You have responded to a lot I didn’t say. Guns firing bottle necked cartridges, do typically have longer barrels for the bore, than the same bore with a straight walled case. Yes there are exceptions. I didn’t mention expansion ratio, because it wasn’t needed. The statement I did make: that the burn rate is a function of the case volume, bore diameter, sectional density of the bullet and the length of the barrel, covers all of that. I try not to get too technical in forum answers. Most folks don’t have enough of a physics, and chemistry background to get very far into the details. And I own Brownels “book”, actually a collection of magazine articles, as well as about a dozen others on internal ballistics. Admittedly, most of the books on internal ballistics are more relevant to artillery, because the military has expended far more readership dollars on large arms research than small arms.