Seb7701,
Two things to keep in mind:
1) The main issue is how much powder space there is. For that purpose, since bullet design gives same-weight bullets different lengths, the same COL will not give you the same amount of powder space when you have two different bullet lengths for the same weight. The smaller the powder volume per inch of case length under the bullet as compared to bullet volume per inch of length, the less you have to change bullet seating depth to cause a given percent change in powder space. So this is a relatively modest sensitivity issue in an overbore bottleneck rifle case, but a very big issue in a stubby straight wall (or close to it) pistol case.
For the purpose of powder space, then, it is not COL¹ itself, but its effect on seating depth you want to control. Seating depth is how far the bullet is inserted into the case.
SEATING DEPTH = CASE LENGTH + BULLET LENGTH - COL
Use the above calculation to find the COL of a load whose pressure you want to duplicate. Then add the difference between that bullet's length and your bullet's length to determine a NEW COL that will give your bullet the same seating depth as the original load. Where your bullet is shorter, the difference in length is a negative number, and being longer is positive. If you find keeping track of the rule of addition for a negative number (you subtract its magnitude) too annoying to remember, you get the same result by rearranging the above formula as:
NEW COL = CASE LENGTH + BULLET LENGTH - SEATING DEPTH
2) Bullet material has an effect. The coated lead bullets are softer than jacketed bullets and don't tend to be grasped as firmly in the case neck, so they are unseated at lower pressure with the result they raise pressure a bit less as you change their seating depth. They also require less pressure to swage into the rifling lands, so having them in contact with the throat at firing. Indeed, with all lead and coated bullets, where my magazine length from front to back and the gun's ability to feed will allow it, I always seat these bullets out to contact the lands and I work the loads up with them in that position. It keeps them more concentric in the bore and less prone to being unbalanced by swaging into the bore at an angle, which they are soft enough to do. In .45 Auto with short bearing surface lead bullets, I found this practice cut machine rest groups size by about 40%, and it also greatly reduced leading. A coated bullet doesn't generally cause leading, but it is soft, so the accuracy effect still applies.
Powder or resin coated bullets and thin copper plated bullets respond like lead. Thick soft copper plated bullets are generally between lead and jacketed bullet hardness and behavior, so you have to work your loads up carefully to see what pressure signs may or may not occur.
Second from right is how I seat soft bullets to prevent distortion of them:
hdwhit said:
The rate at which smokeless propellants generate gas is governed by a differential equation with pressure and temperature components, not an exponential function…
Don't forget the first two lines of the famous MIT cheer (which I put down in its entirety for amusement of those unfamiliar with it):
"e to the x, dy, dx,
e to the x, dx.
Secant, tangent, cosine, sine,
3.14159.
Square root, cube root, log base e,
Cheers for math at MIT. "
For more detail of the relevance of the first two lines,
read here. In part, it says:
"By studying the exponential functions, and picking a convenient base, we have inadvertently stumbled on a relationship satisfied by the function and its derivative. That relationship is called a differential equation."
But the exception doesn't disprove the rule in this instance. What you said about the inadequacy of linear interpolation is exactly correct, and it gets worse for those who attempt linear extrapolation beyond provided load pressure data. But for seating depth changes, or for incremental charge weight change, an exponential least squares curve fit generally turns out to be a closer fit than shot-to-shot variation.
If I use QuickLOAD's combustion model, here is an example:
Code:
.45 Auto, 230 grain FMJ, 5 grains Bullseye
Δ COL COL peak psi Δ psi
0 1.275 16325
-0.025 1.250 17856 1531
-0.025 1.225 19751 1895
-0.025 1.200 22136 2385
-0.025 1.175 25265 3129
The reason each increment deeper seating depth produces greater change in peak pressure than the previous one did (and does so with a close fit to an exponential correlation (R² = -0.997)) is that each successive subtraction of the same volume from the case represents a greater portion of the remaining powder space than subtraction of the preceding increment did. The powder type affects the actual amount of bend in the curve, of course, as does the bullet weight, as will anything that changes starting pressure (crimping, jamming the lands, differing bullet hardness, etc.). I don't think anyone meant to suggest there is a universal usable exponent value.
¹
COL stands for Cartridge Overall Length. You also see COAL (Cartridge Over-all Length), CL, OAL, and OL. The hyphenated form of 'overall' as 'over-all' used to be employed to distinguish the former, meaning all things considered, from the latter, meaning the total length of a boat or arrow or other missile. By the 1960's the hyphen was dropped from Webster's and the single form, overall, came to be used for both meanings. In general, according to Webster's, hyphenation is a practice gradually disappearing from the English language, with the married names of women being the only area of growth in their use.
