PRACTICAL EXPLANATION OF THE EFFECT OF VELOCITY VARIATION IN SHAPED PROJECTILE PAINTBALL MARKERS. Document Authors David Cady & David Williams

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1 PRACTICAL EXPLANATION OF THE EFFECT OF VELOCITY VARIATION IN SHAPED PROJECTILE PAINTBALL MARKERS Document Authors David Cady & David Williams Marker Evaluations Lou Arthur, Matt Sauvageau, Chris Fisher & David Williams August 14, 2017

2 TABLE OF CONTENTS: ABSTRACT... 3 INTRODUCTION... 3 Figure 1: Example Statistical Summary Report... 4 Shifting the : Example Statistical Summary Report... 5 Table 1: Measured vs Adjusted Values... 5 Figure 2: Graphical Summary of Measured vs Adjusted Values... 6 Figure 3: Measured and Shifted Values... 6 OBJECTIVE... 7 EQUIPMENT... 7 PROCEDURE... 7 CALCULATING VERTICAL SHOT OFFSET... 8 Figure 4: Derived Non-linear 100 Yard Impact Equation... 8 Table 2: Example Muzzle Velocities and Calculated Vertical Impact Points... 9 Figure 5: Graphical Statistical Summary of Vertical Shot Offset for SAR12 BA RESULTS/ DATA Figure 6: Graphical Probability for Individual Markers Tested Figure 7: SAR12 SASS G2 Shot Number vs Muzzle Figure 8: MCS/RAP4 DMR Shot Number vs Muzzle Figure 9: SAR12 SASS G2 Graphical Summary Figure 10: MCS/RAP4 DMR Graphical Summary Figure 11: SAR12 SASS G2 Theoretical Impact 100 yards Figure 12: MCS/RAP4 DMR Theoretical Impact 100 Yards Figure 13: Theoretical Impact 100 Yards, All Markers Tested MUZZLE VELOCITY FPS VARIATION PROBABILITY Table 3: Individual Marker probability of Muzzle and Vertical Spread CONCLUSION(S) APPENDIX Figure A-1: FS Weight Distribution Per Case Figure A-2: CCM SR1-HPA/ Weight Matched FSR Figure A-3: CCM SR1-HPA/ Comparison of Weighed FSR Figure A-4/ A-13: Individual Tested Marker Shot Strings Figure A-14/ A-23: Graphical Summary of Individual Markers Figure A-24/ A-33: Individual Marker Theoretical Impact 100 Yards PAGE 2

3 ABSTRACT: In 2009, the game of paintball got a huge technological improvement when shaped paintball projectiles were introduced to the market. Since then, companies have been developing marker platforms that operate and function reliably when using these shaped projectiles. For the most part, almost all these companies have been focusing on modifying existing equipment to reliably feed and fire the rounds. But, what was the effect of these modifications on the performance of those paintball markers? Since the inception of paintball, and leading up to the release of First Strike rounds, the main indicators of paintball marker performance were reliable feeding of round balls, velocity consistency, and air efficiency. Due to the inherent physical limitations of round smooth projectiles, often coupled with manufacturing or packaging imperfections, shot velocity was somewhat irrelevant at variations tighter than +/-5 fps because the markers were designed to shoot many rounds sequentially. With the introduction of shaped projectiles, a new type of play style became more practical the long range sniper role. Using these markers that are designed to fire the shaped projectiles, players can now effectively hit targets previously unreachable. Shot accuracy and repeatability have become much more important. Players are using scopes and they want to know that their round will hit close to where they are aiming. When in this situation, should players be concerned with shot to shot velocity variation? This paper attempts to answer the question: Does shot to shot velocity variation really matter? INTRODUCTION: Initially the purpose of this project was to evaluate the performance of the SAR12 second generation semi auto engine against the known performance of the bolt action engine. Within the group of Carmatech Beta Testers, we wanted to validate, or invalidate the design of the semi auto. In the early stages of this testing, our focus was on continuous improvement on tighter fps swings. Once the testing was completed and results of the semi auto engine were analyzed, curiosity set in as paintball players. We wanted to see what different platforms provided in terms of shot to shot velocity variation. To players, these tests can be valuable, regardless if they are just entering the market, or are already participating in magfed. In the science of statistics, in order to produce accurate normal distribution curves, which can predict future performance of that particular setup, we must use a sample size of 30 units or more. Using fewer units will more than likely tighten up the standard deviation (+/- fps in this case); however, it cannot be assumed to represent the total population. For example, let s look at a three shot string PAGE 3

