the conditions on our home alley. The gravitational acceleration (g) is relatively constant in the Thornbury area with a value of about 9.81 m/s2 (although there is allegedly a significant mascon in the vicinity of Tytherington!) Observation of Geordies suggests that speed of delivery (V) is typically in the range 1 to 5 m/s perhaps as high as 10 m/s, occasionally 15 m/s, for Farmer Hall.
The following figure illustrates behaviour for a friction coefficient of 0.3. A ball launched at 5 m/s will slide for 2 m and will roll thereafter. A ball launched at 10 m/s under these conditions will be sliding for 8 m, i.e. most of the length of the alley.
Once pure rolling is achieved the linear velocity will be about 0.7V. The coefficient of rolling friction is between 0.002 and 0.05 and will not slow the ball significantly before pins are hit (or not).
Swerve
Swerve only occurs while the ball is skidding. Once pure rolling has begun, the ball will move in a straight line - assuming that the ball has no bias and the alley is level. There are three components of spin, only one of which directly affects a skittler's ability to swerve the ball:
- 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.
If a ball of radius r released at speed V is spinning on release, the angle through which the ball swerves (ψ) and the transverse movement (x) are given by C.B. Daish (Chapter 14 of The Physics of Ball Games) as follows:
tanψ = 2ω1r / (7V - 2 (V - ω2r))
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 ranges of speed 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!
Bounce
Speed
[It may be worth emphasising that the only recreational drug used by The Geordies is paracetamol which assists morning-after recovery following a hard night's skittling.]
The speed of delivery influences the following:
- Momentum available to share with pins - assuming a collision. Momentum is directly proportional to speed. For initial speeds less than 10 m/s, linear momentum will have been reduced to about 70% of its initial value when the pins are reached. For speeds above 10 m/s, less of the initial energy will have been converted into rotation and a greater proportion of linear momentun will be retained.
- Ability to overcome alley condition - the higher the speed of release, the lesser deflection caused by variations in alley level, imperfections, etc.
- Ability to swerve the ball - see above.
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