Saw that one before. Looks like good science.
Also read one where it was suggested that the shot travels in an inverted cone shape. No science to support it, but at least it offers one assumption for some figurin'.
The question in my mind, for doves or clays, is if the most outer pellet at the front edge of the shot string misses the dove, does the last pellet in the string have a chance of hitting it?
Assume a dove flying 40 mph (~60 fps) perpendicular to the shooter, 1200 fps of shot in a homogeneous inverted cone with a 30" pattern at the front and a single pellet at the rear of the shot cone 6' feet back, but on the center line of the cone.
The outermost pellet at the front of the shot string is 15" from the centerline of the cone and just misses the dove's beak. Will the last pellet in the cone hit the dove? (I am figuring this out in my head as I type, so check my math and trig).
The last pellet has to travel 6 feet in (6/1200) sec or .005 sec. to get to the same distance the first pellet was when it missed the dove.
The dove needs to fly 15" or more (to the centerline of the cone) in .005 sec to "fly into" the last pellet.
60 fps x .005 sec = 0.3 ft, or 3.6 inches. Doesn't make it the 15" or more to get hit by the last pellet.
Hmmm, that sucks. The trailing pellet of the shot string didn't do anything for my lousy lead on the bird.
For the math to work, the dove would need to be going 170+ mph to fly into the last pellet after missing the first. When they start doing that, Ifind another sport.
Of course that is for the inverted cone idea.
If it really comes out in a "cloud", might still have a chance.
Way more physics homework than I am willing to do this late at night.
Still, I am going to load some heavy loads, and regardless of the length of the shot string, i will see if twice as many pellets and possibly a more open choke help my chances of hitting anything.