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Diminishing Returns?

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Chris Nolin

32 Cal.
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I've heard the term "Point of Dimisnishing Returns" before from long-time blackpowder shooters, and it's mentioned in the Lyman handbook, but always as assumed knowledge. As in, "of course, the Law of Diminishing Returns says..." But I have never seen it defined completely. A quick search on this forum revealed nothing.

I think it has something to do with the increasing size of a BP charge eventually reaching a point where energy peaks, and then starts to decrease. Factors seem to include ball weight, BP charge, and maybe barrel length.

But it this point of diminishing returns something that should be known by the shooter? If so, why and how do you calculate it? And what is the practical use of this knowledge?
 
The point at which each increase in powder charge results in less velocity increase than the previous load. That is the point of diminishing returns. Velocity increases are still realized past this point; they just get smaller and smaller.
 
I'll see if I can quantify some of the responses you have got here.

This is some data from my 45 cal shooting between 70 and 110 grains of FFF in 10 grain increments.

(the data was ran to figure point blank range with escalating charges and not specifically for "diminishing returns" but the results are what they are - in this instance I will compare the speed and foot pounds of retained energy at 100 yards - a good "max" range with a 45 cal)

Grains - speed @ 100yds in FPS - FtLbs @ 100

70 grns - 908 fps - 250 ft/lbs
80 grns - 949 fps - 274 ft/lbs (14% more powder = 10% more "thump")
90 grns - 973 fps - 287 ft/lbs (12.5% more powder = 2.5% more "thump")
100 grns - 985 fps - 295 ft/lbs (11% more powder = 2.8% more "thump")
110 grns - 1007 fps - 308 ft/lbs (10% more powder = 4.4% more "thump")

For "MY" 45 diminishing returns starts right around the 80 grain mark.

Moving from 70 to 80 grains of powder (which is a powder increase of 14%) I get 10'ish%/24 lbs more "energy" on target.

The next increase of 10 grains to 90, which is 12 1/2% increase in the powder charge "only" results in 7 more pounds which is only a 2 1/2% increase over shooting 80 grains.

Yes, the velocity and energy continue to climb all the way up to 110 grains, but I'm "consuming" SIGNIFICANTLY MORE powder for a very minimal gain.

I gained 10% going from 70 to 80 and had to go all the way to 110 grains to gain another 10%.

That, is a diminishing (albeit, non-linear) return.
 
Sorry, didn't address your question about how it's determined.

The only way to specifically address your personal rifle is to have it chronographed with different powder charges - mine was measured at 15 ft from the muzzle and the results were plugged into a ballistics calculator to extrapolate the results at various distances.

You don't have to go to that extreme. Often times data collected by others using a similar rifle/barrel will be "close enough" to apply - likewise, sources such as Lyman publish data that will also be close enough to help you determine if using say 100 grains is significantly better than 80 grains (or whatever).

For "me" black powder is expensive ($34/lb including tax) and I have to drive 3 hours, one way, to buy it.

Shooting 80 grains I get about 90 shots per pound. If I move up to 110 grains I only get about 65 shots per pound.

And for shooting all that extra powder I only would get 10% more retained energy = NOT WORTH IT, in my case...
 
I agree with all the above explanations and might add another factor. There may be a decrease in accuracy at some point while increasing powder charges. There have been many on this forum who have said they experimented extensively to find that sweet spot in accuracy. If using the cost. Of powder and shot (even excluding a missed deer). This would certainly be another thing we might consider as a diminished return.
 
Don't forget that recoil continues to increase. More powder means more ejecta mass (I like that term), either unburned powder or in the form of gasses. That extra 10% might hurt 120%.
 
You did not specify what kind of bullet was used in that test. The velocities seem awfully slow for a ball.
 
Sorry, this is a 36" Colerain barrel (7/8" ATF straight).

The load was a .445 RB (Hornady) wrapped in pre-lubed .010 Ox-Yoke cotton patch.

The powder was Goex FFF.

Unlike some of the testing done by Lyman, T/C, Hornady and even Goex I could never get close to 1700 fps muzzle velocity with 70 grains that they "advertise".

My 10 shot average, shot in two relays of 5 shots (so shot 5 rounds at each charge, then did it again) for 70 grains was right around 1535 fps (at 15 feet from the muzzle) - the max speed shot was just over 1550 fps.

This was shot on an outdoor range. I didn't record the temp/humidity/wind etc, because like I noted was doing this to determine point blank range for a +/- 2" trajectory from line of sight in “real world” conditions which is more valuable to me in a hunting situation.

I would be interested to see actual measurements from others who have chrono'd their 45 cal. Those that I have, have had similar results to mine.

Perhaps in a climate controlled, indoor test range the results would have been different, but I'm consistently getting about 10% less velocity than the MFG claim their various products will produce.

And that particular rifle has been chrono'd on different occasions with at least three different machines with fairly consistent results - so it wasn't a "one off uncalibrated machine"
 
Thanks for what you wrote. I used to load for bear, and then found out for me it was just a waste of powder. PRB has such poor performance in the transonic range it just dont buy you any advantge on game to have a mach 2 muzzle velocity, unless you can get the deer to stand at the muzzle.
 
I do patch loose in all my rifles. Don't shoot for points and usually only sight at 50 yards.

If I patched tight figure I could squeeze out a little more speed.

I'm doing a build right now with a 42"/45 cal barrel and will test it compare it to my 36" - also figure that will increase the velocity by 40/50 fps.

