Projectile Dispersion of a Marker Ball Launcher 

by Peter J. Fazio 

ARL-TR-3319 October 2004 

Approved for public release; distribution is unlimited.
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Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5066 

ARL-TR-3319 October 2004 

Projectile Dispersion of a Marker Ball Launcher 

Peter J. Fazio 

Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution is unlimited.
ii

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4. TITLE AND SUBTITLE 

 Projectile Dispersion of a Marker Ball Launcher 

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 Peter J. Fazio (ARL) 

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14. ABSTRACT 

The Weapons Technology Analysis Branch of the Ballistics and Weapons Concepts Division, Weapons and Materials Research 

Directorate of the U.S. Army Research Laboratory conducted a test of the firing ability of a marker ball launcher mounted on a 

robotic research laboratory vehicle. The robotic vehicle was used as a technology demonstration platform for autonomous and 

semi-autonomous behaviors. Some of the behaviors included the ability to return fire against enemy targets. In the interest of 

safety and simplicity, it was decided that a marker ball launcher would be used as the robot’s “weapon” system. A fully integrated marker ball launcher and turret assembly, the return fire simulator (RFS), was mounted on the robotic vehicle. The RFS 

mounts a 0.68-inch caliber, 16-inch-long launcher barrel onto a Directed Perceptions pan-and-tilt assembly. Some of the 

autonomous robotic behaviors require the robotic vehicle to fire a specified number of rounds to achieve a 90% probability of 

hit (pHit). To meet this requirement, an estimate of the launcher round dispersion, based on the range to the target, was needed. 

A test was developed to determine an estimate of the number of rounds required to achieve a 50%, 75%, 90%, 95%, and 99% 

pHit against a target of a specified cross-sectional size at various ranges. The test ranges were 20, 40, 60, and 80 feet from the 

muzzle of the launcher to the target board. At each range, 20 rounds were fired and their impact points were recorded. For each 

round fired, the optical aim point, produced by a class II laser, was recorded. The data were collected and analyzed to generate 

the azimuth (x coordinate) error and elevation (y coordinate) error and the total (x and y coordinate) error. The statistical means 

and standard deviations of these errors and of the muzzle velocities were calculated. The means of the azimuth error and 

elevation error were used to calculate the azimuth and elevation angular offsets, respectively. These data and the target crosssectional size were used to calculate the number of shots required to achieve the probabilities of hit at the four target ranges. 

15. SUBJECT TERMS

 dispersion; launcher; marker ball; pHit 

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 Peter J. Fazio 

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iii

Contents 

List of Figures iv

1. Introduction 1

2. Procedures 3

3. Discussion 5

4. Summary 12 

Appendix A. Dispersion Test Data 15 

Distribution List 20 
iv

List of Figures 

Figure 1. All-terrain research vehicle. ............................................................................................1 

Figure 2. Return fire simulator........................................................................................................2 

Figure 3. Radar chronograph. .........................................................................................................3 

Figure 4. Target box........................................................................................................................4 

Figure 5. Dispersion pattern (range = 20 feet)................................................................................7 

Figure 6. Dispersion pattern (range = 40 feet)................................................................................8 

Figure 7. Dispersion pattern (range = 60 feet)................................................................................9 

Figure 8. Dispersion pattern (range = 80 feet)..............................................................................10

Figure 9. Number of shots, uncorrected pHit. ..............................................................................11 

Figure 10. Number of shots, corrected pHit. ................................................................................12 
1

1. Introduction 

The Weapons Technology Analysis Branch of the Ballistics and Weapons Concepts Division, 

Weapons and Materials Research Directorate, U.S. Army Research Laboratory (ARL) conducted 

a test of the firing ability of a marker ball launcher mounted on a robotic research laboratory 

vehicle. The robotic vehicle, an iRobot all-terrain research vehicle (ATRV) shown in figure 1, 

was used as a technology demonstration platform for autonomous and semi-autonomous 

behaviors. Some of the behaviors included the ability to return fire against enemy targets. The 

ability to return fire necessitated that some form of weapon system be implemented on board the 

robotic vehicle to properly evaluate the behavior. 

