Being a retired Engineer, I thought I would apply some basic physics to the Pin Shoot.
WARNING! MATH AHEAD!!!
We went to an antique show this weekend, and what did I find but a used bowling pin. It stands 15” high and weighs 2 lbs 11 oz. Looking online at the standards for pins, it matches up in height (15” is correct), and is close for weight (the standard is 3 lbs 8 oz, apparently).
I wanted to use this pin to work up some Dry Practice setups, and also figure out the splits for a winning time next year.
I started by working up a spreadsheet. First, I entered the paramters for the bullet (.45 ACP, 230 grains) and the assumed weight of the pin (3.5 lb), plus a few useful constants for later:
Attachment 91087
The first thing I wanted to do was work how long it would take for the last pin to hit the ground, after it’s shot. This is important, since the score timer doesn’t stop until the pin hits the ground. Since the force of gravity (vertical) and the pin moving backwards (horizontal) are independent, all I have to do is use the Newtonian motion calculation for time of drop, from arbitrary height H.
Attachment 91088
I plugged in 7’ for average height of the pins. The prediction is a pin will take just under 0.7s to fall to the ground, from that height.
Now, with the winning time this year of around 5.4s in mind, I can now allocate a time budget, consisting of:
1) time to first pin
2) splits for pins 2 to 5, and finally
3) the time to fall prediction,
for an overall “time budget” for dry practice:
Attachment 91089
Last piece of data, and this was done empirically, based on the bowling standards, but I found a source that stated the C of G of the standard bowling pin was 5.71” from the bottom of the pin. I took my “sample” pin and marked where that should be.
Mathematically, hitting the C of G should theoretically result in the most horizontal motion of the pin, with the least amount of force vector imparted rotationally. It’s not quite “center of the white part”, but pretty close. I’l use this point for an aiming mark.
Attachment 91090
So, there you have it. When I get back to FL, I will set this pin out in the garage, add some paper copies, and have a method to practice to do better in the match next year. :cool: