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Old September 9, 2020, 01:40 PM   #1
Bulletmann
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Importance of Standard Deviation

Brand new and first time forum user. I have shot black powder cartridge rifle 45-70 for years. Now have pacemaker and am looking for something with less recoil to shoot 1000 yds and closer, on steel.

Am currently in the process of working up a load for my 38-35 cal rifle with smokeless powder. I am not experienced in loading smokeless powder, so the learning curve is steep.

Had a discussion with a fellow reloader and friend about the importance of Standard Deviation (SD) in long range shooting.

He doesn't think it's important and I do. Would appreciate your comments!

Thank you! Mac
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Old September 9, 2020, 03:07 PM   #2
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SD only represents your ability to make uniform loads, it won't make you a better marksman or your gun preform better. It only gives you a better chance. And it does matter.
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Old September 9, 2020, 03:14 PM   #3
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Standard deviation (usually abbreviated as the lower case “s” or Greek sigma, or sometimes sd or SD) is one of a number of different but somewhat related measures of the variability, or dispersion, in a set of measurements, or in the population from which the sample set is drawn. Others include the variance (which is the square of s), the range, the coefficient of variation, and the mean or average deviation. Each of these can be useful, but s has the advantage that, in a normally distributed population (and most “velocity” – technically, because it’s a scalar not a vector, “speed” – measurements associated with reloaded ammunition that I’ve tested are, in fact, normally distributed or acceptably close to being so), the mean plus or minus s will include about two-thirds of the population, +/- 2s will include 95%, and +/- 3s will include 99%.

I think most reloaders would agree that, all else being equal, consistent velocity is a desirable characteristic of reloads – it’s hard to imagine a situation where an increase in variability would be a desirable goal. So, to that extent (but see below), your friend is most definitely incorrect. What there’s much less agreement about is how small s should be for a particular load to be considered “good.” And that leads us into one of the deficiencies of s as a measure of variability, namely that it will vary (i.e. is correlated) with the mean velocity. Consider, for example, a handgun load that has an average velocity of perhaps several hundred fps vs. a rifle load humming along as something closer to 4,000 fps. A value of s of, say, 50 means something very different for each of those. The coefficient of variation (s divided by the mean then converted to a percent by multiplying by 100) takes that into account, in effect “adjusting” s by the value of the mean. I rarely see much discussion of CV in reloading circles, but I think of it as more valuable than s, although again there will be differing opinions on what’s a “good” CV.

All of that said, the most important consideration is how well the loads perform in your firearm with you at the controls. The results – and there are much better measures than group size, but that’s a whole ‘nother discussion - are incorporating the net effect of all sources of variability, not just the variability in velocity. If your groups are acceptably small then it really doesn’t matter much what s is. So, in that particular case, I’d have to say your friend has a point. However, if your groups are larger than you like, knowing the associated value for s can help to isolate the reason.

Sorry for the long-winded reply. I used to work with this stuff at one time, but don’t have much opportunity to discuss it now in retirement.
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Old September 9, 2020, 03:27 PM   #4
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Yes, standard deviation matters, but...there's always a but...I have had loads that shot very well with a decidedly unimpressive Std. When working up loads over a chronograph, I sometimes see the Std increase as I approach maximum. Maybe reaching a point of diminishing return? So, it's one piece of data that you need to consider.

Is your caliber a typo, or am I ignorant of an old round? I load 38-55 (if that's what you meant to type) and do well with 255 Barnes "Original" over IMR-4895. And my Std is 11.8.
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Old September 9, 2020, 03:48 PM   #5
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Welcome to tfl!

Standard deviation is a mathematical (statistical) thing. It is going to exist anytime things are not exactly identical.

When it becomes important is when the amount of deviation reaches the degree that has an effect on real world performance.

A handful of fps variation is usually insignificant. A double handful seldom is, but more can be. It all depends on the amount of the variation, compared to what you are shooting and what results you hope to obtain.

Say your loads vary by 35fps. Usually not an issue. 50fps or more might be, and 100fps difference shot to shot usually often is.

Yes, consistency matters, but only after it reaches the point where it affects your group sizes and trajectory, and that will differ a lot depending on what you are shooting,

Pistol rounds @ 25 yds? not so much
scoped match grade bolt gun looking to put them all in one bullet size hole at 100 yds? can matter quite a bit.

