I'm the kind of professor that would be quite happy to see you explain this in partial differential equations if you would. I can handle the physics just fine too, but you have yet to say anything that is helpful at explaining the differences between the two hypothetical bores. I take it from your tone, you either cannot do it or, at least, are not interested. Just say so. I can find something else to do with my time that will save you the trouble of the insults.
Brent, don't even bother thinking of physics. Rather, think of it this way: If bore diameter absent constriction had anything to do with making a pattern tighter, then we'd all be shooting smaller bore guns in order to get tighter patterns. That little .410 with no choke would produce way tighter patterns than that big .730 diameter 12ga. But in fact, if both the .410 and the .730 have no constriction at all, then they will both produce very open patterns that are very similar. The only advantage a smaller bore has over a larger bore when the concept of choke is applied is that a .410 requires less constriction to produce a full choke pattern than does a 12ga. That's because it's not the AMOUNT of constriction involved that gives a tighter pattern, but rather the PERCENTAGE of constriction compared to the bore diameter. .010 constriction in a .410 is thus more significant than it is in a .730 12ga.
