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Old August 31, 2012, 06:56 PM   #1
farmerboy
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SD and ES???

could someone explain in lamins terms what the two mean? is it standard diveation and extreme spread or not and whats the difference? I know this is a question for those chrony guys. Im just interested and thinking I have always played around with powders, charges, bullets, primers so on and so on until I could punch a single hole, never cared what any fancy gadget could tell me. My targets have always done that but Im now getting alittle curious. Thanks for the replys
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Old August 31, 2012, 07:12 PM   #2
Bart B.
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ES is extreme spread. For velocity it's the difference between the slowest and fastest bullet in feet per second. For example, 50 fps between 3100 and 3150 feet per second.

SD is standard deviation. Math's used to calculate the velocity difference between the average of all shots and the speed of each one. If the average velocity of all shots is 3125 fps, then there'll be from zero to 25 fps difference for bullet's velocity from the average of all. Then math gets the average difference of all shots; the standard deviation from average. It's typically about 1/3rd of the extreme spread. In the above ES example of 50, SD would be about 17 fps. And that's about 1/3rd of 50. Most of the bullet velocities will be within one SD of average.
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Old August 31, 2012, 07:27 PM   #3
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so SD will take overall average (middle) and then calculate what each individual bullet does from that number? Very clear on ES now im just trying to grasp SD.
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Old August 31, 2012, 07:27 PM   #4
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After frustrating myself for years with chronography I learned the following:


Standard deviation means the amount of deviation from the standard, or mean velocity. This is not an average. Extreme spread is the difference in velocity between the fastest and the slowest rounds measured.

At some point almost all casual users of chronographs discover that these terms and measurements have no relation to their observed downrange performance. That is: a group of shots that shows a poor standard deviation may well and quite often is--a very small group on target--and-- vice versa. The same goes for ES and all chronograph data we get in the field using consumer type machines. Chrony measurements do not give you data on penetration or expansion or --well anything, really, except in the most general and abstruse way.

So--why is that?

1-- the number of shots/groups we can sample are insignificant as far as statistics are concerned. Very very very few of us have the money/time/patience to sit and shoot the number of shots required to make a statistically significant result possible--and even then-

2--almost none of us in the field have rigged blast/flash screens to prevent anomalous readings on the Chrony. It's a safe bet that very few handloaders even heard of the screens or think there is a need once the do hear of them. (the ones that don't think the need is there need to rethink or have this explained to them by someone who knows the real skinny--like I had explained/demonstrated to me)

3- most of us start out trying to duplicate load data we see in loading manuals even though we are not shooting the exact same bullet or primer or barrel or barrel twist or-- you see where this is going?

4- we can't control conditions in the field as we can in the lab

5- The meager bits of data we can get from field consumer chronography is useful for what? If you were shooting targets only at known distances--you do not care about velocity you care about placement on target and we know that a chronograph is not going to predict that. If we are shooting for hunting purposes at the most common hunting ranges in the US 300 yards or below the above still applies and the deer or moose does not fall over faster just because you think you hit him 100 fps faster.....or not.

Snipers, long range varmint shooters or long range hunters like to have a baseline for doing the calculations that really lead to a hit at variable range and conditions--a chrony will provide this---but--there is so much better--lab produced ballistic data for factory cartridges and also computation programs for handloads, that it's hard to see where spending money for a tool of questionable accuracy and questionable use is worthwhile.........

Money spent on a chrony would be better spent on some wind flags and steady rests to use at the club you joined in order to be able to practice frequently and when working up loads or zeroing scopes and also for the books that actually teach shooting skills............
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Old September 1, 2012, 07:50 PM   #5
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You've gotten Extreme Spread well explained.

Standard Deviation is difficult to put into layman terms.

Without digging out my Statistics textbooks, I am limited, but here goes:

Take any set of random data (weight of every schoolchild in the second grade or the weight of each grape in a bunch at your local supermarket).

Extreme spread and Range are the same thing

Let's consider the string of values 2, 3, 3, 4, 5, 7, 18

Average, also called "Mean" Simple arithmetic 6.14 is the average of the string

Median is the middle value 4 is the middle value of the string. There are three values above 4 and three values below 4. If you have an even number of values, you may have a hard time selecting the median, so you average the two candidates.

Mode 3 is the value that comes up most often (twice, though is pretty thin evidence)

These are all simple.

It is interesting to note that when you have a truly random sample without skewing characteristics, the mean, median and mode will be the same (or VERY close).

If you draw a graph of all the values, you get the "Bell Curve" so beloved by statisticians.

Count 8 9 11 13 18 13 11 9 8
Value 16 17 18 19 20 21 22 23 24

There are 100 values (population of 100) represented above with an extreme spread of 8 (24-16). The mean, mode and median are all 20.

