It does depend on the type of powder, and the amount of it. It also depends on the payload being moved and the characteristics of the payload, ie crush section of the wad and weight of shot.
"The area under the curve" will determine final velocity, the slower powders peak later (thus they are called "slower") but not anywhere as much as you have described.
How far 'down the barrel' is down the barrel? The shot charge starts someplace between 2" and 3.5" down the barrel already.
Curves and traces from Winchester are presented in Butler "The American Shotgun". Corrected 'travel distance' of all loads in that book show less than one inch when the peak is over.
The average seems to be that the peak happens at about .5 millisecond, the shot charge has moved just less than an inch, and at that point it's going about 400fps.
You tell me how far 'down the barrel' that is. For a 3" shell it approximates 4" I suppose from the breech.
The salient lesson from all this is that the peak pressure happens in the chamber, thus "peak chamber pressure".
We need to add a little to this post. Remember the powder charge always lies "Behind" the shot charge. The pressure starts to rise immediately upon the powder being "Lit". Pressure stays behind the shot & wad. So look at the position of the shot charge inside the hull, then add that inch. The peak is not going to occur an inch out side the hull but rather inside it. The Gunmakers weren't barking up an empty tree when they put the thickest area of the walls over the chamber rather than 4-6 inches down the bbl.
William Apperson;
I'm not trying to be a Smart Alec either, but if your set-up is revealing maximum pressures @ 4-6 inches down the bbl you definitely need some more guidance. There has simply been too much verifiable data accumalated over the past 100 years or so for this to be the case.
