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Thread: Vertical POI testing

  1. #1
    Join Date
    Jul 2015
    Posts
    51

    Vertical POI testing

    This weekend had a calm morning (0-3mph breeze) to do some testing at my home range. I shoot from a bench in the garage to a pellet trap on the driveway, 28 yd, with about the first 1/3 indoors.

    For these tests I used my RAW BM500 with poly barrel, Randolph front rest/rear bag, shooting JSB 13.4gr Monsters at HV power level. The barrel was cleaned as it is for matches (1 wet / 2 dry patches), with 5 "throw away" shots to stabilize before firing test shots. Each run consisted of 20 test shots over a chronometer, aiming at points on a graph paper target (see image). Each group of 20 consisted of 10 shots from left to right and 10 (above the first row) from right to left. There was no attempt to hold off for breezes that occurred, and I used a flag to indicate when wind was calm enough to shoot.

    The tests were meant to check the effect of velocity (FPS) on vertical POI, and also the effects of pellet sorting (two batches of Monsters were sorted by a friend: weighed and air-gauged, the same as he uses in matches).

    The bottom two 20-shot strings were shot with Monsters out of the can, from a lot which shoots well in my gun. The top two 20-shot strings were shot with my friend's sorted pellets.

    After shooting, I used a magnifier to estimate the vertical POI distance from the horizontal POA line (X-axis). The small increments on the graph paper were 1mm, and I was able to estimate down to 0.5mm. These up (+) and down (-) POI-POA measurements were paired with the respective shot velocity from the chronometer. These measurements were then analyzed with statistics.

    Here are the means (average FPS), standard error, and standard deviation (variance) of the four 20 shot groups (st1,2 out of the can, st3,4 sorted):

    Descriptive Statistics: st1, st2, st3, st4

    Variable N N* Mean SE Mean StDev
    st1 20 0 783.85 0.805 3.60
    st2 20 0 784.20 0.863 3.86
    st3 20 0 783.90 0.732 3.28
    st4 20 0 787.60 0.407 1.82

    >>st4, one of the sorted group, had higher velocity and lower variance in velocity than the other three - which were about the same.

    Here is the same analysis for vertical POI-POA distance:

    Descriptive Statistics: POI1, POI2, POI3, POI4

    Variable N N* Mean SE Mean StDev
    POI1 20 0 -0.350 0.264 1.182
    POI2 20 0 0.900 0.282 1.263
    POI3 20 0 -0.125 0.294 1.317
    POI4 20 0 0.500 0.281 1.257

    >Note that on average POI2 shot highest (0.9mm above x-axis), even though POI4 shot fastest (about 4FPS faster). Also note that even though st4 had the lowest standard deviation of FPS, it's POI standard deviation was not the lowest.

    Next I pooled data from the four strings, and looked at only POIs that were either above or below the x-axis (disregarding those that hit vertically dead-on, at zero). Here is a comparison of the mean FPS for the Up POI vs Down POI:

    Two-sample T for up FPS vs dn FPS

    N Mean StDev SE Mean
    up FPS 36 785.67 3.58 0.60
    dn FPS 26 784.69 3.38 0.66

    >>As expected, for all shots velocity was higher if POI was above the line than below the line - though different only by 1FPS.

    Here is another statistical test (ANOVA) comparing POI for the four 20-shot groups:

    One-way ANOVA: st1, st2, st3, st4

    Source DF SS MS F P
    Factor 3 197.6 65.9 6.29 0.001
    Error 76 796.4 10.5
    Total 79 994.0

    S = 3.237 R-Sq = 19.88% R-Sq(adj) = 16.72%


    Individual 95% CIs For Mean Based on
    Pooled StDev
    Level N Mean StDev --------+---------+---------+---------+-
    st1 20 783.85 3.60 (------*------)
    st2 20 784.20 3.86 (------*------)
    st3 20 783.90 3.28 (-------*------)
    st4 20 787.60 1.82 (------*------)
    --------+---------+---------+---------+-

    >>Again we see the first 3 groups are almost identical (in mean velocity and variance of velocity), but one of the sorted groups st4 had higher velocity and less variance. You might think this would translate into smaller POA-POI. So to test this I compared the absolute value of POI-POA to see which, if any, group did best:

