Standard Deviation and Spread Question

[TC]

Agree. Not right. Defective NP or piston seal or breech seal... 900+ FPS is within reach of this rifle with 7.9 gr. I would not worry about the SD results, you have a bigger issue.

[MicErs]

Seeing some examples here where an extreme spread of around 20fps is deemed to be reasonable, that would amount to only 2.5% for a rifle shooting a 14.3gr Crosman pellet at 800fps. 

At 50 yards, that would amount to a difference in elevation of 0.07".  Best wishes on shooting a springer well enough to detect that 1/16 of an inch.

A true measured extreme spread of 20 ft/sec would equate to an SD of about (20/2)/3 = 3.3 ft/sec.  That would also suggest a large sample size, say 30 shots.  If you had that many shots in your sample THEN you could make assumptions about the SD for the sample.

If the extreme spread is 20 ft/sec then the highest value observed is around ten ft/sec above the mean and the lowest value observed is around ten ft/sec below the mean.  Since we know that 99.7% of observed values will fall in the range +/- 3 sigmas, we also know that 10 ft/sec is approximately 3 sigmas in THIS example.  That is how we come to estimate one sigma at 3.3 ft/sec.  Three ft/sec is about 0.4% of the muzzle velocity in your example and not 2.5% as you suggest.  0.4% deviation from the mean would be an excellent showing for the rifle AND the pellet.

Now then Chairgun (I am a lazy fellow) says that an extreme spread of 20 ft/sec for the pellet you mention at a muzzle velocity of 800 ft/sec will equate to a vertical string of about 0.33 inches (+/- .16 inches) at 50 yards.  That is still a deviation which would be minuscule relative to other factors when shooting at that range.   As an aside, at 50 yards with a m.v. of 800 ft/sec the an extreme spread of 60 ft/sec only represents a vertical spread of 1 inch using the pellet we have been using in our model.

BUT that is not the question the OP asked.  He did not ask what was a good SD for accuracy.  He asked what SD would show him his gun was operating properly.  I explained that SD describes the entire system he is testing, not just the gun.

[MicErs]

Then check out the .177...

Code: [Select]

Shot End Shot Start Time Velocity
31.43764 31.434625 0.003015 995.024875622627
55.650135 55.64712 0.003015 995.024875622627
18.77503 18.771905 0.003125 959.999999999782
45.60621 45.60313 0.00308 974.025974026896
11.929085 11.92586 0.003225 930.232558139397
40.56219 40.559035 0.003155 950.871632329764
2.207145 2.20409 0.003055 981.996726677497
34.485475 34.482435 0.00304 986.842105263613
58.798399 58.79499 0.003409 880.023467291201
18.868185 18.864975 0.00321 934.579439252549
Average Standard Deviation
958.862165422595 36.291257105228

Since mine is a mutli-caliber platform it's easy for me to conclude the .177 pellets are not as consistent as the .22.  Also pretty easy to tell this by how random the fit int he barrel for the .177 is.

But what about the three data sets for the .22?  On the first two the stdev remains about the same, but the average velocities are pretty different.  Third one the average velocity is closer to the second, but then the SD goes way up.

Exactly!

You have a power plant that produces reasonable results in one caliber but not in the other caliber.  This is the same gun with different barrels, right?  What does that tell you?  What changed?  The pellet changed.  Get better .177 pellets and try again.

[SagaciousKJB]

Then check out the .177...

Code: [Select]

Shot End Shot Start Time Velocity
31.43764 31.434625 0.003015 995.024875622627
55.650135 55.64712 0.003015 995.024875622627
18.77503 18.771905 0.003125 959.999999999782
45.60621 45.60313 0.00308 974.025974026896
11.929085 11.92586 0.003225 930.232558139397
40.56219 40.559035 0.003155 950.871632329764
2.207145 2.20409 0.003055 981.996726677497
34.485475 34.482435 0.00304 986.842105263613
58.798399 58.79499 0.003409 880.023467291201
18.868185 18.864975 0.00321 934.579439252549
Average Standard Deviation
958.862165422595 36.291257105228

Since mine is a mutli-caliber platform it's easy for me to conclude the .177 pellets are not as consistent as the .22.  Also pretty easy to tell this by how random the fit int he barrel for the .177 is.

But what about the three data sets for the .22?  On the first two the stdev remains about the same, but the average velocities are pretty different.  Third one the average velocity is closer to the second, but then the SD goes way up.