Count 8 9 10 11 24 11 10 9 8
Value 16 17 18 19 20 21 22 23 24

There are 100 values (population of 100) represented above with an extreme spread of 8 (24-16). The mean, mode and median are all 20.

But if you graph the values, the second set of data is more centrally located and the first set of values is more spread out. It has a larger standard deviation (which is a measure of how "tight" the population is - smaller S.D. means tighter population.

S.D. of the first population is 10. S.D. of the second population is 5

In a normal distribution of populations, 68% of the population is within one S.D.s of the mean and 95% is within three S.D.s of the mean.

What it means to the shooter is that knowing 95% of your velocities are within a narrow velocity range is better than knowing that 95% of your velocities are within a wide velocity range.


For more detail, this site does a better job of it that I can
http://www.robertniles.com/stats/stdev.shtml

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Last edited by Lost Sheep; September 1, 2012 at 07:58 PM.
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Old September 1, 2012, 08:52 PM   #6
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One SD = 1σ ("one sigma") in the following chart:



it essentially says that the next shot you take has a 68% probability of being within ±1 SD away from the average, and/or a 96% probability of being within ±2 SD.

Essentially it's an indicator of predictable behavior.
Small SD's R "good"
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Old September 1, 2012, 09:22 PM   #7
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Thank you guys very much. clear now... Next question is I had always heard that if you chrony a load and ES and SD are very low that the load will have to group very well. Then you hear others say that you can have a very low load on chrony and still shoot like crap. Confused? like I said I shot through a friends chronograph about 8 years ago just to see what mine were fps but dont remember ES and SD but I had a 30-06 that day with handloads at 100 yards put all seven about the size of a nickel. what have yall witnessed true or not. not just hear sea.
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Old September 1, 2012, 10:22 PM   #8
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Nothing in stone that says a low sd or es will result in better groups, but your odds are better since your loads are more consistent.
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Old September 2, 2012, 02:24 AM   #9
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1stmar is right on.

Every time you launch a bullet out of a casing it begins a journey down your barrel. Factors such as how much tension the case exerts on the bullet and how far the bullet jumps to the rifling and how the bullet swages to conform to the rifling affect that launch. How fast the powder burns and the pressure that builds up and then falls as the bullet travels are major factors, too.

Then the barrel flexes or "whips" from the impulse, too.

There is a lot going on.

Google the "Audette ladder test" for just one of the methods of trying to dope out how to get good groups. It seeks to ensure your bullet exits the muzzle when your barrel is at the same (and most stable) point in its whip, thereby sending your bullets on the same flight path.

The "barrel time" of the bullet is critical. Here is one site that discusses the matter in layman's terms and the graphic is most revealing.
http://www.6mmbr.com/laddertest.html
Unfortunately, I don't know how to embed a graphic in my post like hehavey can or I would have done it with the bell curve. Thanks mehavey.

The science you have begun studying is "Internal Ballistics". It is wonderfully complex and can keep your mind occupied for a lifetime.

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Old September 2, 2012, 06:23 AM   #10
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To illustrate some points made here, I was testing 7 mag loads yesterday: Hornady 162 SST and Speer Hot Core 160 over Reloder 22. In both cases, lowest loads showed high ES and SD, decreasing until I got to the max loads when they opened up a bit. As is often the case, loads just below published max were most consistent. But all of the rounds, especially the Speers, grouped very well. It's useful data, and I always work up with a chronograph, but it doesn't tell you everything.
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Old September 2, 2012, 06:41 AM   #11
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Long range shooting it becomes more important, velocity differences will have a larger impact on poi and energy.
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Old September 2, 2012, 08:18 AM   #12
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Nothing is set in stone and experience will back that up. I read through amamnn's fine post (#4 in this thread) and while I can appreciate his experience in this and all of his posts here, I have a difficult time subscribing to it in this case.

I think many folks have found that if you build some new loads and and they report a very WIDE extreme spread, you will typically go looking for a reason why you have that spread. When you have a high ES, it's mathematically impossible to have a low SD unless you simply have erroneous readings with your chrono.

Being that my bread and butter is handgun loading, shooting and chrono'ing, that's where my experience is. In the short time I've been working with a chrono, I find that my largest ES will typically come from a particular bullet more so than a particular powder in any one given chambering. I believe it's mostly due to the amount of bullet pull or case mouth tension I have on those bullets in concert with that particular brass.

I bought a large lot of a particular slug in .358" and though I can get serviceable shooting/plinking from it, I have a difficult time getting consistent chrono results with -ANY- powder when using this bullet. When I switch to a similar weight bullet with a different profile, makeup and including a cannelure, I notice instant improvement in my ES and SD when I chrono the load across all the different powders I use.