    One-way ANOVA: |PO1|, |PO2|, |PO3|, |PO4|

    Source DF SS MS F P
    Factor 3 2.284 0.761 0.99 0.402
    Error 76 58.438 0.769
    Total 79 60.722

    S = 0.8769 R-Sq = 3.76% R-Sq(adj) = 0.00%


    Individual 95% CIs For Mean Based on
    Pooled StDev
    Level N Mean StDev -------+---------+---------+---------+--
    |PO1| 20 0.8500 0.8751 (----------*----------)
    |PO2| 20 1.3000 0.8176 (----------*----------)
    |PO3| 20 0.9750 0.8656 (----------*----------)
    |PO4| 20 0.9500 0.9445 (----------*----------)
    -------+---------+---------+---------+--
    0.70 1.05 1.40 1.75

    >>The best group was the first one shot (from the can), with mean |POI-POA| of 0.85mm. The most consistent velocity sorted group (PO4) was second best. PO2 - which had a 3.5mm "flyer", shot worst.

    Since score is based more on big misses than small, for I compared the absolute POI-POA of the worst 3 misses for each group:

    |PO1||PO2| |PO3||PO4|
    1.5 2.5 3 3
    2.5 3.5 2.5 2.5
    1.5 1.5 1.5 2.5

    5.5 7.5 7 8 (sum)

    Interestingly the sorted pellets (POI3 and 4) had the most mms of vertical miss, and the tightest velocity group PO4 had the most mm of all.

    //////

    These tests suggest that pellet sorting has less effect on vertical POI than other factors (barrel, breeze, etc). They also show very little correlation between vertical POI and FPS velocity. So within limits, ultra-low ES may not contribute to accuracy.

    Kim

    Edit: I forgot to mention that st4 had the lowest ES = 8. The others were in 12-16 range
    Attached Thumbnails Attached Thumbnails Click image for larger version. 

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    Last edited by KimZ; 04-17-2017 at 11:11 AM.

  2. #2
    Join Date
    Apr 2016
    Posts
    7

    Wow

    Very thorough Kim. I will digest all of this information. I probably won't do such fine tooth comb test, but I want to test sorted vs. unsorted pellets in a couple of ways... just to see!!

  3. #3
    Join Date
    Nov 2006
    Location
    Augusta, Maine & Palm Coast, Fl
    Posts
    5,427

    This is the method I went to

    for testing .22 Rimfire ammo. I found that if I can find lots that show very little vertical dispersion, the lot will be as good as I can do. It's the short way to testing, I have found.

    Having said that, I think a great barrel eliminates a lot of problems with everything. Wish there were more of them.

    Pete

  4. #4
    Join Date
    Dec 2015
    Posts
    8
    Hi Kim,
    Unfortunately, a group of 20 probably isn't large enough to calculate results with high enough statistical significance. I'd be curious to see your individual measurements.
    Thanks for sharing.
    Albert

  5. #5
    Join Date
    Jul 2015
    Posts
    51

    stats

    Hi Albert

    I have the numbers at home and can post them later. But if you look at how close the means are, it is doubtful one would find significance even with n=100.

    That said a better experiment would be to repeat this in an indoor range - fully enclosed, draftless, etc.

    kim

  6. #6
    Join Date
    Dec 2015
    Posts
    8
    Hi Kim,
    When shooting high quality (Eley Tenex) rimfire ammo off a stable fixture in a well-controlled indoor facility, velocity dispersion contributes very little to impact distributions. One is lucky to see any correlation with fewer than 100 rounds. Often many hundreds are necessary. (For example, take a look at Post #121 in the following thread: http://www.rimfireaccuracy.com/Forum...bilities/page7).
    I suspect that you are correct. Determining the dominant factors that influence pellet impact distributions requires shooting off a stable rest indoors. I would guess that velocity contributions are small in top quality rifles shooting good pellets. However, I haven't seen enough data to draw any conclusions.
    Thanks.
    Albert

    Quote Originally Posted by KimZ View Post
    Hi Albert

    I have the numbers at home and can post them later. But if you look at how close the means are, it is doubtful one would find significance even with n=100.

