EDG - I do think we're saying the same thing, except I must not be phrasing it very clear. Nothing to do with how long the curve is, nor have sharp the spike is, what matters is the area under the curve. The shape of curve could be a sharp spike and quick drop. OR - it could be a fast rise, but slow fall of pressure to end of barrel - and as long as the area under the two curves are equal, the velocity produced by both curves should be very close to the same.
OK, I agree the example I used was a bit on extreme size spec'ing one as "x" and the other as "2x", perhaps I should have used "x" (20K psi) and "1.25x" (25 psi) but having the shape of curve so the area under both curves are the same. Of course the barrel id the same length, bullet weight/shape is same, everything is the same except for speed of powder to give different curve profiles, BUT - repeat again, the "area under curve" is equal for both powders.The curves are not so similar that they would make your example true.
One half the pressure will not translate into a curve that is twice as long
Interesting paper, and always amazing to me how tests from 50 or 100 yrs in past can still be so valid today - that paper was 1965. In your link, table IV on page 55 it is interesting how much difference there is in the same 40 grain charge of 3031 powder - from 44.3K to 51K psi. Seems like a good size range.
Ken H>