My main deer rifle is a 40 cal and I get through and through with that shooting 60 grains under a (what) 92 grain ball (I think it is).

Most deer are shot sub-50 yards, you don't need to load a "howitzer" load to take one down.

(for me) too much can go wrong beyond 50 yards or so - bit of breeze, a slight twitch and now your 3" group at 100 with a max charge either turns into a clean miss (ok, not bad) or a poor hit.

Bambi deserves better than a "hail Mary" shot because you are trying to turn a front stuffer into a center fire...
 
In the real world, the "point of diminishing returns" of powder loads can depend on the powder being used.

These graphs were made using Lymans Blackpowder Handbook values and some of the loads clearly show the point where adding more powder gains less velocity.

If the line stops its rapid climb, the point has been reached.



Each square represents an increase of 10 grains of powder.
 
Keep in mind that the 'law of diminishing returns' applies to all things, not just powder charges. Velocity as a function of barrel length, speed as it pertains to wind resistance, dosage of medicine related to results, ad inf.
 
For me it would start right when you increase the powder load to anything past the most accurate load for the rifle.

I'm mostly into accuracy myself and if I can shoot ya in the eye it wont matter how fast the ball is moving past about 15 grains of powder!
 
Lapoudre said:
I think it has something to do with the increasing size of a BP charge eventually reaching a point where energy peaks, and then starts to decrease. Factors seem to include ball weight, BP charge, and maybe barrel length.

I think you have a grasp on it in the above quote. Except it is not "a point where energy peaks". It is a point where the increase in returns markedly diminishes in correlation with continued change.

It can be (and is) widely applied, not just within M/L. It is used to decide many many things. How many meatballs are in spaghettios? Someone worked out just how many you need in a can for people to say "yea it has enough meat in it" adding more meat past that point would sell a few more cans, but would add the cost of added meat to every can (diminishing returns).

I think :hmm: you were looking at it in too small a scope.

How far to follow a gold vain into a rock.
How many hounds in a pack.
How big a tent do you pack into the woods.
How many roses to give the wife the day AFTER her birthday :doh:
How large a round ball to shoot a White Tail with ( :stir: :doh: ) :surrender: That one could start a book.

It is only a point, you don't have to stop there, but it is good to understand where it is. One can continue on getting less & less gain at the same incremental increase in cost/effort.
 
Zonie's post is an excellent way of showing the point of diminishing returns. If you will notice that the lines are linear up to a point and then began to curve slightly to the right. Right at the point where the line is no longer straight but begins to bend to the right, it the point of diminishing returns. Each additional charge of powder yields less and less of an increase in velocity.

There is an equation, albeit not a very accurate one, with which you can calculate an approximation of the maximum efficient load. In other words it approximates the point at which you reach the point of diminishing returns with a specific barrel. You calculate the volume of the bore in cubic inches. Then you multiply this number by 11.5 and it will give you an approximation of how much powder that barrel will burn efficiently. Exceeding this amount will only yield powder that will be unburned in the bore and simply blown out of the barrel unburned. That is the theory, anyway. The fly in the ointment is that it does not take into consideration the brand nor granulation of powder. So, it is not a truly accurate calculation of the maximum efficient load, merely an approximation of it. I include it just as a point of interest. :thumbsup:

Note: The volume of the bore is calculated by
Pi (3.14126) times the square of the radius of the bore (in inches) multiplied by the length of the bore (in inches). The result will be the volume of the bore in cubic inches. You probably knew this already but I tossed it in just in case.

Example: Assume a .50 caliber barrel that is 28 inches long. The radius is 1/2 the diameter or .25. .25 squared is 0.0625. So Pi times 0.0625 times 28 is 3.1416 X .0625 X 28= 5.4978 or roughly 5 1/2 cubic inches of bore volume. Multiply this number by 11.5 and you get 5.5 X 11.5 = 63.25. Round that off to 63 grains. Theoretically, that is an approximation of how much powder that particular barrel can burn efficiently.
 
The whole concept seems like the proverbial tempest in a teapot, to me. I'm not really interested in efficiency, I'm interested in velocity. All the charts and graphs show that the velocity and resultant energy continue to increase, and that's the pay dirt, for me. If it takes a bit more powder to achieve that, so what?

Spence
 
I fully understand what you are saying, Spence. But some folks, myself included, want to understand a process at a deeper, possibly a more intelectual level. :hmm: No harm in that. :hatsoff:
 
George said:
The whole concept seems like the proverbial tempest in a teapot, to me. I'm not really interested in efficiency, I'm interested in velocity. All the charts and graphs show that the velocity and resultant energy continue to increase, and that's the pay dirt, for me. If it takes a bit more powder to achieve that, so what?

Spence

Yes, but will the increase in energy make the round more or less accurate? I'll take accuracy over power(energy) every time. if 70 grns. of 3fff gives me 2 inch groups at 50 yards, I'll take it over 3 inch groups using 80 grns. even if the 80 grns. gives me 100 more foot lbs. of energy. Less Recoil also.
 
armakiller said:
Yes, but will the increase in energy make the round more or less accurate? I'll take accuracy over power(energy) every time.
I don't know of any reason increased velocity/energy directly causes decreased accuracy. A person's ability to shoot heavy charges may mean he can't shoot them accurately, of course. The ability to shoot heavy charges is a learned skill at which some people are more adept, but it's a shooter's problem, not one built into the charge.

Spence
 
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