Figure 1. All-terrain research vehicle. 

In the interest of safety and simplicity, it was decided that a marker ball launcher (paintball gun) 

would be used as the robot’s “weapon” system. A turret capable of azimuth and elevation 

changes was also needed for the marker ball launcher to allow the robotic vehicle to precisely 

point the launcher tube during targeting behaviors. A fully integrated marker ball launcher and 

turret assembly, the return fire simulator (RFS) shown in figure 2, was purchased from 

Bristlecone Corporation. The RFS is typically used as a stationary tactical training device for 
2

military and law enforcement personnel. The RFS simulates enemy fire during close quarter 

tactical scenarios, such as military operations in urban terrain and law enforcement special 

weapons and tactics operations in urban dwellings. The RFS mounts a 0.68-inch caliber, 

16-inch-long launcher barrel onto a Directed Perceptions, Inc., pan-and-tilt assembly. The 

standard trough-like paintball magazine was replaced with a vertical acrylic tube magazine in an 

effort to reduce the load on the turret drives. A low power class II laser was used as an optical 

pointing aid for targeting during the testing. The RFS launcher and turret assembly, along with 

the carbon dioxide propellant and regulator, were mounted on top of the ATRV to create a 

mobile autonomous robotic gun system surrogate. 

Figure 2. Return fire simulator. 

Some of the autonomous robotic behaviors require the robotic vehicle to detect an enemy target, 

sight the weapon system on the target, and then fire a specified number of rounds to achieve a 

90% probability of hit (pHit). To meet one of the requirements for these behaviors, namely, 

number of rounds to achieve 90% pHit, an estimate of the RFS launcher round dispersion based 

upon the range to the target was needed. A test was developed to determine an estimate of the 

number of rounds required to be fired to achieve a 50%, 75%, 90%, 95%, and 99% pHit against a 

target of a specified cross-sectional size at various close quarter ranges. The test consisted of a 

series of trials where the RFS was fired at a fixed target setup from four close quarter ranges. 
3

The test ranges were 20, 40, 60, and 80 feet from the muzzle of the launcher to the target board. 

At each range, 20 rounds were fired and their impact points were recorded. For each round fired, 

the optical aim point, produced by the class II laser, was recorded and the launcher re-aimed 

when necessary. The projectile’s muzzle velocity was also recorded for each round fired via a 

radar chronograph, shown in figure 3. The data were collected and analyzed to generate the 

azimuth (x coordinate) error and elevation (y coordinate) error and the total (x and y coordinate) 

error. The statistical means and standard deviations of these errors and of the muzzle velocities 

were calculated. The means of the azimuth error and elevation error were used to calculate the 

azimuth and elevation angular offsets, respectively. These data and the target cross-sectional 

size were used to calculate the number of shots required to achieve the probablities of hit at the 

four target ranges. 

Figure 3. Radar chronograph. 

2. Procedures 

The ATRV robot, which was outfitted with the RFS projectile launcher and a class II laser, was 

used as the surrogate weaponized autonomous robotic vehicle to evaluate the system’s ability to 

achieve a probability of target hit within a specified number of shots fired. The ATRV, which is 

manufactured by iRobot Corporation, is a small, lightweight wheeled research robot. The 

vehicle is approximately 4 feet long, 3 feet wide, and 2.5 feet high and weighs 250 pounds. The 

chassis is a four-wheeled, skid-steered platform employing battery-powered electric drive 

motors. The RFS is a projectile launcher that uses compressed carbon dioxide propellant. The 

launcher tube is 16 inches long with a 0.68-inch diameter bore. The propellant is regulated to 

maintain a muzzle velocity of approximately 300 feet per second. The projectiles used for this 
4

test were made of hard nylon and had a mass of approximately 28 grains. The launcher is 

mounted to a turret assembly comprised of a pan-and-tilt unit, manufactured by Directed 