4 From this given information we can calculate the average to be 280 fps. It would be common of players to say "This marker is performing at +/-1 fps This very small data set limits our "view" of that markers true capability. If we continued on with additional data points, the spread would widen. For example Summary Report for 10 shot string Anderson-Darling Normality Test A-Squared 0.28 P-Value StDev 2.26 Variance 5.12 Skewness Kurtosis N Minimum st Quartile Median rd Quartile Maximum % Confidence Interval for % Confidence Interval for Median % Confidence Interval for StDev % Confidence Intervals Median Figure 1: Summary Report of Above Population Notice how the first three shots that we believed to yield +/-1 fps results, no longer gives us that variation. With 10 shots, our standard deviation is now fps. In statistics, the minimum number of samples needed to ensure the data are normally distributed is 30. Normally distributed data makes analysis much easier and allows us to make assumptions about the population. Because of this, our study used a minimum of 30 samples yielded from each marker. PAGE 4

5 SHIFTING THE MEAN Another operation that was performed on each data set was to shift the mean of the data to 280 so that each shot graph would line up to the same point on the x-y axis. This was accomplished quite simply by the following method: 1. Determine the mean of the 30 measured velocity values. 2. Determine the difference between this mean and Add this difference to each measured value. 4. The result has no effect on the statistics or for determining standard deviation as shown in the following example. Shot Number Measured Difference from 280 Shifted velocity Table 1 Measured vs adjusted values for the SAR12 Bolt Action PAGE 5

6 Summary Report for Measured Vel. - SAR12 Bolt act Anderson-Darling Normality Test A-Squared 0.50 P-Value Summary Report for Shifted - SAR12 Bolt A Anderson-Darling Normality Test A-Squared 0.50 P-Value StDev 1.36 Variance 1.84 Skewness Kurtosis N StDev 1.36 Variance 1.84 Skewness Kurtosis N 30 Minimum st Quartile Median rd Quartile Maximum Minimum st Quartile Median rd Quartile Maximum % Confidence Interval for 95% Confidence Interval for % Confidence Interval for Median % Confidence Interval for Median % Confidence Interval for StDev 95% Confidence Interval for StDev % Confidence Intervals 95% Confidence Intervals Median Median Figure 2 Graphical summary of measured and shifted mean values for velocity SAR12 Bolt Action Boxplot showing no affect of shifting mean SAR 12 Bolt Action Data Measured Vel. - SAR12 Bolt act Shifted - SAR12 Bolt A Figure 3 Measured and shifted mean values for velocity SAR12 Bolt Action PAGE 6

7 OBJECTIVE(S): The objectives of these tests are to: 1. Measure and document a 30 shot sample set per marker. 2. Using Minitab, calculate statistical information about each shot string, including standard deviation, mean, and whether the data are normal 3. Graph each sample sets velocity per shot 4. Graph the distribution, 5. Calculate the vertical shot offset of each shot at 100 yards and graph them 6. Note: These graphs will represent the best or ideal case scenario. This assumes that all other variables are ignored, such as wind, temperature, humidity, projectile weight / dimension differences, projectile imperfections, barrel to projectile match, barrel length, barrel characteristics. EQUIPMENT: 1. Xcortech 3200X optical chronograph (>99% accuracy) 2. Xcortech 3500X optical chronograph (>99% accuracy) 3. Shooting Chrony Beta optical chronograph (> 99% accuracy) 4. Hawke Chairgun Pro software 5. Minitab statistical software 6. MS Excel software 7. Carmatech SAR12C G2 Semi Auto rifle - Stock 8. Carmatech SAR12C Bolt action rifle - Stock 9. Dye Dam Semi Auto Rifle Lapco barrel 10. Maxtact TGR R1 Semi Auto Rifle - Stock 11. Milsig M17 (Semi Auto Config) Rifle - Stock 12. CCM SSR Bolt Action Rifle, Lapco rifled barrel 13. First Strike T15 - Stock 14. Hammer 7 - Stock 15. MCS/RAP4 DMR SP Barrel 16. Ninja 800 psi output 13/3000 air system 17. Ninja 500 psi output 13/3000 air system 18. First Strike rounds, right out of the box. PROCEDURE: The procedure was rather simple and repetitive across all markers being tested. 1. Setup the chronograph 2. Air up the marker 3. Shoot through the sensors on the optical chronograph 4. Make needed adjustment to marker to get fps close to Once adjusted, take another shot 6. Document velocity as displayed 7. Repeat, being cautious about repeating time interval between shots 8. Marker evaluation completed after 30 consecutive shots PAGE 7