.38-55? A single shot or old lever gun? I would think one of those to be more "forgiving" than a benchrest rifle.
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Old September 9, 2020, 03:56 PM   #6
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A popular solution to big velocity spreads is putting a tuning weight on the barrel near the muzzle. It can be adjusted so slowest bullets leave at higher angles above the line of sight to compensate for their greater drop at target.
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Old September 9, 2020, 04:04 PM   #7
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Flyfish is correctly describing standard deviation except for the symbols don't all mean quite the same thing. The Greek lowercase "σ" (sigma) is reserved for population standard deviation, while SD (capital or lower case, regular, bold, or italic) and "s" are used for sample standard deviation which is what your chronograph calculates and which is actually an estimate of what the population standard deviation will turn out to be by the time you've shot and measured the velocity of all of the copies of that particular load you will ever shoot from that gun and barrel. As you increase the size of your sample, that estimate of population standard deviation becomes increasingly accurate.

What affects the length of long-range stringing is the extreme spread of the velocity in the particular shots you fire on it. This depends on only two shots, the fastest and the slowest, and, being just two shots out of the collection, will vary from group-to-group some. SD, however, will vary much less, and for that reason gives you a more reliable estimate of future behavior. The differences in velocity change the total time of flight to the target which changes how long gravity is pulling down on it, so it changes the point of impact. This has almost no clearly discernable effect at 100 yards for anyone not shooting groups under about an eighth of an inch C-T-C. But at 1000 yards, the time difference builds up and the resulting difference in the bullet's speed of fall caused by gravity increases because gravity accelerates that. If the velocity variation is wide enough, the differences in resulting barrel time can move you off a muzzle deflection sweet spot, too, possibly opening groups in any direction the vibration is in at that time. Sometimes that is vertical, but sometimes it is diagonal or even somewhat sideways. In any case, you don't want it.

A third thing SD can tell you is that your load is powder-position sensitive. A fourth thing is that your ignition is inconsistent, as from incompletely or improperly seated primers. Any kind of inconsistent primer performance is usually accompanied by inconsistent delay times between when the primer is first struck by the firing pin and when the powder really starts building pressure. That's like having variable lock time, which exaggerates shooter errors.
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Old September 9, 2020, 04:05 PM   #8
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Sorry I didn't clarify. Yes, I am shooting a 38-35 which I believe is an old Savage round from the late 1800s. It's basically a 38-55 case cut down to 1.6 inches. I have read that one can obtain the same ballistics (or close to same) as the 45-70 with much less felt recoil. This includes essentially velocity and trajectory. Since my health forbids shooting heavy recoiling rifles, I've opted to try this.

The man who I am copying felt that SD was important due to the long ranges being fired.

I understand his rationale. If there is a big difference in SD/velocity, it follows that trajectory would vary greatly. What are your thoughts?

Am going to be away for a few days. Appreciated all your responses.

MAC
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Old September 9, 2020, 05:00 PM   #9
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The 38-35 is actually an old Stevens round. Without knowing what your 45-70 load's bullet shape or BC are and what its muzzle velocity was and what bullet you are hoping to get working in the 38-35, I can't comment on their possible relative performance. I also don't know what the peak pressures should look like in that cartridge. I gather the Stevens rifle for them was weaker than 38-55 rifles. So the pressure may be more like the 38-40 Winchester, which is about like a 38 Special, which would put you at a big disadvantage compared to the 45-70. I just don't know. You will definitely be loading entirely by pressure signs with this one.

For minimizing the SD, I would look for a powder that fills the case well. Make sure your mainspring is in strong shape and that you seat primers fairly hard.
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Old September 9, 2020, 05:57 PM   #10
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Light in the Darkness

Uncle Nick and FlyFish, please cast some light into the darkness. Without remembering the source, I read that after a reloader determines the best powder load for a particular cartridge to rifle combination, the bullet seating depth needs to be determined. To do this, one observes the SD between cartridges fired with the same charge but different bullet seating depths. The lowest SD is the ideal bullet seating depth. I would guess that this is caused by powder position? What more can you discuss about SD and bullet seating depth?
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Old September 9, 2020, 07:07 PM   #11
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Long range accuracy is the combination of 3 inter-connected factors. Rifle/shooter intrinsic accuracy, short range load development and standard deviation.

Standard Deviation: This is a huge factor for elevation. Look at what 50 fps does at 1000 yards. 50 fps is 11” with my load. My round shoots pretty flat. Most rounds would be like 15”. Slower rounds, much more. ...64” on a 45-70 load I looked at. Cutting that in 1/2 is a big improvement. Reducing to 10 fps is a huge improvement!
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Old September 9, 2020, 08:11 PM   #12
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Two schools of thought on it. One school swears by the math, the other says any variations in velocity will be canceled out by barrel harmonics. I go with the math crowd just cause I can

Berger's take on it - https://bergerbullets.com/nobsbc/sta...he-bell-curve/


Precision Rifle Blog's How much Does it Matter Series on SD https://precisionrifleblog.com/2015/...ot%20variation.