Perceptions, Inc. A class II laser, with a maximum power output of less than 1 milliwatt, was 

mounted to the launcher barrel to allow for optical aiming of the RFS. The specified target size 

for the pHit calculations was a 3-foot by 3-foot square, which reasonably represents the crosssectional area of the target vehicle. The target vehicle for the autonomous behavior being 

evaluated was a wheeled research robot that had a size similar to the ATRV. A 4-foot by 4-foot 

square target box, shown in figure 4, was constructed. This size target was assumed to be large 

enough to accept the total shot dispersion pattern of the launcher for the required test ranges. 

Figure 4. Target box. 

The target region was made from a heavy weight craft paper that was held in tension across the 

target box to allow for the projectiles to make a clear perforation upon impact. The horizontal 

and vertical sides of the target box had graduated rules attached to allow for accurate measuring 

of the azimuth and elevation optical laser aim points and projectile hit points. The testing began 

upon completion of the final assembly of the various pieces of hardware. The ATRV with its 

mounted projectile launcher was emplaced at the initial test range from the target box. A radar 

chronograph was set up below and slightly ahead of the launcher tube’s muzzle to record the 

projectile muzzle velocity. We aimed the launcher by observing the red laser spot generated by 

the class II laser, via a remote mounted joystick controlling the turret drives. The laser spot 

image produced on the target area was measured to record its azimuth and elevation position. 

The launcher was pressurized with propellant and a projectile fired at the target. The projectile 
5

hit point perforation through the craft paper was measured to record its azimuth and elevation 

position. The projectile’s muzzle velocity was measured by the radar chronograph and recorded. 

Twenty shots were fired (in total) at the first test range, and the aim points, hit points, and 

muzzle velocities were measured and recorded for each shot. The procedures were duplicated 

for the successive test ranges. The data were analyzed for each group of shots at a particular test 

range and then analyzed across the series of test ranges to develop a dispersion trend based on 

range to the target. We calculated an azimuth and elevation error for each test shot by 

subtracting the aim point from the actual hit point. A mean azimuth error, a mean elevation 

error, and a total error was calculated for the group of 20 shots for each of the four test ranges. 

The standard deviations for the azimuth and elevation errors were calculated, as well, within the 

groups of shots. We calculated the azimuth angular offset of the launcher by taking the inverse 

tangent of the azimuth error mean divided by the test range. The elevation angular offset was 

calculated similarly with the elevation error mean and the test range. Two sets of pHit numbers 

were calculated for these data: the first, an uncorrected set of pHit numbers based on the raw 

data, and second, a set of corrected pHit numbers, where the azimuth and elevation biases were 

removed. Removal of the azimuth bias required that the azimuth error mean be subtracted from 

the azimuth errors. The resulting corrected azimuth errors were then used to calculate the 

standard deviation for the corrected group of hit errors. 

A similar procedure was applied to the elevation errors, with the elevation error mean to create a 

set of corrected elevation errors. The standard deviation of the set of corrected elevation errors 

was then calculated, as well. An algorithm was developed (ƒ) that generated the number of shots 

required to achieve the various levels of pHit for each group of shots. The azimuth and elevation 

standard deviations of the group of shots, the azimuth and elevation standard deviations of the 

gun bias and the width and height of the target are entered in the algorithm to produce the pHit. 

The azimuth and elevation standard deviations of the gun bias, in this particular test, were always 

zero because a single launcher was used throughout the testing. The width and the height of the 

target were both 3 feet. The standard deviations of the uncorrected and the corrected azimuth 

and elevation errors were used as the input to the algorithm. The output generated by the 

algorithm was the number of shots required to achieve the probabilities of hit of 50%, 75%, 90%, 

95%, and 99% for the uncorrected and corrected errors. The data are shown in appendix A. 

