Of Optimal Barrel Timing, Choosing Powders & Paper Ballistics
Well, I've been "hard at it" trying to come up with a calculation of some sort of Figure of Merit that incorporates Optimal Barrel Timing and the output of QuickLoad. Here's the latest version.
The "Score" you see in the 11th column is derived from evaluating velocity, chamber pressure, barrel timing and efficiency. The equation looks like this:
ABS ((ABS (MAX ($D$12:$D$37)D12))/50+1/(ABS($G$3E12))*1000(ABS('OBT Tool'!$O$36G12)*1000)ABS(MAX($J$12:$J$37)J12)/10)*10
Yikes! Lemme explain. (ABS means "take the absolute value"  in other words, ignore whether the value is positive or negative).
The first term  ABS(MAX($D12$:$D$37)D12)/50  calculates the difference between the velocity produced by the powder in question (located at cell D12) and the highest velocity produced by any of the powders in question (determined by MAX($D$12:$D$37)), then divides that difference by 50.
The second term  1/(ABS($G$3E12))*1000  subtracts the value of the chamber pressure of the powder in question (located at cell E12), from the maximum SAAMI chamber pressure (located at $G$3), takes the inverse of that number, and multiplies it by 1000.
The third term  (ABS('OBT TOOL'!$O$36G12)*1000  calculates the difference between the actual timing of the powder in question (located at G12) from the "ideal" barrel timing for a barrel of the specified length (more on that later), and multiplies the difference by 1000.
The final term  ABS(MAX($J$12:$J$37)J12)/10  calculates the difference between the "efficiency" of the powder in question (located at J12) from the highest efficiency produced by any of the powders in question (determined by MAX($J$12:$J$37)) and divides the result by 10. (Efficiency is the muzzle energy in ftlbs, divided by the charge. The units are ftlbs/grain.)
The initial "ABS", and the final "*10" simply get the "Score" to a positive value, and scale it so that we're not looking at differences of 0.01 in "Score".
I'm sure it'll help to walk through an example. Let's use the numbers from the first table below.
The powder with the highest Score is Alliant Reloder19. The charge is 46.72 grains; the % of the case used by that charge is 100; the velocity is 2804 f/s; the max chamber pressure is 56091 PSI; the amount of powder burned before the bullet exits the bbl is 98.3%; it takes 1.2290 ms for the bullet to exit the muzzle; the pressure at the muzzle is 12705 PSI; and the resulting Score is 0.2. Here's how we get that score:
First, the max velocity in this group is 2874.6 f/s. Therefore, 2874.6 minus 2804.4 equals 70.2 f/s. 70.2 divided by 50 equals 1.404. Therefore the velocity "score" is 1.404.
Second, the maximum SAAMI chamber pressure for this cartridge is 61641 PSI. (Pounds per square inch.) The chamber pressure for the Rel19 load is 56091 PSI. The difference is 5550 PSI. The inverse of that is 0.00018 SI/P (Square inches per pound); multiplied by 1000, we get 0.18.
Third, the "ideal" timing for node number 5 for a 24" bbl is 1.22852 ms. (More on "timing" later.) The timing for the Rel19 load is 1.22897. The difference between the two is 0.0000448 ms; times 1000 equals 0.448.
Finally, the maximum Efficiency among this group is 63.51 ftlbs/gr. Rel19's Efficiency is 52.32 ftlbs/gr. The difference is 11.19 ftlbs/gr; divided by 10 is 1.119.
So, we have... 1.404 + 0.18  0.448  1.12 = 0.018 * 10 = 0.18
Rounded to a single decimal place, that’s 0.2.
Let’s look at a powder with a lower Score – say I3031.
Velocity is 2732 – velocity score is 2.85
Chamber pressure is 59311 – chamber pressure score is 0.429
Timing value is 1.2290 – timing score is 0.505
Efficiency value is 61.10 – efficiency score is 0.241
For a Score of (2.85 + 0.429 .505 .241)*10 = 25.34
In closing, let me explain the multipliers/dividers a bit. The variables; velocity, chamber pressure, timing, and efficiency all have vastly difference scales. In order to insure that one did not have undue influence simply due its scale, each needed to be appropriately resized. Differences in velocity aren’t too big a deal to me. Therefore, it takes a difference of 50 f/s to equal one whole point in the final Score. Chamber pressure is very important to me, but chamber pressure is measured in tens of thousands of units. Hence the inversion and subsequent 1000 multiplier. Ditto WRT the Timing variable – the differences are measured in microseconds, hence the 1000 multiplier. Efficiency wasn’t that important to me, so it takes a difference of 10 ftlbs/gr to make one unit of difference in the Score.
This is just the first installment. Next come what this means to building a rifle – namely barrel lengths. There are some very interesting results. If you stayed this long, stay tuned. The best is yet to come.
Paul
