Science - basics

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:

Bristol style pin 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).

North American perspective on ninepins 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 cross section 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.

Diamond 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 3 or 4 chance of hitting wood if the ball runs parallel to the centreline, increasing to about 1 in 2 or 3 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.
Bounce

Not encouraged! Sometimes a ball slips out on the down swing or its release is delayed until the upswing in which cases bounce occurs and damage to the alley is likely. On many alleys there is a line before which the ball must land on the alley or a foul is called; in practice a foul is not often enforced.

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. See slide 'n roll)
  • 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 Swerve.