3. Discussion 

The data from this test show a fairly consistent tendency for the launcher to create a dispersion 

pattern bias in both azimuth and elevation (see figures 5 through 8). The elevation bias, which is 

negative across all target ranges, becomes fairly large at the longer ranges because of the lack of 

 ƒ

 Algorithm developed by Dr. Joseph K. Wald, ARL, 2003. 
6

a fire control compensating for increases in super-elevation based on range to the target. The 

muzzle velocities stayed quite consistent throughout the test with an overall mean of 308.6 feet 

per second and a standard deviation of 2.66 feet per second. The azimuth bias is positive for all 

the target ranges. There is a strong positive azimuth bias for all but the 80-foot range. The lower 

three target ranges show a consistent tendency to fire to the right of the aim point. The azimuth 

bias at the 80-foot range, while positive, is close to zero. It was observed during testing that the 

flight characteristics tended to be more erratic at the longest range, possibly causing the 

deviation from the general azimuth bias trend toward the right of the aim point. Notably, at the 

80-foot range, a couple of shots hit above the aim point, producing a positive elevation error, 

thus giving more credibility to the conjecture that the erratic flight behavior may have influenced 

the trend of the data. The erratic flight behavior of some of the projectiles at the longest range 

may have been caused by manufacturing defects in the projectiles themselves. During the 

testing, an occasional shot was fired that passed through the target box backstop and impacted a 

solid surface, causing the nylon projectile to crack or split open. Upon inspection of the cracked 

open projectile, a void was typically found to be present inside. The void inside the nylon 

spheres tended to be of approximately the same volume, thus maintaining a consistent mass of 28 

grains for each projectile, but was situated rather randomly about the sphere’s geometric center. 

This offsetting of the void caused the projectile’s center of mass to be situated away from the 

geometric center, as well. Having some projectiles with a non-centroidal center of mass likely 

contributed to the erratic flight behavior which was sometimes observed during firing at the 

longest range. To eliminate this variation, the dispersion testing could be redone with projectiles 

having no internal void or having a homogeneous density throughout the sphere. 

The dispersion data were then run through the algorithm to generate the pHit numbers for the 

various ranges. When we look at the bar chart in figure 9, which shows the number of shots 

required to achieve the various pHit levels at the four ranges without correcting for the 

dispersion bias, it is clear that only one shot will be required to achieve a 99% probability of 

target hit at the ranges of 20 and 40 feet. The 60-foot range will only require one shot to achieve 

a 95% pHit but will require two shots to attain the 99% pHit level. The longest range, 80 feet, 

shows a linear increase in the number of shots required from two shots needed at the 50% pHit 

level to five shots needed at the 95% pHit level. A further increase to seven shots is needed to 

achieve the 99% probability of hit. When we look at the bar chart in figure 10, which shows the 

number of shots required to achieve the various pHit levels at the four ranges with correction for 

the dispersion bias, we see that only one shot is required to achieve the 99% pHit level for the 

20-, 40-, and 60-foot target ranges. The 80-foot range requires only one shot to achieve the 50% 

pHit level, two shots to reach the 90% pHit level, three shots for the 95% pHit level, and four 

shots to achieve the 99% pHit level. The data on the bar charts clearly show that to achieve a 

relatively high probability of hit at close quarter ranges will require a minimal number of shots 

fired when the gun-pointing angles are adjusted to compensate for the dispersion biases. Further, 

it is likely that the number of shots required to achieve the specified pHit levels at the 80-foot 
7

range would be reduced because of a tighter dispersion pattern, if projectiles with a consistent 

center of mass were used. 

