OK, I thought maybe you had set up equipment like those of us who measure the performance of our reloaded cartridges. It is not that hard to measure the real world velocity of projectiles at a distance but there are additional challenges with shot.
But like you mentioned... with projectiles that are the same shape... the smaller the object, the quicker its speed will bleed off. I haven’t looked it up recently, but I believe it is a logarithmic relationship... It reminds me of the endless debates of the merits of 7.62x39 vs 5.56 vs .308 vs. 30-06. It is always an entertaining way to get a fiery discussion going on a firearms forum.
Having suffered through the endless 9mm vs. 38 articles of the 80’s, I reached the conclusion that bald me will fight to the death over a comb.
Tons of work have been done trying to figure out what shotgun patterns do, how they develop, etc... High speed photography, doppler artillery radar stuff, and it’s still something of a mystery.
A guy in the 40’s had his wife drive by with a target on a trailer to try to determine arrival time of the pellets at different ranges.
A chronograph is OK for determining muzzle velocity of a shotgun charge, and there’s probably a formula for calculating deceleration due to wind resistance, humidity, etc. Add that to a time of flight measurement to target, and you can get close.
I do know that altitude affects patterns. I shoot at 7500’, with an air density about 75% of sea level, and very low humidity. We shoot fairly open chokes and kill clays at pretty decent distances. We had an outgoing target once that was edge on at a measured 55 yards and on a lark I could break it with fair regularity with my 20 gauge with skeet chokes and #9 shot. The thinner air slows down pattern development and the shot speed stays higher.
I just ran across a technique that was used to determine the time of arrival of the shot pattern and duration (first to last pellet). A pattern was shot with a spinning disk (known rpm)behind the target. This could determine the time of arrival of the bulk of the pattern and roughly it’s location in the pattern.