Trying again, with the hope that we can stay on topic, which I believe is an important one for those of us using vintage guns.
The topic is NOT why does the chamber pressure rise when using long for chamber length shells, which was investigated 130 years agoSporting Guns and Gunpowders
, “Tests Of Strain On Breech Actions”, 1892
1 1/4 oz. 3 1/2 Dram Bulk Smokeless Pressures in 2 3/4” casehttps://books.google.com/books?id=inQCAAAAYAAJ&pg=PA86
Long Tons/ sq. inch converted to PSI by Burrard’s formula
(Proof) with 6 1/4 Drams “Tower Proof” Black Powder and 1 2/3 oz. shot – 4.51 tons = 14,034 psi
3 1/2 Drams Curtis & Harvey’s No. 4 T.S. Black Powder – 4.2 Tons = 12,992 psi
“Schultze” – 4.28 tons = 13,260 psi
(In a 3” case, with additional wadding the pressure for “Schultze” was 4.93 = 15,445
“E.C.” – 4.92 tons = 15,411 psiC&H No. 4 T.S. 3 1/2 Dr. with 1 1/4 oz. in a 2 1/2” case “would increase the strain (pressure) about 40%; with the same charge in 2 3/4" cases, the increase would be about 50%."
Interesting that the 10% additional increase is similar to Bell's findings.
And all of us get that "feathering" of the case mouth is evidence of a potential problemThe question is "Can lengthening forcing cones mitigate the rise in breech pressure which occurs when using long for chamber shells?"
Sherman Bell's study suggested that it could, but his sample was small and he made clear that was not the point of his study; which is summarized here about 1/3 way down here, along with more vintage studieshttps://docs.google.com/document/d/1ZIo0y746UsSRZIgRuuxwAbZjSBHitO_EanvwLYc-kGA/edit
and this one is interesting, from 1897: https://books.google.com/books?id=inQCAAAAYAAJ&pg=PA280
A trial of 1 1/8 oz. 3 Dr. Eq. 2 1/2” shells in 2” chambers with "an exceedingly long and gradual cone" showed very little increase in pressure.
(1.72 Tons by Burrard's conversion is only 4,660 psi and most period reported numbers for 1 1/8 oz. 3 Drams Bulk Smokeless were 6000 - 8000 psi)
Miller's observation is here, which is an application of the inverse relationship between pressure and volume (when temperature remains constant)https://www.doublegunshop.com/forums/ubbthreads.php?ubb=showflat&Number=37158&page=2
"Changing the forcing cone angle (lengthening) would give a very "Slight" increase of volume in the area, which would tend to slightly decrease pressure. A "Slight" change in friction could also accomplish the same purpose."
An interesting study NOT regarding cone lengthening on pressure but on pattern performance, with a short discussion at the beginning regarding the increase in volume issue. Comments are made by tim99 who is a mechanical engineerhttps://www.trapshooters.com/threads/model-12-forcing-cone.286074/Other opinions are certainly welcome.IF
the primary issue is frictional, one would think that the "chamberless" barrels would have revolutionized barrel design; which they did not
The chamberless Tolley "Altro" was introduced in the mid-1890shttps://books.google.com/books?id=BFRDAAAAIAAJ&pg=PA31&lpg https://books.google.com/books?id=Bzo6EAAAQBAJ&pg=PT92&lpgCountry Life
, June 25, 1921 adhttps://books.google.com/books?id=a0YxAQAAMAAJ&pg=RA8-PT8&lpg
Dr. Charles J. Heath chamberless patentForest & Stream
1922 Sporting Firearms of Today in Usehttps://books.google.com/books?id=9XMCAAAAYAAJ&pg=PA95&lpg Field & Stream
, August 1922https://books.google.com/books?id=XQQ-AQAAMAAJ&pg=PA470&lpg
So in summary, Richard P. Feynman, Professor of Theoretical Physics at the California Institute of Technology
“It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it’s wrong.”
Possibly someone with the interest could build on Bell's work and clearly establish that lengthening cones (and how long?) will substantially lessen (how many less psi is substantial?) the rise in pressure when using long for chamber shells.
I had a mechanical engineer friend who was enthusiastic about investigating pressure testing using a hydraulic device, but a real job and marriage has unfortunately gotten in the way.