Think about this. The velocity consistency 15 feet from the muzzle does not much matter if the BC of your bullets is not consistent
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Old September 9, 2020, 08:33 PM   #13
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Quote:
other says any variations in velocity will be canceled out by barrel harmonics.
I would love to see that velocity SD matters, BC SD matters. Both are variations impacting group size at 1000.

This barrel harmonics thing is real. In recoil, battles whip and twist. At 100 yards, with a strong rifle round, load development finds consistency and harmony between the load and the rifle.

Actually, there are methods like the Saterlee method where you take a great rifle, find flat spots in the charge vs velocity curve and look for SS under 5! Basically forget about harmonics.
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Old September 9, 2020, 09:23 PM   #14
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a lot has to do with the cartridge also certain cartridges are inherently accurate and load tolerant

6PPC
6BR
.243 Win
6.5 CM
6.5/284
30 BR

are some examples, I sure that list can be added to

My 30 Grendel is about as load tolerant as it gets as long as you hard jam the bullet. I can darn near dip the case in N120, tap out enough to seat the bullet and get consistent .1's and .2's at 100.

some rifles are just more accurate than makes sense also. Kidd .22's (Ruger 10/22 clone) have a flimsy tupperware stock (Magpul) with a single action screw that shoots as well as .22's that cost three times as much. The action practically flops around in the stock

more I learn about this stuff the less it makes sense sometimes
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Old September 9, 2020, 10:09 PM   #15
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back on task

Let me try to get back to Bulletman's question about SD. In a simple layman's explanation, this is how I would tell my friend who disagreed that SD doesn't matter. Let's say we both reload. Measure A is accurate to +/- .1grain. Measure B is accurate to +/- .5grain. Which is he going to use? Answer: A, because his loads will be more consistent and be more accurate. That's the same with SD. If you have a larger SD, you are not going to shoot as accurately.

I'd like the rest to answer this question. To me, harmonics is like the wave we use to kick down the bathtub as kids. The wave hits the wall, comes back, splashes in the wall behind us, and returns. The bath tub water is calmest then. The node is where the splash hits the wall and that's were the receiver is. The bullet must leave the muzzle at the time the shock wave is at the receiver. Am I pretty close to what's going on?
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Old September 10, 2020, 02:36 AM   #16
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Quote:
Originally Posted by 44 AMP
A handful of fps variation is usually insignificant. A double handful seldom is, but more can be. It all depends on the amount of the variation, compared to what you are shooting and what results you hope to obtain.

Say your loads vary by 35fps. Usually not an issue. 50fps or more might be, and 100fps difference shot to shot usually often is.
But aren't you talking about extreme spread here, not standard deviation?
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Old September 10, 2020, 07:31 AM   #17
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back to the OP if you plan on using cast bullets the variation in BC between the bullets will probably null out any variation in velocity differences
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Old September 10, 2020, 08:41 AM   #18
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Quote:
Originally Posted by Nathan
Actually, there are methods like the Saterlee method where you take a great rifle, find flat spots in the charge vs velocity curve and look for SS under 5! Basically forget about harmonics.
Apples and oranges as near as I can tell. Velocity flat spot tuning makes muzzle swing have less effect and tuning to muzzle swing makes velocity variation have less effect. The very tightest groups seem to come when you get the two synchronized. So you could shoot a velocity ladder and then use a barrel tuner or a stock contact control like the Smart Stock to match muzzle swing to it and get some really small groups. Bullet seating depth can also be tuned, and I think it acts somewhat like a poor man's barrel tuner by shifting barrel times a bit, but I don't have hard data to show that; it is just an impression.


Burbank,

When you change bullet seating depth you also affect pressure, so you have to watch out for pressure signs when you do it. Another way is to find your load with the bullet jammed into the lands (highest pressure for most) then back it out. But usually, you are looking for the smallest group size as you change the seating depth. SD may or may not improve with it. Ideally, you get muzzle swing, low SD and smallest group-producing seating depth all lined up at once. It can be quite a bit of work to get three independent variables all playing well together. A barrel tuner does make that simpler.

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Old September 10, 2020, 10:18 AM   #19
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Quote:
Bulletmann wrote: .....

Had a discussion with a fellow reloader and friend about the importance of Standard Deviation (SD) in long range shooting.

He doesn't think it's important and I do. Would appreciate your comments!

I believe, too, its important for long range shots.
Also think its a good indicator for reloading consistency.