8 9. Repeat steps two through eight with next marker 10. Calculate the mean of the shot string and shift to 280fps 11. Calculate the vertical shot offset from zero 12. Calculate the probability of velocity ranges for each marker 13. Derive the formula for vertical shot offset for each marker s data set to calculate the vertical offset at any velocity 14. Graph the vertical shot offset for each marker for each velocity range CALCULATING VERTICAL SHOT OFFSET FROM ZERO: In order to calculate the vertical impact point of a shaped projectile at a given velocity, ballistics software Hawke Chairgun Pro was used. First strikes have a known ballistics coefficient that was calculated from experimental data during the impact testing for the ASTM subcommittee. Go here to view the report: Velocities (from 200fps to 350fps) were plugged into the software, along with the ballistics coefficient, and the calculated points of impact were recorded. The resulting scatterplot yielded a 3 rd order quadratic curve, meaning the data relationships are nonlinear. We can then use nonlinear regression, with the velocity and impact points (all other variables ignored) to derive a formula for impact point distance from horizontal at a given velocity. Fitted Line Plot Point of 100y = (FPS) (FPS)^ (FPS)^3 Point of 100y Regression 95% CI 95% PI S R-Sq 100.0% R-Sq(adj) 100.0% (FPS) PAGE 8

9 Figure 4: Derived Non-Linear 100 Yard Impact Equation Now that we have the equation for Vertical shot offset from zero at any given velocity, we can calculate the vertical shot offset variation for each 30 velocity shot string for each marker. For example, following are the SAR12 bolt action velocity data and the calculated vertical impact point variation: SHOT VELOCITY DROP FROM THEORETICAL DEVIATION BARREL AT 280 FPS FROM YRDS CENTER (INCHES) Shot # (FPS) (INCHES) (INCHES) Table 2: Example Muzzle Velocities and Calculated Vertical Impact Points PAGE 9

10 Summary Report for SAR Bolt Action Vertical Offset Anderson-Darling Normality Test A-Squared 0.50 P-Value StDev Variance Skewness Kurtosis N Minimum st Quartile Median rd Quartile Maximum % Confidence Interval for % Confidence Interval for Median % Confidence Interval for StDev % Confidence Intervals Median Figure 5: Graphical statistical summary of vertical shot offset for SAR12 Bolt Action From the above graph, we can say that the vertical impact point variation at 100 yards is , based on the shot to shot velocity variation. DATA AND RESULTS: Graphical data to be shown in the following lists in the appendix: 1. Shot Count vs. Muzzle a. The best and worst markers tested (Figures 7-8) b. All markers tested are in the Appendix in Figures A4-A13 2. Minitab statistical graphical summary of each shot string, showing mean, standard deviation and Anderson Darling normality test. a. The graphs of each shot string for the best and worst marker tested (Figures 9-10). b. The graphs of each shot string for all markers are in the Appendix in Figures A14-A23 3. Theoretical point of vertical impact based on individual shot velocities. a. The graphs of each shot string for the best and worst marker tested (Figures 11-12). b. The graphs of each shot string for all markers tested are in the Appendix in Figures A24-A33 4. Summary of theoretical vertical shot locations, for all markers (Figure 13) 5. Probability Table, based on 30 shot strings (Table 3) PAGE 10

11 "OUT OF THE BOX" SHOT CONSISTENCY OF DIFFERENT FIRST STRIKE CAPABLE MARKERS (30 CONSECUTIVE SHOT SAMPLE SIZE) TALLER CURVE = GREATER SAR12 G2 SEMI +/ FPS SAR12 BOLT ACTION +/ FPS SSR-HPA,.683 LAPCO +/ FPS DYE DAM +/ FPS MAXTACT TGR1 +/ FPS MILSIG M17 +/ FPS HAMMER 7 +/-3.75 FPS SSR-CO2,.683 BRL +/ FPS FIRST STRIKE T15 +/ FPS MCS DMR +/ FPS Figure 6: FPS Probability based on 30 shot sample size for the individual markers tested PAGE 11