XY error, Range = 20 feet

-4.5

-3.5

-2.5

-1.5

-0.5

0.5

1.5

2.5

3.5

4.5

-4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5

X error (in), Azimuth

Y error(in), Elevation

Figure 5. Dispersion pattern (range = 20 feet). 
8

XY Error, Range = 40 feet

-8

-6

-4

-2

0

2

4

6

8

-8 -6 -4 -2 0 2 4 6 8

X error (in), Azimuth

Y error (in), Elevation

Figure 6. Dispersion pattern (range = 40 feet). 
9

XY Error, Range = 60 feet

-25

-20

-15

-10

-5

0

5

10

15

20

25

-25 -20 -15 -10 -5 0 5 10 15 20 25

X Error (in), Azimuth

Y Error (in), Elevation

Figure 7. Dispersion pattern (range = 60 feet). 
10

XY Error, Range = 80 feet

-40

-30

-20

-10

0

10

20

30

40

-40 -30 -20 -10 0 10 20 30 40

X Error (in), Azimuth

Y Error (in), Elevation

Figure 8. Dispersion pattern (range = 80 feet). 
11

pHit 50% pHit 75% pHit 90% pHit 95% pHit 99%

20

40

60

80

0

1

2

3

4

5

6

7

s

Range

20

40

60

80

Figure 9. Number of shots, uncorrected pHit. 

Number of shots for pHit by range (uncorrected)

Number of 

shots
12

pHit 50%

cor. pHit 75%

cor. pHit 90%

cor. pHit 95%

cor. pHit 99%

cor.

20

40

60

80

0

0.5

1

1.5

2

2.5

3

3.5

4

ts

Range

20

40

60

80

Figure 10. Number of shots, corrected pHit. 

4. Summary 

A robotic vehicle, the iRobot ATRV, was used as a technology demonstration platform for 

autonomous and semi-autonomous behaviors. Some of the behaviors included the ability to 

return fire against enemy targets. The ability to return fire required the use of a weapon system 

on board the robotic vehicle to properly evaluate the behavior. The weapon of choice was an 

integrated marker ball launcher and turret assembly, the RFS, which is typically used as a 

stationary tactical training device for military and law enforcement personnel. The RFS was 

mounted on top of the ATRV to create a mobile autonomous robotic gun system surrogate. One 

of the autonomous behaviors requires the robotic vehicle to locate an enemy target, sight the 

weapon system on the target, and then fire a specified number of rounds to achieve a 90% 

probability of hit. To properly evaluate this behavior, the launcher’s round dispersion at various 

ranges was needed to estimate the number of shots to achieve the specified level of pHit for a 

given size target. 

Number of 

shots

Number of shots for pHit by range (corrected)
13

A test was developed to estimate the number of rounds required to achieve a 50%, 75%, 90%, 

95%, and 99% pHit against a target with a 3-foot by 3-foot cross-sectional size at four target 

ranges. The ranges used in the test were 20 feet, 40 feet, 60 feet, and 80 feet. Twenty rounds 

were fired at each range. For each round fired, the hit point and the aim point were recorded. 

We calculated an azimuth error and elevation error for each round by subtracting the respective 

aim point from the hit point. A mean azimuth error, a mean elevation error, and a total error was 

calculated for the group of 20 shots for each of the four ranges. The standard deviations of the 

errors were calculated, as well. The error means were used as the dispersion pattern biases. The 

pattern bias for all but the 80-foot range was low and to the right of the aim point. The 80-foot 

range showed only a slight bias to the right and a consistently low elevation bias. The number of 

shots required to achieve the various pHit levels over the four ranges was calculated with the 

azimuth and elevation error standard deviations, the azimuth and elevation standard deviations of 

the gun bias (in this case, it was always zero since we used a single launcher throughout the test), 

and the 3-foot by 3-foot target size. Two sets of pHit numbers were generated. A first set was 

based on the raw azimuth and elevation error standard deviations, and a second corrected set was 

based on azimuth and elevation error standard deviations where the error biases had been 

removed. The uncorrected data showed that only one shot will be required to achieve a 99% 

pHit at the ranges of 20 and 40 feet. The 60-foot range required one shot to achieve a 95% pHit 

but required two shots for 99% pHit. The 80-foot range shows a linear increase in the number of 

shots required from two needed for 50% pHit to five needed for 95% pHit. An increase to seven 

shots is needed to achieve 99% pHit. The corrected data showed that only one shot is required to 

achieve 99% pHit for the 20-, 40-, and 60-foot ranges. The 80-foot range requires one shot to 

achieve 50% pHit, two shots to reach 90% pHit, three shots for 95% pHit, and four shots to 

achieve the 99% pHit level. 