I like to see the SD divided by average velocity to be 0.5% or less for my rifle reloads.
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Old September 10, 2020, 10:59 AM   #20
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Over the years reloading has turned into a mind numbing science. Back it the early 70's I had a 7mm Rem Mag that consistently shot 160gr Speer Hot Core's into little 5/8" groups. I never had any idea what the SD was. In fact back then I never even heard of SD! Even today I don't concern myself with it much but I do wonder how some group's are very tight when the SD is so far off in them! If your load is shooting say 1" group's in a hunting rifle, does it really matter what the SD is? Doesn't to me. That is little more than one more thing to chase. Perhaps a match shooter can find a good reason for chasing it, I'm not a match shooter but have several hunting rifle's that will hold close to 1/2" group's and I haven't a clue nor do I care what the SD is!
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Old September 10, 2020, 11:41 AM   #21
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Don,

It sounds like you are talking about shorter range shooting. If I fire a 7 mm Sierra 175-grain SPBT at 2700 fps and again at 2650, at 100 yards the drop difference is only 0.1 inches. Nobody but a top-ranked benchrest shooter is even likely to be able to detect it on the paper, and maybe not even then. At 200, it grows to 0.4 inches difference, and at 300 yards it grows to 1 inch. Those numbers are all within what most people consider darn good shooting at those distances. But if you are shooting at 1000 yards, the drop difference grows to 16 inches and that's enough to cause you to miss a gong or popper or drop points on a target.

So, I think the answer to your observation about the increasing complexity is that when very few people were shooting at long ranges (before F-Class competition in particular), few people shot far enough for it to matter and most matches were held using targets developed for service rifles that didn't require super-precision. But between Bryan Litz and others spreading the ballistics gospel, it became apparent that people who had detailed technical knowledge won more matches or rose in the winning ranks more rapidly than those who didn't.

So, while it is still possible to win a match without deep ballistics understanding or to find good loads by more rudimentary trial and error, the people who delve into the science have been found to have a competitive edge. Competitors want that (or any other edge they can get; just look at what is spent on top equipment and supplies). The up-and-coming competitors don't want to cede that edge to the top competitors, either. So, with the help of computers and cell phone apps and some top people experimenting and publishing, the technical deep-dive has taken on a life of its own.
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Old September 10, 2020, 02:01 PM   #22
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Standard deviation is the result of mathematical massaging of the data and gets a lot of attention on the gun boards because most consumer chronographs will spit it out automatically. In my use it is just a general indication of ammo quality because I am not doing statistical analysis of my ballistics.

Extreme spread is actual data and is what the OP needs to be watching.
At long range velocity variation equals elevation variation, accentuated by the low velocity of a cast bullet driven by black powder. Also, the BPCR shooter has less scope to look for nodes and no option of hanging weights on his barrel.

I don't know where the OP will end up with .38-35 Nitro.

The best small bore I heard about was Dan Theodore's development of the .35-55 Maynard, but he was still shooting with black powder and complaining that the NRA disallowed it because they weren't sure it was a standard 19th century chamber.
I saw a junior shooter shooting a round with .357 Maximum brass and a long heavy bullet seated very shallowly to make room for powder. I don't recall what period round that was supposed to approximate.
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Old September 13, 2020, 07:57 AM   #23
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Quote:
and tuning to muzzle swing makes velocity variation have less effect
How can “muzzle swing” impact external ballistics? Velocity and BC Sd are all about minimizing the variation in flight. I’m wondering as I know that you know your stuff.


Quote:
, I'm not a match shooter but have several hunting rifle's that will hold close to 1/2" group's and I haven't a clue nor do I care what the SD is!
...and that works great at 100-400 yards, but things will start open up without understanding variation beyond that.

Last edited by Nathan; September 13, 2020 at 08:08 AM.
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Old September 13, 2020, 09:39 AM   #24
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Everything is relative. There are some 1000 yard guys who have turned in 5 shot groups under 1.5". To do that SD is more important than the level of accuracy you're going to achieve with a 45-70 or 38-35.
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Old September 13, 2020, 10:25 AM   #25
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And for a meaningful SD statistically, a minimum sample is 10 is required. More is always better of course. I shoot 15. Allows me to throw out obvious fliers if applicable. My testing is mostly with pistol/revolver cartridges as that is what I like to shoot. I've also found that SD is usually always in the ballpark of 1/3 the Extreme Spread. Therefore I care more about the ES. Consistency never hurts accuracy, it can only help of course. Yet, the load still may not be accurate for some reason. That's why we work up loads to find 'the' load we feel is 'right'. My two cents.
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