The best definition of accuracy is “how close does each bullet hit, compared to where I was aiming, for every shot of a comparable set.”
The sets that are compared could be things like “for this exact load” or “during this competition” or “on this day” or “at this exact temperature and atmospheric pressure and wind” etc etc including every combination one can think of.
Locations can be measured in the Cartesian system (x,y,z) which is (length, width, height) or in polar coordinates (r, theta, phi).
Polar coordinates may seem more complicated but are a powerful tool for many applications, especially when dealing with circles, balls, the earth, astronomy, and when pointing at things.
The Cartesian system is named after Renee Descartes, French mathematician who invented GRAPHING in about 1625 or so. Until then, no one knew how to make a graph, everyone used tables.
It should be noted that Descartes, being really smart, didn’t feel restricted in using coordinate systems that were orthogonal… that is, his x, y and z didn’t need to be at right angles to each other. He could define the transformations and then graph away, for his particular data, and understood what it meant.
Being really smart like that, not many other people could figure his graphs out.
After Newton invented the cookie, Billybob Polar invented the Polar system. In this case, we could compare all bullet hits for all ranges by measuring the angular deviation… beta squared = theta squared + phi squared.
Strictly speaking, the famous marksman Pythagoras shot at the inside spherical section with a radius of 100 strides, so his misses were at the same range as his exact hits. It’s only because of shipping and manufacturer demands that we notice that for very large radii, a flat target’s radius squared= x squared + y squared + z squared results that within practical measurements was the same as x squared. Around 1910, the Government started doing accuracy tests at oh-about-waaaaay-far for the .30 cal Springfield using flat paper targets.
Long story short, in the Polar system, deviation between point of aim and point of impact, independent of target distance, is most easily measured in angular deviation.
The French, wanting to gamble, invented statistics. This way, they did not need to measure the impact of every bullet and could get on with playing cards, drinking wine and wearing berets.
Oh, we use a system of degrees… 360 degrees per full rotation
‘Minutes’… 60 minute per degree (‘) and
‘Second’… 60 seconds per degree
Because of the Slide Rule, which says “give me a few hundred years to invent the decimal system and a few hundred more to invent the calculator.”
Base 60 is very good when using fractions- it’s divisible by 2,3,4,5,6 and 10 by old farts who learned the times tables. Having done that, we pull out our phones like normal people when dividing real world numbers.
Us old farts insist that “accuracy” and “precision” are distinct and very important different concepts, often confused.
An accurate rifle shoots a tight group on the X
A precise rifle shoots a tight group low and to the right… correctable later.
My new shotgun is accurate but horribly not precise… the huge even widely spaced group is centered on the x.