The data show that to achieve a relatively high probability of hit at close quarter ranges will 

require a minimal number of shots fired when the gun-pointing angles are adjusted to 

compensate for the dispersion biases. 
14

INTENTIONALLY LEFT BLANK
Range(ft) 20 

Date 10/9/2003 Time 13:00 Temp(F) 76 Ambient Pressure(mb) 1028 Projectile  Type Nylon  Caliber 0.68  Mass(g) 1.8 Shot # Aim X(in) Aim Y(in) Hit X(in) Hit Y(in) 

Muzzle Velocity(ft/s) X Error(in) Y Error(in) To

1 24.5 24.25 25.75 21.75 304 1.25 -2.5 2 24.25 24.25 25.375 21.5 310 1.125 -2.75 3 24.75 24.125 24.375 23.25 309 -0.375 -0.875 4 24.75 24.125 26.5 21.25 304 1.75 -2.875 5 24.8125 24.125 26.75 21.5 305 1.9375 -2.625 6 24.875 24.0625 25.5 20.125 307 0.625 -3.9375 7 24.9375 24 25.875 21.75 306 0.9375 -2.25 8 24.75 24.25 25.5 23.25 310 0.75 -1 9 24.8125 24.125 26.75 23.25 306 1.9375 -0.875 

10 24.875 24.125 23.875 22.375 305 -1 -1.75 11 24.875 24.0625 25.25 23 306 0.375 -1.0625 12 24.9375 24 24.6875 21.125 305 -0.25 -2.875 13 24.9375 24 24.9375 23.5 312 0 -0.5 14 24.675 24.25 24.875 21.375 305 0.2 -2.875 15 24.75 24.1875 26.125 21 305 1.375 -3.1875 16 24.675 24.25 26.75 21.675 304 2.075 -2.575 17 24.75 24.675 24.6875 24.125 308 -0.0625 -0.55 18 24.75 24.675 25.125 24.1875 306 0.375 -0.4875 19 24.75 24.5625 25.675 22.875 311 0.925 -1.6875 20 24.75 24.5625 25.25 22.75 304 0.5 -1.8125 

Mean 306.6 0.7225 -1.9525 Standard Deviation 2.521486612 0.846680826 1.032566743 Azimuth Offset(deg) -0.172483649 Elevation Offset(deg) 0.46611475  pHit 50% pHit 75% pHit 90% pHit 95% pHit 99% # of shots (uncorrected) 1 1 1 1 1 # of shots (bias removed) 1 1 1 1 1 

15 
Range(ft) 40 

Date 10/16/2003 Time 14:00 Temp(F) 71 Ambient Pressure(mb) 1027 Projectile  Type Nylon  Caliber 0.68  Mass(g) 1.8 Shot # Aim X(in) Aim Y(in) Hit X(in) Hit Y(in) 

Muzzle Velocity(ft/s) X Error(in) Y Error(in) T

1 23.5 30.5 27.875 27.25 308 4.375 -3.25 2 23.5 30.5 24.675 24.75 307 1.175 -5.75 3 23 30.875 23 25.75 305 0 -5.125 4 23.125 30.75 25.675 29.675 313 2.55 -1.075 5 23.125 30.6875 25.8125 24.875 308 2.6875 -5.8125 6 23.125 30.675 23.75 30.25 311 0.625 -0.425 7 23.125 30.675 22.6875 27.5 311 -0.4375 -3.175 8 23.25 30.675 23.675 27 308 0.425 -3.675 9 23.3125 30.5625 22.6875 25.75 309 -0.625 -4.8125 