When I chrono a load and I get a high or wild ES and a high SD, I don't tend to try REALLY hard to fine tune that load. However, when I get a load that wants to show me a low ES and very low SD, that load gets my interest and I end up chrono'ing it again, and maybe again, to ensure it will consistently report these "good" results.

Indeed, it has been -- or has seem to have been my experience that load ES & SD makes for smaller groups when two different loads are directly compared/contrasted.

However! I must keep in mind that if I'm not chronoing the SAME two loads from the SAME handgun in the SAME day and at very nearly the SAME time, there's really only limited conclusions that I can draw from the experience.

Simply fact is that I can be shooting better on any given day than another and chrono results can be more consistent on a particular day more so than another. Or a dozen other things that may skew my results.

In the perfect world, I'd have a setup where I could bench rest on sand bags in a very controlled environment with consistent sunlight, temp, humidity and heat and get SERIOUS about the "results" from my "experiments." I'm astute enough to know that my results are not hard, strong and extremely well controlled data, it's more of a hobbyists collection of notes and anecdotes.
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Old September 4, 2012, 06:59 PM   #13
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A bunch of us folks were working up a load for one of Sierra's new match bullets soon to be released for retail sales. For our prototype sample bullets used, we tried several powders and charge weights. The one that gave the least spread in muzzle velocity was the most inaccurate of all at 1000 yards. The powder we chose was middle of the road as far as SD and ES for muzzle velocity, but it was by far the most accurate.

The only explanation we could think of was the bullets left the muzzle on its way up from recoil (just before it reached its highest angle) and the faster bullets left sooner than the slower ones. That's called "positive compensation." Faster bullets don't need as much up angle as slower ones to strike the point of aim.
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Old September 4, 2012, 07:15 PM   #14
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Bart B.,

Right on.

That makes sense, but I cannot help but believe that if you achieved the same muzzle velocity (or maybe more critically, the same barrel transit time, or both) with a lower SD (which, I admit, might be impossible) that your groups would shrink.

Your point is well taken (as others have pointed out, too). There is more to small group size than just one or two factors and some factors may work to even each other out as you so succinctly and descriptively point out in your conjecture.

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Old September 4, 2012, 07:41 PM   #15
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All good guys! One other thing. For a meaningful ES/SD the more shots fired the better (alluded to above). From what I understand a minimum of 10 shots is necessary for SD to have any meaning. I like 15 shots myself... and if I like what I see, I'll sometimes shoot another 30 later to see if data stays consistent (again alluded to above).

Here is where I differ from the purists. I mostly chrono handgun loads. That said, when I shot 15 or more shots, it allows me to eye-ball the data I have written down (put into a spreadsheet) and throw out an extreme value. Maybe the neck tension was bad, crimp not the same, or primer burn was different or.... for example if 14 of the shots are within 15fps of the average and one is 60fps away, I'll throw it out as an aberration. Usually really obvious when this happens. Sometimes the chronograph will give a bad value as well (like 1500fps when all are in 900fps range) and I don't even write it down. You know it wasn't 1500fps because the 'kick' was about the same as the last one....
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Old September 5, 2012, 05:38 PM   #16
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To answer the OP's question directly, the standard deviation is a standard measure of deviation. That's all the name means. There is no way to figure out what it is from the name; someone just has to tell you what is, so I will.

Mathematically, the standard deviation started out as a coefficient in the equation that generates the statistician’s bell curve¹ for a normal distribution. It controls both how wide and how low the bell curve shape is, such that the area under the curve always equals one. That area is used to represent one population (100% of a population). In an infinite population with a normal bell curve distribution, the standard deviation turns out to be about 20% smaller than the average deviation and about half again bigger than the median deviation (the 50% population deviation). The reason one of those two more sensible sounding measures of deviation didn't become the standard is just that you have to find the coefficient that we use as the standard deviation to find them. That would complicate many calculations unnecessarily and make their relationships harder to understand. Such additional calculations are made for some statistical purposes, but only when needed.

You can calculate backward from your measured deviations to find the standard deviation of the bell curve they lie under. In a normal distribution the standard deviation turns out also to be equal to the root mean square of all the individual deviations in the population. You subtract the mean (average) value from each individual value to find the individual deviations. You then square each deviation to get rid of all the negative numbers from the minus side deviations (which you need to do because the average of all deviations, with original signs, is just zero). You next average those squares and then take the square root of that average. Voila, you have the standard deviation and can plug it into the statistician's bell curve equation to make your own bell curve.

Why would you want your own bell curve? The bell curve is what is called a frequency distribution. That means its height above any particular deviation value is proportional to how frequently samples of an infinite population with a normal distribution will have that value; that is to say, how often the value occurs in the population. That's how the probability of any particular sample randomly deviating that far from average may be figured out. Fortunately, the properties of bell curves are so well known and so commonly used that you can just use lookup tables and standard solutions with your standard deviation without having to plot an actual bell curve.