12 300.0 SAR G2 SEMI SHOT COUNT VS MUZZLE VELOCITY (30 CONSECUTIVE SHOT SAMPLE SIZE) VELOCIT Y SPREAD (FPS) Figure 7: Factory SAR G2 Semi, Muzzle velocity per shot (Stock) PAGE 12

13 305.0 RAP4/MCS DMR SHOT COUNT VS MUZZLE VELOCITY (30 CONSECUTIVE SHOT SAMPLE SIZE) VELOCIT Y SPREAD (FPS) RAP4/ MCS DMR INCH HH BARREL, 30 SHOT FPS Figure 8: MCS/ RAP4 DMR, Muzzle velocity per shot (0.686 SP barrel) PAGE 13

14 Summary Report for - SAR12 G2 Semi Anderson-Darling Normality Test A-Squared 0.15 P-Value StDev 1.35 Variance 1.83 Skewness Kurtosis N Minimum st Quartile Median rd Quartile Maximum % Confidence Interval for % Confidence Interval for Median % Confidence Interval for StDev % Confidence Intervals Median Figure 9: Graphical summary of SAR G2 Semi Automatic (Stock) PAGE 14

15 Summary Report for - RAP4 DMR Anderson-Darling Normality Test A-Squared 0.35 P-Value StDev Variance Skewness Kurtosis N Minimum st Quartile Median rd Quartile Maximum % Confidence Interval for % Confidence Interval for Median % Confidence Interval for StDev % Confidence Intervals Median Figure 10: Graphical summary of Rap4 MCS DMR (0.686 SP barrel PAGE 15

16 SASS G2 THEORETICAL SHOT 100 YRDS (30 CONSECUTIVE SHOT SAMPLE SIZE, ALL VARIABLES REMOVED EXCEPT MARKER MUZZLE VELOCITY) VERTICAL SPREAD (INCH) % OF ALL 75% OF ALL SHOTS LAND 99.7% OF ALL SHOTS LAND HERE PROBABILITY SPREAD (%) Figure 11: Factory SAR G2 Semi, Ideal conditions Shot Displacement at 100 yards, based on Muzzle PAGE 16

17 MCS/ RAP4 DMR THEORETICAL SHOT 100 YRDS (30 CONSECUTIVE SHOT SAMPLE SIZE, ALL VARIABLES REMOVED EXCEPT MARKER MUZZLE VELOCITY) 20.0 VERTICAL SPREAD (INCH) % OF ALL 75% OF ALL SHOTS 99.7% OF ALL SHOTS LAND HERE PROBABILITY SPREAD (%) Figure 12: MCS/ RAP4 DMR, Ideal conditions Shot Displacement at 100 yards, based on Muzzle PAGE 17

18 THEORETICAL VERTICAL IMPACT 100 YRDS (30 CONSECUTIVE SHOT SAMPLE SIZE, ALL VARIABLES REMOVED EXCEPT MARKER PERFORMANCE) (DERIVED FROM EXTERNAL BALLISTIC FORMULA) VERTICAL SPREAD (INCH) SAR12 G2 SEMI, 12.6 INCH MAX SPREAD SAR12 BOLT ACTION, 16.0 INCH MAX SPREAD SSR HPA, 24.4 INCH MAX SPREAD DYE DAM, 23.4 INCH MAX SPREAD TGR R1, 28.6 INCH MAX SPREAD MILSIG M17, 33 INCH MAX SPREAD HAMMER 7, 40.9 INCH MAX SPREAD SSR CO2, 45 INCH MAX SPREAD FIRST STRIKE T15, 86.4 INCH MAX SPREAD MCS DMR, 120 INCH MAX SPREAD Figure 13: Vertical Shot Displacement at 100 yards, all markers, ideal conditions. PAGE 18

