Pinning Alley

Let's start with some basic facts about the popular sport called "tenpin bowling". (Less popular are "candlepin" and "duckpin" bowling--and other variants--so we'll ignore those here.) Each tenpin weighs 3.5 pounds (my calculator computes that as about 1590 grams), and they are positioned in a triangular pattern such the the center-to-center distance between any close pair of pins is 1 foot (30.48cm).

Meanwhile, bowling balls are about 8.5 inches in diameter (the official rules actually state that the circumference cannot exceed 27 inches, so divide that by pi to get 8.59-and-a-fraction inches). That's 21.59 to 21.83 centimeters in diameter (21.75, anyone?). The weight of a bowling ball ranges from 6 pounds to 16 pounds (2724 to 7264 grams of mass). While 16 pounds is the maximum allowed weight, I think that lesser balls don't have to have weights that are exact pounds. That is, if you wanted a ball that weighed 12.3 pounds, somebody might be willing to make one, and so far as I know it would be legal. Also, I don't know that 6 pounds is the lower limit; I'm pretty sure I once encountered a kid who had a 5-pound ball. (There is a PRACTICAL lower limit, though, when you think about the fact that you want that lightweight ball to knock over a total of 35 pounds of tenpins!)

Finally, the bowling lane itself is 4 feet wide, and 60 feet from the "foul line" (don't cross the line or your score will be zero) to the first bowling pin. That's about 1.22 and 18.29 meters, respectively.

I think early versions of this sport predated the metric system, so that's why the internationally accepted measurements are in old-fashioned "English" units.

In the olden days of bowling, people called "pin chasers" had the job of manually setting up the pins at the far end of the bowling lane. Nowadays there are complicated automatic machines that do this job, and pin-chasers are mostly also mechanics, with the job of keeping the machines running. It is normal for a pin-setting machine to be stocked with 20 pins, so that while 10 are sitting on the lane, the other 10 can be in the process of getting moved to the part of the machine where it can set down the next batch of pins (the bowlers don't have to wait as long between fresh sets of pins).

For the purposes of the game of "pinning", we will stick with the 11 common ball-weights (from 6 to 16 pounds), and we will need one of each weight.

Note that bowling balls are almost always drilled with holes so that a person can easily grip a ball by inserting fingers into the holes. This has a side-effect of making a bowling ball no longer perfectly spherical; each hole can be considered somewhat equivalent to a "flat spot" on the surface of the ball. This is a Good Thing; we NEED at least one such flat spot on each bowling ball used for the game of "pinning".

Our complicated machine at the back of the lane will be loaded up with 11 bowling balls, as previously described. At random 10 of them will be set on the lane, "flat spots" down, in the same locations as is normal for tenpins. Since the balls are less than 9 inches in DIAMETER, they are less than 4.5 inches in radius, and the distance between two pin-spots is 1 foot, more than twice as much as 4.5 inches. The balls will fit just fine on the lane, without modifying anything except the machine (which needs humongous modifications, of course).

A standard tenpin has dimensions such that part of it, the "neck", is just about perfect for being gripped by the hand (no finger holes needed). The "pinner" grips the pin firmly, and approaches the foul line, and (underhand throw, like in bowling or softball) heaves the pin toward the triangular array of bowling balls, 60 feet away.

Since the flat spots on the balls are pretty small, it should not take a big impact to get a ball to start rolling. That's good, since the pin only weighs 3.5 pounds, and needs to shove as much as 16+15+14+...+7=115 pounds of balls off the lane...

You get two attempts, of course. If your first attempt misses the first ball in the triangular array, you will probably need your second try.

Enjoy!