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Pressure "IS" directly related to payload & velocity, just not peak pressure. The pressure curve can be Re-Arranged by varying the burning rate of the propellant. Powders used in the .410 for even normal loads are already slower, more progressive than those used in the larger gauges except for possibly a few extreme Magnum loads. As you have a lot smaller powder charge to ignite in a much smaller space bloopers are likely not going to be as critical in the small bore as in larger gauges. The primer is putting out the same amount of "Fire" to light the smaller charge. While 7625 is a Slow powder in a 12ga it is a Very Fast one in a 3" .410. It's all relative, but yes when you look at total pressure its always going to be higher in the .410.
The good part is the .410 will handle a higher pressure than will the larger bores.

Exactly. Related, but not directly proportional.

SRH

Keep in mind that when a shotshell is fired pressure fills the Whole barrel. Maximum or peak pressure is definitely not proportional to payload/velocity. Total pressure is very close to it. There are a few other factors which enter the picture which prevents it being exactly proportional. One such factor is difference in bore contact. If loads were exactly proportional to bore size they would have identical column lengths in the bore & weight would be proportional to the square of the bore diameter, but bore contact area would be proportional to the diameters. Thus if we compared a .410 & 20 which had the same column length of shot the 20 would have a 2.25 heavier charge weight but only 1.5 times more bore contact area. thus the friction of getting the shot down the barrel would be higher in the .410 which would produce a slightly higher total pressure level. "Peak" pressure can of course be varied by changing the burn rate of the powder used in either case. I still find nothing amazing that small bores are normally loaded to a higher pressure level, it's just the nature of the beasts as they say.

Well, "amazing" may be a little too dramatic.

SRH

You may find this interesting, from a Accurate reloading manual:
Background and basic Fundamentals of Shot Shell loading.
� The fundamental difference between a shotshell cartridge and a typical centre fire rifle cartridge is, that the efficiency of the shotshell cartridge is 100% dependant
on the round itself. By this we mean that all the �resistive forces� must be generated within the confines of the round itself. No assistance is provided by the gun.
� The reason for this is that the Maximum Peak Pressure is reached long before the base of the shot/wad assembly has left the case. (In the case of a CF rifle
cartridge, the peak pressure is achieved when the bullet is engraved, therefore the large contribution, as a result of leade/free-bore dimensions on the combustion
process. (I.e. bullet/bore interface fit, bullet hardness, bearing surface etc).
� The reason for this is that the critical engraving force which is so important to the dynamic combustion process present in a CF rifle caliber is totally absent in a
shotgun.
� Shotgun and typical straight-case handgun calibers are actually basically the same in their fundamental ratios and dynamics. A shotgun can be described as an
oversize low-pressure handgun caliber. That�s why the same powders are used in shotgun and handgun calibers.
� This means that the efficiency, regarding ignition and the subsequent increase in pressure, is totally controlled by the integral configuration and assembly of the
round itself. These constitute the main inertial mass (shot mass), the initial internal volume (wad design), the dynamic collapse (primary expansion) of the internal
volume (collapsible section of the wad), plus the displacing of the internal assembly and the unfolding of the fold/crimp (secondary/Final expansion).
� The way this COMBINATION interacts, will determine the efficiency Pressure impulse (Profile and time-base) and the Peak-pressure vs Velocity ratio (P/V). The
resistive force, presented by friction in a shotgun is negligible.
You will notice they claim the resistance of the barrel has nothing to do with pressure.

Well, they really claim it has a "negligible" effect on pressure, and "negligible" is still a relative term, not an actual quantity. If we're worried about gun blow-ups or wear-outs, it may well be true.

But I wonder if it's still true when we're worrying about patterns?