19 MUZZLE VELOCITY FPS VARIATION PROBABILITY: Standard Deviations % of data falling into range of StDev Standard Deviation Lower Higher velocity Low Impact point High Impact point Expected shot spread Platform SAR 12 G2 Semi % Stock % % Standard Deviations % of data falling into range of StDev Standard Deviation Lower Higher velocity Low Impact point High Impact point Expected shot spread Platform SAR 12 Bolt Action % Stock % % Standard Deviations % of data falling into range of StDev Standard Deviation Lower Higher velocity Low Impact point High Impact point Expected shot spread Platform CCM SSR - HPA % Lapco % % Standard Deviations % of data falling into range of StDev Standard Deviation Lower Higher velocity Low Impact point High Impact point Expected shot spread Platform Dye Dam % Stock % % Standard Deviations % of data falling into range of StDev Standard Deviation Lower Higher velocity Low Impact point High Impact point Expected shot spread Platform Maxtact TGR R % Stock % % Standard Deviations % of data falling into range of StDev Standard Deviation Lower Higher velocity Low Impact point High Impact point Expected shot spread Platform Milsig M % % % Standard Deviations % of data falling into range of StDev Standard Deviation Lower Higher velocity Low Impact point High Impact point Expected shot spread Platform Hammer % Stock % % Standard Deviations % of data falling into range of StDev Standard Deviation Lower Higher velocity Low Impact point High Impact point Expected shot spread Platform CCM SSR - CO % Lapco % % Standard Deviations % of data falling into range of StDev Standard Deviation Lower Higher velocity Low Impact point High Impact point Expected shot spread Platform First Strike T % Lapco % % Standard Deviations % of data falling into range of StDev Standard Deviation Lower Higher velocity Low Impact point High Impact point Expected shot spread Platform RAP4 DMR % % % Table 3: Probability of muzzle velocity and impact point PAGE 19

20 CONCLUSIONS: Upon evaluating the data, we can conclude that 1. variation is important when trying to predict where the round will end up down range. If the target is a mask (10 ), a shooter needs to know where to aim to hit it, especially if the target is partially hidden behind a tree or in a window. Sometimes one or two shots is all a player has to make a hit. If a marker cannot perform with consistent velocity (small variation), the chances are high that the round will miss the target. An important note here is that we also know as paintball players that velocity consistency is not the only indicator of shot accuracy or repeatability on a target. For example, a marker with a 1 barrel could provide a shot string with a tight fps variation, but expected performance downrange 100 yards, would be questionable. The point is, we found that a marker must start with velocity consistency to have a chance of being repeatable on target down range; HOWEVER, there are many other variables come into repeatable flight paths. 2. The design of the G2 semi auto has exceeded expectation for repeatability performance 3. Properly matched systems (reg, valve train, barrel, projectile) give the greatest consistency in terms of absolute velocity deviation. 4. With the high end markers taking many variables out of the equation for the consumer, the projectile itself becomes the limiting factor. Round to round deviations, both dimensionally and in weight, create a significant portion of fps variation. For example, after sorting the rounds by weight, Beta Member Matt was able to reduce the Dye Dam's +/ fps down to +/ fps! This process if very tedious, and as shown, limits a players quantity of a specific weight. Within one box, the weight can very as shown in Figure 1 in the appendix. Case in point is the CCM SR1. This marker was tested with CO2 and HPA with both out of the box first strike rounds, and Matched weight first strike rounds. The resulting standard deviation was noticeable. The SSR (HPA) with matched weight First strike rounds saw the standard deviation drop from fps to fps. See figures A-2 and A-3 in the Appendix. 5. As players and manufacturers, we must be very cautious of how we perceive and discuss particular equipment and there capabilities. As discussed in the introduction, shooting a three shot string across a radar chrono will not give you either sufficient or accurate data to formulate any conclusion. Radar based chronographs are capable of holding +/- 3% deviation. At 300 fps, 3% equates to a possible deviation up to +/- 9 fps. Optical chronographs; however, typically are accurate to sub 1%. This yields a measuring capability at 300 fps to be +/-3 fps max. 6. As players and manufacturers, there are many other variables that need to be evaluated, along with velocity consistency, to truly understand the real world expectation of a marker s shot to shot performance on a target at 100 yards. As a group, we plan on continuing to scientifically identify, study, and quantify the other variables when shooting fluid filled projectiles at long distances! PAGE 20

21 APPENDIX: Figure A-1: Weight Distribution of FS rounds PAGE 21

22 Summary Report for - CSM SSR HPA Matched weight FS rounds Anderson-Darling Normality Test A-Squared 0.44 P-Value StDev 1.52 Variance 2.32 Skewness Kurtosis N Minimum st Quartile Median rd Quartile Maximum % Confidence Interval for % Confidence Interval for Median % Confidence Interval for StDev % Confidence Intervals Median Figure A-2: CCM SSR with HPA and weight matched First Strike rounds PAGE 22

23 SR1 HPA, - CSM SSR HPA matched FSR Data SR1 HPA - CSM SSR HPA matched FSR Figure A-3: CCM SSR HPA with and without weight matched First Strike rounds PAGE 23