    That said a better experiment would be to repeat this in an indoor range - fully enclosed, draftless, etc.

    kim

  7. #7
    Join Date
    Jul 2015
    Posts
    51

    Here are data for the four shot strings

    FPS mm+/-

    st1 POI1
    787 -1.5
    788 -1.0
    786 -1.5
    784 -2.0
    788 0.0
    783 2.0
    782 0.0
    782 -0.5
    784 -0.5
    777 -2.0
    784 -0.5
    780 0.0
    777 0.0
    782 0.0
    783 0.0
    781 -2.5
    789 0.5
    784 0.0
    790 2.0
    786 0.5

    st2 POI2
    784 -1.5
    787 1.5
    785 1.5
    786 -0.5
    786 1.5
    784 0.5
    783 1.5
    782 -1.0
    781 2.0
    776 2.0
    782 1.5
    782 3.5
    781 -1.0
    779 1.0
    783 0.0
    784 0.5
    790 2.5
    787 0.5
    790 0.5
    792 1.5

    st3 POI3
    790 -1.0
    786 0.5
    786 3.0
    782 0.0
    778 0.0
    781 -1.0
    782 -1.0
    782 -1.0
    786 0.5
    790 -1.0
    787 1.0
    785 -2.5
    782 0.0
    779 1.0
    782 0.0
    781 0.5
    784 2.0
    783 -2.0
    785 0.0
    787 -1.5

    st4 POI4
    782 -2.0
    788 0.5
    785 0.0
    787 -0.5
    787 0.0
    788 0.5
    786 1.0
    789 2.0
    787 0.5
    790 -1.0
    789 3.0
    788 0.0
    789 -0.5
    788 -0.5
    789 1.0
    790 0.0
    788 1.0
    787 0.0
    787 2.5
    788 2.5

  8. #8
    Join Date
    Jul 2015
    Posts
    51

    fig 62

    Albert I can't log in to that site. But looking at the regression graph for the first figure, vertical POI appears to be highly correlated with velocity. If you have the data I can run the stats. The degree that the points conform to the line - not the slope - is the indication of significant correlation (regression coefficient, R-squared).

    I've run many regressions on real life data, and most do not look as well correlated. A good example is weight vs height for a large population of people.

    Kim

  9. #9
    Join Date
    Dec 2015
    Posts
    8
    Hi Kim,
    Actually, the vertical impacts of the rimfire ammo are only weakly correlated to velocity. The correlation coefficient is 0.57. Most of the dispersion must be due to other factors.

    Also, thanks for posting the raw data. Correlation coefficients for the four sets range from about zero to 0.3 - essentially no correlation. I expect the horizontal and vertical dispersions are similar, also an indication that velocity plays little or no role in this data. I quickly can analyze your impacts with OnTarget software. It is a little tough using the figure you posted. A scanned copy might work well.
    Albert

    Quote Originally Posted by KimZ View Post
    Albert I can't log in to that site. But looking at the regression graph for the first figure, vertical POI appears to be highly correlated with velocity. If you have the data I can run the stats. The degree that the points conform to the line - not the slope - is the indication of significant correlation (regression coefficient, R-squared).

    I've run many regressions on real life data, and most do not look as well correlated. A good example is weight vs height for a large population of people.

    Kim

  10. #10
    Join Date
    Jul 2015
    Posts
    51

    R-squared

    Yes. I think both our studies suggest there are other factors that could explain variance in vertical POI, in addition to velocity. And these factors could be randomly distributed, such as manufacturing tolerances of ammo.

    For those less familiar with stats, R-squared (the square of correlation coefficient) is a good measure of how much variance in one variable (say POI) is explained by another (say velocity). The assumption - and fact of natural processes - is that variables are not perfectly correlated (corr coefficient = 1.0 RSQ =1.0). RSQ of 0.33 (0.57^2) says that one third of the variance in RF POI was explained by velocity...and 2/3 by other factors.

    Here is a good tutorial on RSQ:

    http://blog.minitab.com/blog/adventu...oodness-of-fit

    Albert if you PM me your email I can try to scan and send you the test target for analysis.

    Kim

  11. #11
    Join Date
    Dec 2015
    Posts
    8

    OnTarget TDS analysis

    Hi Kim,
    Here are the analyses of the four data sets. Order is the same as they appear on your target. Unfortunately, I don't know how to post a higher resolution image. The originals look better.
    Gotta run. I'll add some comments later.
    Albert
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