Two formulas which should be of interest to all those having an interest in shotgun ballistics.
Formula #1:
F = MA or Force = Mass time Acceleration. now this formula tells us as was stated a while back that if for instance we accelerate an ounce of shot to say 1200 FPS the required force is the same, matters not whether it be from a 28 gauge or a 12 gauge. This is of course totally true.
Formula #2:
F = PA or in this case Force = Pressure times Area. To avoid confusion for further discussion I will use Ac for acceleration & Ar for area.
Since Force is on 1 side of each equation then the two can b combined & F eliminated & thus we have MAc = PAr or mass times acceleration = pressure times area.
Here of course is where it becomes Extremely obvious that as the gauge of the gun changes then Ar changes with it so P also has to change to maintain a balance.
Using nominal bore sizes of .550" for the 28 & .729" for the 12 then (.550"/.729")˛ shows the 28 gauge has only 57% of the area of the 12ga. Consequently pressure (P) has to be 175% that of the 12 to impart the same 1200 FPS to an ounce of shot as would the 12.
I fully realize that a 28 gauge does not normally produce 175% of the peak pressure of the 12 gauge. Peak or max pressure is however only a small part of the story. A shotgun does not work like a normal Hydraulic system where a pump is putting out a constant stream of fluid under a constant pressure.
Rather a shotgun burns a small amount of powder with a rapid rise to it's peak pressure, then a quick falling away with a reducing amount of pressure to the end of the barrel. What is needed in this formula is the entire average pressure under the curve for the length of the barrel. Thus if one gets the same velocity from the same weight of shot in different size guns it will be found this difference in "Total" pressure is an absolute essential.
If anyone has an interest in further discussion of this in a Civil manner feel free. Before one simply puts it down as Ignorant & Unscientific please make certain you know what you are talking about.
Note also that in order to move an ounce of shot the 28 has to move 4.2 oz per Sq Inch, the 12 only 2.4 oz per Sq inch. This fully explains why harder premium shot is more desirable to minimize shot deformation in the 28.