Exactly!

You have a power plant that produces reasonable results in one caliber but not in the other caliber.  This is the same gun with different barrels, right?  What does that tell you?  What changed?  The pellet changed.  Get better .177 pellets and try again.

And the quest continues lol

The bummer part is that they're the same model pellets. Crosman Pointed, but in two different calibers.  I'm guessing since the .177 sells more, they make more, and the molds are more worn out.  The finger can also tell a lot of this by the extreme differences in resistance to pushing the .177s into the barrel--if I were to sort them out by size I bet I could get better results, because the main difference with the .22s is they were never too loose fitting.  Some of the .177s the head would either be really tight, or the skirts would just barely be the only thing keeping the pellet in, so it's kind of easy to see how it would cause significant changes in velocity if for example the skirt took longer to spread out and grip the rifling on shot one than it did on shot two or three.

The interesting thing is I saw a member here post up a spreadsheet in regards to different pellet selection where he used the standard deviation figure when comparing head sizes.  I wonder how well that works or picking a reliable and performing pellet and then being able to eliminate that as a factor--gonna figure out next time and do some selecting based off that list.  Lucky for me he even tested some of them with an RS2 which is pretty similar to the Kodiak.

As for the OP's concern if I was only seeing 700-800 FPS out of that rifle I'd definitely send it in for warranty.  On my dual-caliber Kodiak I push out 14.3 grain pellets at about 720 fps and the 7.4s at about 960.  So with the increased weight of the .22 and the same spring and everything the feet per second drop down to by about the same difference in velocity as your seeing.  That's too low for sure--I don't think it would be a pellet fit issue unless they were practically falling out of the barrel or had to be hammered in.

[nervoustrigger]

MicErs, please note I was commenting only on extreme spread, not standard deviation.  As such, the 2.5% is correct in terms of a 20fps spread for a MV of 800fps.

To the OP, many consider a 4% ES to be good for shooting up to 50 yards, and 2% for 100 yards.  This point, though, seems to be peripheral to an apparent sub-par velocity based on what others are saying.

[QVTom]

Yes ES and FPS are the only numbers that matter when determining the health of a springer.  The 10 I was referring to was ES based on the OP's mid-range springer call it ~1.5%.  SD is not very helpful unless it a very low value.  Never heard of the "rule of 10".

Tom

[Scotchmo]

Yes ES and FPS are the only numbers that matter when determining the health of a springer.  The 10 I was referring to was ES based on the OP's mid-range springer call it ~1.5%.  SD is not very helpful unless it a very low value.  Never heard of the "rule of 10".

Tom

If you know the SD, you can calculate the likely ES. If you know the ES over a particular number of shots, you can calculate the likely SD.

I don't really know about the "rule of 10" but I remember the three-sigma rule - 68%-95%-99.7%.

5 or 10 shots can give you a crude idea of SD or ES, but 20, 50, or 100 are even better.

When I miss one out of 100 targets that I know should have been easy, I don't sweat it too much. The odds (>3 sigma) just caught up with me. It happens even if I do everything else perfectly.

[QVTom]

Correct me if I'm wrong..... SD can't tell you if you had one large deviations or a series of moderate ones without the underlying data.  I should have stated  shot to shot deviation not ES.  May bad.

Tom

[Scotchmo]

Correct me if I'm wrong..... SD can't tell you if you had one large deviations or a series of moderate ones without the underlying data.  I should have stated  shot to shot deviation not ES.  May bad.

Tom

You are not wrong. SD does not tell you if you had one shot with large deviation in your last string of shots. SD is a measure of variability. SD allows me to predict the probability of having a large deviation in a future string of shots. That's important to me when preparing equipment for a match or shoot.

[MicErs]

MicErs, please note I was commenting only on extreme spread, not standard deviation.  As such, the 2.5% is correct in terms of a 20fps spread for a MV of 800fps.

To the OP, many consider a 4% ES to be good for shooting up to 50 yards, and 2% for 100 yards.  This point, though, seems to be peripheral to an apparent sub-par velocity based on what others are saying.

I am sorry.  I misunderstood your post.  The numbers you quote for ES seem reasonable to me.  I've never thought about it in those terms.

