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I think it's safe to say the vast majority of people on this forum know that varies significantly, depending upon bullet caliber, bullet mass, cartridge propellant, cartridge primer and primer type, not to mention the length of the barrel, twist of rifling grooves, depth of the rifling grooves, width of the rifling grooves, type of barrel steel, the way the barrel was made (cast, forged, hammered, drilled, rolled, cut/lathed), and the way the barrel was heat-treated (hardening).

Having take a class or three in materials engineering, I do believe this can be reduced to some approximating equations, but some of the coefficients must be placarded. That is, they're discrete elements, which vary in steps between the above mentioned factors, such as the type of powder that was used. I'm not going to begin to dig into my college texts to derive a single equation t=f(x), but let's at least figure out which components can be parameterized and which will require tabular data. Here's my initial stab at it:

**Continuous**(can be included in the equation using algebraic and/or calculus equations):

bullet caliber

bullet jacket (affects friction)

bullet composition (jacket and composition affect in-barrel deformation, which affects both friction and its ability to seal against propellant gases)

bullet mass

cartridge propellant

length of the barrel

twist of rifling grooves

depth of the rifling grooves

width of the rifling grooves

**Discrete**(varies widely from one brand to another, and so much be introduced via placard coefficients into the equation):

cartridge propellant

cartridge primer (via make and model)

barrel make and model*

*barrels: So many factors go into making a barrel that it's extremely difficult to parameterize them all. It's easier to test a specific set of barrels all made

**to the same manufacturer's specification, but rather,**

__not__*all made in precisely the same way*, and note the performance under different rounds, than it is to attempt to parameterize sub-elements of the barrel like:

- type of barrel steel (although, if specific ratios off the steel phase diagram are known, they might be able to be parameterized, above)
- the way the barrel was made (cast, forged, hammered, drilled, rolled, cut/lathed)
- the way the barrel was heat-treated (hardening)

Why? Because it's there. It may also help hand-loaders get the most out of their loads and propellants while remaining on this side of the limits of safety.

On a more practical note, it's sufficient for nearly all practical purposes to use the cartridge manufacturer's specifications with respect to both round performance, and if you're loading your own, use the powder's performance charts to determine how much to use given the caliber and mass of bullet.

Then, there's this outstanding resource.

And this one.

Finally, there's always Grandpa's answer: 'Bout that long...