24 300.0 SAR G2 SEMI SHOT COUNT VS MUZZLE VELOCITY (30 CONSECUTIVE SHOT SAMPLE SIZE) VELOCITY SPREAD (FPS) Figure A-4: Factory SAR G2 Semi, Muzzle velocity per shot (Stock) PAGE 24

25 SAR12C BOLT ACTION SHOT COUNT VS MUZZLE VELOCITY (30 CONSECUTIVE SHOT SAMPLE SIZE) VELOCITY SPREAD (FPS) Figure A-5: Factory SAR Bolt Action, Muzzle velocity per shot (Stock) PAGE 25

26 300.0 CCM SR1-HPA SHOT COUNT VS MUZZLE VELOCITY (30 CONSECUTIVE SHOT SAMPLE SIZE) VELOCITY SPREAD (FPS) Figure A-6: CCM-HPA, LAPCO.683, Muzzle velocity per shot PAGE 26

27 300.0 DYE DAM SHOT COUNT VS MUZZLE VELOCITY (30 CONSECUTIVE SHOT SAMPLE SIZE) VELOCITY SPREAD (FPS) Figure A-7: Factory Dye Dam, Muzzle velocity per shot (Lapco Barrel) PAGE 27

28 300.0 TGR R1 SHOT COUNT VS MUZZLE VELOCITY (30 CONSECUTIVE SHOT SAMPLE SIZE) VELOCITY SPREAD (FPS) Figure A-8: Factory Maxtact TGR R1, Muzzle velocity per shot (Stock) PAGE 28

29 300.0 MILSIG M17 SHOT COUNT VS MUZZLE VELOCITY (30 CONSECUTIVE SHOT SAMPLE SIZE) VELOCITY SPREAD (FPS) Figure A-9: Factory Milsig M17, Muzzle velocity per shot (Stock) PAGE 29

30 300.0 HAMMER 7 SHOT COUNT VS MUZZLE VELOCITY (30 CONSECUTIVE SHOT SAMPLE SIZE) VELOCITY SPREAD (FPS) Figure A-10: Factory Hammer 7, Muzzle velocity per shot (Stock) PAGE 30

31 300.0 CCM SR1-CO2 SHOT COUNT VS MUZZLE VELOCITY (30 CONSECUTIVE SHOT SAMPLE SIZE) VELOCITY SPREAD (FPS) Figure A-11: Factory CCM SR1 with CO2, (CARTRIGE REPLACED EVERY 12 SHOTS) (Lapco Barrel) PAGE 31

32 TIBERIUS T15 SHOT COUNT VS MUZZLE VELOCITY (30 CONSECUTIVE SHOT SAMPLE SIZE) VELOCITY SPREAD (FPS) Figure A-12: First Strike T15, Muzzle velocity per shot (Lapco Barrel) PAGE 32

33 305.0 RAP4/MCS DMR SHOT COUNT VS MUZZLE VELOCITY (30 CONSECUTIVE SHOT SAMPLE SIZE) VELOCITY SPREAD (FPS) Figure A-13: MCS/ RAP4 DMR, Muzzle velocity per shot (Stock) PAGE 33

34 Summary Report for - SAR12 G2 Semi Anderson-Darling Normality Test A-Squared 0.15 P-Value StDev 1.35 Variance 1.83 Skewness Kurtosis N Minimum st Quartile Median rd Quartile Maximum % Confidence Interval for % Confidence Interval for Median % Confidence Interval for StDev % Confidence Intervals Median Figure A-14: Graphical summary of SAR G2 Semi-Automatic (Stock) PAGE 34

35 Summary Report for - SAR12 Bolt Act Anderson-Darling Normality Test A-Squared 0.50 P-Value StDev 1.36 Variance 1.84 Skewness Kurtosis N Minimum st Quartile Median rd Quartile Maximum % Confidence Interval for % Confidence Interval for Median % Confidence Interval for StDev % Confidence Intervals Median Figure A-15: Graphical summary of SAR Bolt Action (Stock) PAGE 35

36 Summary Report for - Dye Dam Anderson-Darling Normality Test A-Squared 0.34 P-Value StDev 2.80 Variance 7.85 Skewness Kurtosis N Minimum st Quartile Median rd Quartile Maximum % Confidence Interval for % Confidence Interval for Median % Confidence Interval for StDev % Confidence Intervals Median Figure A-16: Graphical summary of Dye Dam (Lapco Barrel) PAGE 36