[rwt]

My original purpose for starting the thread was to find out if we can use chrony data to determine the "health" of a springer/nitro-piston airgun.  Specifically, the measurements in question are Average Velocity, Standard Deviation, and Extreme Spread.  I've been testing (7) different pellets from (4) different companies, including (6) different weights.

I already stated that the average velocity was ~150 FPS slow.  Standard deviation originally ranged from 10.5 to 22.38.  Extreme spread originally was from 34.8 FPS to 57.4 FPS.  I contacted Crosman and they suggested getting some RMC Oil and putting a couple of drops in the chamber and lubing the breech seal.  Having done that and shot pellets until velocities stabilized again, I have a new set of data.

The average velocities improved significantly, but are still ~70 FPS slow.  Standard deviation ranges from 6.21 to 9.77.  Extreme spread now ranges from 18.4 (2.1%) to 37.1 (4.4%).  After examining the breech seal, it appears to be worn a bit.  Also, accuracy at 20 yards when measured from edge to edge ranges from ~3" to ~8".  IMO, accuracy is terrible!

I understand that these measurements only tell me how well a particular pellet is working in my rifle.  I'm thinking with 7 pellets being tested, if the measurements are poor with all of them, I can assume that the issue is with the rifle.  By trying the RMC oil I've concluded that Crosman's recommendation of lubricating every 200 shots could have a significant impact on how well any gun of this type performs.

I've now put close to 400 pellets through this rifle.  How long do we keep shooting hoping for accuracy to improve?

[MicErs]

A best of three inches at 20 yards is unacceptable in a any gun old or new.  There is something else wrong here.  What sighting system are you using?

You are getting consistent pellet velocities so the power plant is not the problem.  Well, if it is a problem it is not likely the problem with accuracy. , just power. Accuracy happens because things are consistent.  Since your velocities are consistent your accuracy problem is not related to the power plant of your gun.  JMHO.

[nced]

When dealing with springers and nitro pistons, I'm curious as to what SD is considered good or indicative of a healthy gun?  Also, I've heard some say the spread is a better indicator of gun health.  If that's true, what percentage of avg. velocity would be considered healthy for spread?  What are the key indicators that show that a gun needs a rebuild or seals, etc.?  Yes, I've searched the forum and found bits and pieces of information, but nothing that addresses what I'm asking concisely and directly.

Another observation that I find curious is that the pellet that my RWS 52 shoots most accurately doesn't have the lowest SD or spread of all pellets tested.  It's sort of in the middle of the pack. 

Presently, I'm evaluating a Crosman Vantage NP refurb that I received.  After roughly 300 pellets, it's shooting 125 - 150 FPS slow no matter what pellet is selected, the SD ranges from 10 - 22, and the spread is 5 - 7 percent of average FPS.  SD on my RWS 52 ranges from 3 -8.  With 30 days to evaluate if the Vantage is really in refurbished condition, any assistance would be helpful.  I have no desire to rebuild a gun that is supposed to be factory refurbished.  If it needs that kind of work, they can have it back.

For my .177 R9 piston gun I strive for a single digit spread (less than 10fps).

I do know of a few PCP shooters that have no issues with a 30fps spread out to 50 yards when shooting from a full pressure air reservoir till they need to refill to full pressure.

I don't know why the difference between the recoiling piston gun vs the PCP but I do know that even a 20fps variation with my R9 will affect the poi at 50 yards!

[rwt]

Just a quick update.  I contacted Crosman and we've agreed that this rifle needs to go back.  When I get it back (or a replacement) I'll start this process all over again.  I've learned a bit through this process and appreciate all the comments.  Hopefully, if others have the same questions I've posed here, they'll find this thread in a search and it can help them too.

[grauhanen]

For purposes of accuracy within typical air rifle ranges with spring piston rifles, an ES (extreme spread) of no more than 4% is desirable.  For a gun shooting at 500 fps that means, of course, the ES would preferably be less than 20 fps.  Standard deviation cannot be reliably predicted based on ES.  In other words, two rifles shooting with the same ES of 20 fps will not necessarily have the same SD.  For example, one rifle may shoot a 15 shot string with the majority of  shots at the extreme ends of the 20 fps spread, while another has only two shots of the 15 shot string having a 20 fps spread and the majority of shots close to the middle.  The first rifle will have a larger SD; the second will have a much smaller one.  Standard deviation will vary by type of pellet used in the same gun.  A standard deviation of less than 2 fps is very good.  If it is less than 5 fps it's not bad.