Just show him this and say a physicist did a very simplistic calculation especially for him to comprehend:
Velocity / Mass = Momentum (Linear)
Momentum indexed with target
Airgun and Pigeon
Velocity = 950fps
Mass = 25Gr
Distance 100y
Target size (Kill Zone) = 1” sq
950 X 25 = 23750
23750 / 100 = 237.50
237.5 X 1 = 237.50 Index
Centre Fire Rifle and Deer
Velocity = 2500fps
Mass = 120Gr
Distance = 400y
Target Size (Kill Zone) = 20” sq
2500 X 120 = 300 000
300 000 / 400 = 750
750 X 20 = 15000 Index
Comparison (Indexed)
15000 / 237.50 = 63.15 Times more difficult to hit a Pigeon at 100yards than a deer at 400yards.
Not sure this is a very good comparison. Using the parameters listed above I ran the numbers for a howitzer. It turns out that it is 140 times easier to hit a deer
in the vitals at 2 miles with a Howitzer than it is to take a deer at 400 yards with a 308.
I based it on an MV of 1640 FPS and 33-pound 105 mm projectile. I might have goofed up the math so please feel free to check it. The velocity and projectile weight were obtained off the internet which is famous for being correct 110% of the time.
I absolutely agree that a pigeon at 100 yards is a difficult shot and is quite impressive. There are so many variables that play into the question that it really is an apples to oranges comparison. I used to shoot long distance (1000-yard range) and one of my favorite guns was a 22-250 that shot a 53gn ballistic tipped bullet. I remember one day it was shooting particularly well so I put a golf ball out at 710 yards. It took me two tries to hit it. A golf ball is about 1 5/8 inches in diameter so at that distance it is about a 1/4 MOA target. The kill zone on a pigeon is roughly the size of a golf ball (plus or minus) so which is the better shot? I have shot golf balls at 100 yards with a pellet gun many times so here are my thoughts:
I feel like the time of flight for the 22-250 is longer (but not by a huge margin) at 710 yards than a pellet at 100 yards so the drop is going to be more with the 22-250, but I think the wind probably may have more effect on the pellet at the respective distances. I have shot golf balls at 100 yards with a pellet gun many times and when the wind consistent, then shot is not too difficult. My gut tells me that the 22-250 shot is more difficult but again, not by a huge margin.
So, with all that said, the pigeon at 100 yards with a pellet gun is probably a little more difficult than the deer at 400 yards with a 308. The point at which they become equal is dependent on many factors such as the gun, the scope, the quality of the ammo, etc. etc. etc. For example, to a scope, 100 yards is 100 yards and even an entry level scope will give you a decent picture at the distance. At 500 yards, mirage can really come into play. If I were to hazard a guess, assuming a good quality gun, scope, and ammo, equivalency is probably in the neighborhood of 400-600 yards.
Just my opinion and worth exactly what you paid for it