37 Summary Report for - SR1 HPA Anderson-Darling Normality Test A-Squared 0.22 P-Value StDev 2.27 Variance 5.14 Skewness Kurtosis N Minimum st Quartile Median rd Quartile Maximum % Confidence Interval for % Confidence Interval for Median % Confidence Interval for StDev % Confidence Intervals Median Figure A-17: Graphical summary of CCM SSR with HPA (Lapco Barrel) PAGE 37

38 Summary Report for - Maxtact TGR R1 Anderson-Darling Normality Test A-Squared 0.26 P-Value StDev 3.18 Variance Skewness Kurtosis N Minimum st Quartile Median rd Quartile Maximum % Confidence Interval for % Confidence Interval for Median % Confidence Interval for StDev % Confidence Intervals Median Figure A-18: Graphical summary of Maxtact TGR R1 (Stock) PAGE 38

39 Summary Report for - Milsig M17 Anderson-Darling Normality Test A-Squared 0.19 P-Value StDev 3.46 Variance Skewness Kurtosis N Minimum st Quartile Median rd Quartile Maximum % Confidence Interval for % Confidence Interval for Median % Confidence Interval for StDev % Confidence Intervals Median Figure A-19: Graphical summary of Milsig M17 (Stock) PAGE 39

40 Summary Report for - Hammer 7 Anderson-Darling Normality Test A-Squared 1.63 P-Value < StDev 3.75 Variance Skewness Kurtosis N Minimum st Quartile Median rd Quartile Maximum % Confidence Interval for % Confidence Interval for Median % Confidence Interval for StDev % Confidence Intervals Median Figure A-20: Graphical summary of Hammer 7 (Stock) PAGE 40

41 Summary Report for - SR1 CO2 Anderson-Darling Normality Test A-Squared 0.68 P-Value StDev 5.18 Variance Skewness Kurtosis N Minimum st Quartile Median rd Quartile Maximum % Confidence Interval for % Confidence Interval for Median % Confidence Interval for StDev % Confidence Intervals Median Figure A-21: Graphical summary of CCM SSR with CO2 (Lapco Barrel) PAGE 41

42 Summary Report for - FS T15 Anderson-Darling Normality Test A-Squared 0.67 P-Value StDev 7.98 Variance Skewness Kurtosis N Minimum st Quartile Median rd Quartile Maximum % Confidence Interval for % Confidence Interval for Median % Confidence Interval for StDev % Confidence Intervals Median Figure A-22: Graphical summary of First Strike T15 (Lapco Barrel) PAGE 42

43 Summary Report for - RAP4 DMR Anderson-Darling Normality Test A-Squared 0.35 P-Value StDev Variance Skewness Kurtosis N Minimum st Quartile Median rd Quartile Maximum % Confidence Interval for % Confidence Interval for Median % Confidence Interval for StDev % Confidence Intervals Median Figure A-23: Graphical summary of MCS/ RAP4 DMR (Stock) PAGE 43

44 SASS G2 THEORETICAL SHOT 100 YRDS (30 CONSECUTIVE SHOT SAMPLE SIZE, ALL VARIABLES REMOVED EXCEPT MARKER MUZZLE VELOCITY) VERTICAL SPREAD (INCH) % OF ALL 75% OF ALL SHOTS LAND 99.7% OF ALL SHOTS LAND HERE PROBABILITY SPREAD (%) Figure A-24: Factory SAR G2 Semi, Ideal conditions Shot Displacement at 100 yards, based on Muzzle PAGE 44

45 9 7 SAR12C BOLT ACTION VERTICAL SHOT 100 YRDS (30 CONSECUTIVE SHOT SAMPLE SIZE, ALL VARIABLES REMOVED EXCEPT MUZZLE VELOCITY) 5 VERTICAL SPREAD (INCH) % OF 75% OF ALL 99.7% OF ALL SHOTS LAND HERE PROBABILITY SPREAD (%) -7-9 Figure A-25: Factory SAR Bolt Action, Ideal conditions Shot Displacement at 100 yards, based on Muzzle PAGE 45

46 9.0 SR1-HPA VERTICAL SHOT 100 YRDS (30 CONSECUTIVE SHOT SAMPLE SIZE, ALL VARIABLES REMOVED EXCEPT MUZZLE VELOCITY) VERTICAL SPREAD (INCH) % OF 75% OF ALL 99.7% OF ALL SHOTS LAND HERE PROBABILITY SPREAD (%) Figure A-26: Factory CCM SSR with HPA, Ideal conditions Shot Displacement at 100 yards, based on Muzzle PAGE 46