A complication is that as standard deviation gets smaller, the bell curve gets narrower and taller, and vice versa. This is necessary to keep the area under the curve at the constant value of one, so that 100% of the population just fills it. So a given frequency value represents a different portion of the population in a curve when the standard deviation is different. To get around that, real deviations are divided by the standard deviation to see how many standard deviations each one is. Once you have scaled your deviations to the standard deviation this way, you have a number that is adjusted for the height and width of your particular bell curve.

Another problem with all the above is that most of us have less than complete populations of data to work with. We don’t usually fire all the rounds we will ever fire of a particular load over the chronograph or into groups, unless it is a bad load that we decide to drop. So, we settle for the fact the number we do fire are just a representative sample taken from the population we will eventually fire. Unfortunately, you can't know exactly how representative they are. This means the standard deviation of the sample and the mean of the sample are not likely to be an exact matches to the standard deviation and mean of the whole population. Therefore, the standard deviation and mean we get from samples are only estimates of these numbers for the population. These estimates have different symbols to indicate they are estimates. The letters SD are commonly used for sample standard deviation, where σ is used for population standard deviation. The symbol ͞x (x with a bar over top if your browser isn't seeing it correctly; not a standard font character, unfortunately) is used for sample mean, where μ is used for population mean.

The estimated standard deviation is calculated slightly differently from the root means square method I described for population before. Instead of simply taking the average of the squares of your deviations in that step of the calculation, you subtract one from the denominator, the number of samples, making the result slightly larger than average. Some think that’s to compensate for error due to samples being small. Actually it’s just part of Fisher’s ANNOVA method and has no real meaning other than it fits into his other calculations better. There is some tendency for small samples to underestimate standard deviations a little, so it can help with that a little, but it’s usually too little when the sample numbers get very small. Indeed, some statisticians say it has no real meaning until you have at least six to eight samples to work with.

Chronographs are useful for several purposes if properly deployed. I’ll just suggest that you need it far enough away that muzzle blast cannot get to the start screen before the bullet has cleared the stop screen behind it. Reports of chronographs started or stopped by blast from guns fired on adjacent firing points are numerous. You really don’t want vibration or light distortion or actual debris messing with its triggering. Get the thing away from your muzzle and others. Cardboard screens like horse blinders can help with adjacent firing points on a busy range, but you’ll need stands for them. I normally don’t even think about less than 15 foot spacing for a rifle, and one board member found 18 feet necessary to get his .338 Lapua Mag to stop false triggering the thing. The military 78 foot standard (26 yards) isn’t a bad one to use. I’ve shot through chronographs 100 yards away to get ballistic coefficients. Just set the rifle up on bags so the sights stay on target and put a good laser bore sighter in it. You can then set the chronograph up at any distance by adjusting its tripod so the laser spot illuminates the center of a piece of paper or the palm of your hand held in the center of each screen. You may need a spotting scope or binoculars to read it, but it will be clear of muzzle blast.

One use chronographs have is to compare average velocity for two lots of the same powder in a known good load. You can adjust for the new powder that way. Also, when you have a good shooting load and you change something about it, say, how hard you seat your primers, and you observe a drop in SD and ES, then you know you’ve taken a proven load and improved its consistency. I will mention that I’ve calculated several times that common standard deviations encountered in rifles at 100 yards account for drop differences of only a fraction of an inch, so most shooters have other group contribution problems that are greater. But at long range that won’t be true unless you happen to have the right amount of the positive compensation Bart described. If a gun with very rigid barrel is in a rigid machine rest, a velocity spread that creates only an eighth of an inch of vertical stringing at 100 yards may create two feet of stringing at 1000 yards, depending on the bullet and velocity. Unfortunately, knowing whether that will happen in your actual rifle or if you’ll get enough compensation is something you just have to try.

There is also a distinction to be made between a load that produces the most consistent muzzle velocity and a load that produces the most consistent lock time + barrel time combination. Marginal primer function can create short delays in the burn getting established, but without affecting actual ballistic efficiency much. Those delays would have the same effect that irregular lock time would, putting a greater burden on the shooter’s follow-through being perfect. They also allow more time for the striker mechanism’s vibration, trigger overtravel slap, or other mechanical vibration to disturb the muzzle. Conversely, you could have a powder that lights so fast and easily that that it reduces such errors more than it adds to velocity error. I believe (unproven) I’ve experienced this with IMR 4198 in the .222 Remington.

Nick


¹ The bell curve has a very general form, y = A exp(-(x-B)²/2C²) which allows bell curves centered at C and defining any size area to be created. Statistics replaces the symbol B with the symbol σ (sigma, for standard deviation) and C with the symbol μ (mu; for mean) and A with 1/(σ(√2π)). That last replacement keeps the area under the curve equal to one.
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