I have in an earlier thread on this forum theorized that the amount of powder required in a handload goes up with the SQUARE of the velocity required. I think I accidentally got proof the other day.
I was testing the new 250g Hybrid Tactical 338 bullet from Berger in my TRG Model 42 in 338 Lapua Magnum, using:
Lapua cases
Federal 215M primers
Berger's "new" 250g Hybrid Tactical bullet
Retumbo powder
Here is a table of the summarized chronograph results I obtained:
Grains / fps / (no. of successful fps readings):
91.0 / 2684 / (4) (note: Lowest was 2646, highest was 2710)
92.0 / 2744 / (4) (note: lowest was 2741, highest was 2746 !)
93.0 / 2781 / (3) (note: 2792, 2772, 2778 so ES = 20)
94.0 / 2820 / (1) (Chrono stopped reading altogether after 1 shot)
95.0 / 2849 / (3) (2850, 2848, 2848. Wow! But, groups not as good as 92.0 to 94.0 grains depsite that)
So . . .
Gain from 91.0 to 92.0 grains = 60 fps
Gain from 92.0 to 93.0 grains = 37 fps
Gain from 93.0 to 94.0 grains = 39 fps
Gain from 94.0 to 95.0 grains = 29 fps
This by itself SUGGESTS a relaiton of the form:
grains of powder = some constant x velocity squared
This makes sense since the pwoder supplies energy, some of which is actually used to propel the bullet (the rest is lsot as muzzle blast and heat).
But, if this is true, then the math looks like this:
If energy = 1/2 x mass x velocity x velocity, then:
grains of powder = some constant x velocity squared
or
constant = grains of powder / velocity squared
So, I did the math on the data values listed above. Here are the results for all the data values from 91.0 grains to 95.0 grains:
91 grains / 2694 squared = .0000126
92 grains / 2744 squared = .0000122
93 grains / 2781 squared = .0000120
94 grains / 2820 squared = .0000118
95 grains / 2849 squared = .0000117
Note though that dividng grains by stright (not squared velocity) works pretty well within a NARROW band of grains, as the differences between direct and squared relationship are small for SMALL changes:
91/2684 = .0339
92/2744 = .0335
93/2781 = .0334
94/2820 = .0333
95/2849 = .0333
So if we stay within a narrow band (like when fine tuning), the direct relationship is probably close enough, but will break down as the velocity / powder grains range broadens.
(Jim G edit 2012-03-12 11:56am - had accidentally posted wrong columns in 1st post)
I'd say that is pretty good correlation between prediction and actual. Amount of powder required IS closely proprotional to the square of the velocity desired or attained.
Note that the best accuracy, consistently, was for way LESS than the maximum that the (Hodgdon) loading manual showed (98.0 grains, compressed load). The ebst accuracy was at 92.0, 93.0 and 94.0 grains, with 93.0 being the best of the 3, with the limited number of rounds fired (50 total) and my lack of skill (some groups were clearly shooter error).
Best "velocity-for-the-buck" was at the lower end, where 92.0 grains, where you pick up 60 fps by adding 1 grain of powder.
If this correlation holds in further testing, it gives us a way to "design" our loads in advance of actual testing, and then test to see how the load actually performs in terms of ACCURACY in our specific rifles, as accuracy depends on additional different factors than sheer velocity. To get starting points for testing, just use the grains and velocities shown in most loading manuals.
The constant will of course be different for each rifle, pwoeder, bulelt, etc, but the point is there appears to be a constant. So, you CAN predict velocity for any pwoder laod in YOUR rifle once you know the velocity at ONE powder load.
And of course, you can predict energy, elevation clicks, and windage clicks too, by using the proper formulas and apps.
Jim G
I was testing the new 250g Hybrid Tactical 338 bullet from Berger in my TRG Model 42 in 338 Lapua Magnum, using:
Lapua cases
Federal 215M primers
Berger's "new" 250g Hybrid Tactical bullet
Retumbo powder
Here is a table of the summarized chronograph results I obtained:
Grains / fps / (no. of successful fps readings):
91.0 / 2684 / (4) (note: Lowest was 2646, highest was 2710)
92.0 / 2744 / (4) (note: lowest was 2741, highest was 2746 !)
93.0 / 2781 / (3) (note: 2792, 2772, 2778 so ES = 20)
94.0 / 2820 / (1) (Chrono stopped reading altogether after 1 shot)
95.0 / 2849 / (3) (2850, 2848, 2848. Wow! But, groups not as good as 92.0 to 94.0 grains depsite that)
So . . .
Gain from 91.0 to 92.0 grains = 60 fps
Gain from 92.0 to 93.0 grains = 37 fps
Gain from 93.0 to 94.0 grains = 39 fps
Gain from 94.0 to 95.0 grains = 29 fps
This by itself SUGGESTS a relaiton of the form:
grains of powder = some constant x velocity squared
This makes sense since the pwoder supplies energy, some of which is actually used to propel the bullet (the rest is lsot as muzzle blast and heat).
But, if this is true, then the math looks like this:
If energy = 1/2 x mass x velocity x velocity, then:
grains of powder = some constant x velocity squared
or
constant = grains of powder / velocity squared
So, I did the math on the data values listed above. Here are the results for all the data values from 91.0 grains to 95.0 grains:
91 grains / 2694 squared = .0000126
92 grains / 2744 squared = .0000122
93 grains / 2781 squared = .0000120
94 grains / 2820 squared = .0000118
95 grains / 2849 squared = .0000117
Note though that dividng grains by stright (not squared velocity) works pretty well within a NARROW band of grains, as the differences between direct and squared relationship are small for SMALL changes:
91/2684 = .0339
92/2744 = .0335
93/2781 = .0334
94/2820 = .0333
95/2849 = .0333
So if we stay within a narrow band (like when fine tuning), the direct relationship is probably close enough, but will break down as the velocity / powder grains range broadens.
(Jim G edit 2012-03-12 11:56am - had accidentally posted wrong columns in 1st post)
I'd say that is pretty good correlation between prediction and actual. Amount of powder required IS closely proprotional to the square of the velocity desired or attained.
Note that the best accuracy, consistently, was for way LESS than the maximum that the (Hodgdon) loading manual showed (98.0 grains, compressed load). The ebst accuracy was at 92.0, 93.0 and 94.0 grains, with 93.0 being the best of the 3, with the limited number of rounds fired (50 total) and my lack of skill (some groups were clearly shooter error).
Best "velocity-for-the-buck" was at the lower end, where 92.0 grains, where you pick up 60 fps by adding 1 grain of powder.
If this correlation holds in further testing, it gives us a way to "design" our loads in advance of actual testing, and then test to see how the load actually performs in terms of ACCURACY in our specific rifles, as accuracy depends on additional different factors than sheer velocity. To get starting points for testing, just use the grains and velocities shown in most loading manuals.
The constant will of course be different for each rifle, pwoeder, bulelt, etc, but the point is there appears to be a constant. So, you CAN predict velocity for any pwoder laod in YOUR rifle once you know the velocity at ONE powder load.
And of course, you can predict energy, elevation clicks, and windage clicks too, by using the proper formulas and apps.
Jim G