47 DYE DAM VERTICAL SHOT 100 YRDS (30 CONSECUTIVE SHOT SAMPLE SIZE, ALL VARIABLES REMOVED EXCEPT MUZZLE VELOCITY) VERTICAL SPREAD (INCH) % OF ALL 75% OF ALL SHOTS LAND 99.7% OF ALL SHOTS LAND HERE PROBABILITY SPREAD (%) Figure A-27: Factory Dye Dam, Ideal conditions Shot Displacement at 100 yards, based on Muzzle PAGE 47

48 TGR1 R1 VERTICAL SHOT 100 YRDS (30 CONSECUTIVE SHOT SAMPLE SIZE, ALL VARIABLES REMOVED EXCEPT MUZZLE VELOCITY) VERTICAL SPREAD (INCH) % OF ALL 75% OF ALL SHOTS 99.7% OF ALL SHOTS LAND HERE PROBABILITY SPREAD (%) TGR-R1, 29 INCH MAX SPREAD Figure A-28: Factory Maxtact TGR R1, Ideal conditions Shot Displacement at 100 yards, based on Muzzle PAGE 48

49 20.0 MILSIG M17 VERTICAL SHOT 100 YRDS (30 CONSECUTIVE SHOT SAMPLE SIZE, ALL VARIABLES REMOVED EXCEPT MUZZLE VELOCITY) 15.0 VERTICAL SPREAD (INCH) % OF 75% OF ALL SHOTS LAND 99.7% OF ALL SHOTS LAND HERE PROBABILITY SPREAD (%) MILSIG M17, 33.0 INCH MAX SPREAD Figure A-29: Factory Milsig M17, Ideal conditions Shot Displacement at 100 yards, based on Muzzle PAGE 49

50 28.0 HAMMER 7 VERTICAL SHOT 100 YRDS (30 CONSECUTIVE SHOT SAMPLE SIZE, ALL VARIABLES REMOVED EXCEPT MUZZLE VELOCITY) VERTICAL SPREAD (INCH) % OF ALL 75% OF ALL SHOTS 99.7% OF ALL SHOTS LAND HERE PROBABILITY SPREAD (%) Figure A-30: Factory Hammer 7, Ideal conditions Shot Displacement at 100 yards, based on Muzzle PAGE 50

51 28.0 CCM SR1-CO2 VERTICAL SHOT PLACEMENT 100 YRDS (30 CONSECUTIVE SHOT SAMPLE SIZE, ALL VARIABLES REMOVED EXCEPT MUZZLE VELOCITY) VERTICAL SPREAD (INCH) % OF ALL 75% OF ALL SHOTS 99.7% OF ALL SHOTS LAND HERE PROBABILITY SPREAD (%) Figure A-31: Factory CCM SR1 with CO2- Lapco.683, Ideal conditions Shot Displacement at 100 yards, based on Muzzle PAGE 51

52 NOTE: Y AXIS SCALE DIFFERENT FROM FIRST EIGHT (8) TO SHOW ALL DATA POINTS TIB/ FS T15 VERTICAL SHOT 100 YRDS (30 CONSECUTIVE SHOT SAMPLE SIZE, ALL VARIABLES REMOVED EXCEPT MUZZLE VELOCITY) 30.0 VERTICAL SPREAD (INCH) % OF ALL 75% OF ALL SHOTS 99.7% OF ALL SHOTS LAND HERE PROBABILITY SPREAD (%) Figure A-32: First Strike T15- Lapco.683, Ideal conditions Shot Displacement at 100 yards, based on Muzzle PAGE 52

53 NOTE: Y AXIS SCALE DIFFERENT FROM FIRST EIGHT (8) TO SHOW ALL DATA POINTS MCS/ RAP4 DMR THEORETICAL SHOT 100 YRDS (30 CONSECUTIVE SHOT SAMPLE SIZE, ALL VARIABLES REMOVED EXCEPT MUZZLE VELOCITY) 20.0 VERTICAL SPREAD (INCH) % OF ALL 75% OF ALL SHOTS 99.7% OF ALL SHOTS LAND HERE PROBABILITY SPREAD (%) Figure A-33: MCS/ RAP4 DMR, Ideal conditions Shot Displacement at 100 yards, based on Muzzle PAGE 53