10 23.3125 30.5 23.75 25.125 309 0.4375 -5.375 11 23.4375 30.4375 25.675 24.5625 308 2.2375 -5.875 12 23.3125 30.5 23.1875 26.3125 311 -0.125 -4.1875 13 23.375 30.5 26.125 28.5625 309 2.75 -1.9375 14 23.375 30.5 26.9375 29.25 307 3.5625 -1.25 15 23.375 30.5 25.875 30.125 310 2.5 -0.375 16 23.375 30.5 19.75 26.875 307 -3.625 -3.625 17 23.375 30.5 22.675 23.75 311 -0.7 -6.75 18 23.4375 30.5 26.5625 26.5 307 3.125 -4 19 23.4375 30.4375 25.3125 26.75 310 1.875 -3.6875 20 23.4375 30.4375 28.3125 29.375 303 4.875 -1.0625 

Mean 308.6 1.384375 -3.56125 Standard Deviation 2.326053808 2.04507944 1.972662257 Azimuth Offset(deg) -0.165247135 Elevation Offset(deg) 0.425085106  pHit 50% pHit 75% pHit 90% pHit 95% pHit 99% # of shots (uncorrected) 1 1 1 1 1 # of shots (bias removed) 1 1 1 1 1 

16 
Range(ft) 60 

Date 10/17/2003 Time 12:03 Temp(F) 68 Ambient Pressure(mb) 1030 Projectile  Type Nylon  Caliber 0.68  Mass(g) 1.8 Shot # Aim X(in) Aim Y(in) Hit X(in) Hit Y(in) 

Muzzle Velocity(ft/s) X Error(in) Y Error(in) T

1 23 11/16 31 3/16 30 5/8 20.5 313 6.9375 -10.6875 2 23 11/16 31 32 11.5 309 8.3125 -19.5 3 23.5 35 1/8 24 3/4 21 7/8 308 1.25 -13.25 4 23.5 35 3/16 25 11/16 21 1/4 309 2.1875 -13.9375 5 23.5 35 3/16 24 3/8 33 1/4 316 0.875 -1.9375 6 23.5 35 1/8 21 7/8 27 11/16 315 -1.625 -7.4375 7 23 7/16 35 3/16 22 15/16 20 3/4 313 -0.5 -14.4375 8 23 7/16 35 3/16 34 3/4 32 1/8 313 11.3125 -3.0625 9 23.5 35 1/8 31 15/16 21 1/8 310 8.4375 -14 

10 23.5 35 1/8 24 7/16 23 307 0.9375 -12.125 11 23.5 35 1/8 34 3/16 21 1/16 312 10.6875 -14.0625 12 23 7/16 35 1/16 34 1/16 26 5/16 311 10.625 -8.75 13 23 9/16 35 27 1/8 33 5/8 314 3.5625 -1.375 14 23.5 35 31 7/16 32 3/4 308 7.9375 -2.25 15 23.5 35 26 1/16 28 15/16 309 2.5625 -6.0625 16 23 7/16 35 1/16 30 3/16 28 3/4 312 6.75 -6.3125 17 23 7/16 35 35 26 5/16 306 11.5625 -8.6875 18 23 7/16 35 28 3/4 31 1/16 313 5.3125 -3.9375 19 23 7/16 35 26 3/4 23 309 3.3125 -12 20 23 7/16 35 22 5/16 24 3/16 309 -1.125 -10.8125 

Mean 310.8 4.965625 -9.23125 Standard Deviation 2.783409496 4.3722489 5.076434688 Azimuth Offset(deg) -0.395145617 Elevation Offset(deg) 0.734559286  pHit 50% pHit 75% pHit 90% pHit 95% pHit 99% # of shots (uncorrected) 1 1 1 1 2 # of shots (bias removed) 1 1 1 1 1 

17 
Range(ft) 80 

Date 10/22/2003 Time 14:01 Temp(F) 69 Ambient Pressure(mb) 1010 Projectile  Type Nylon  Caliber 0.68  Mass(g) 1.8 Shot # Aim X(in) Aim Y(in) Hit X(in) Hit Y(in) 

Muzzle Velocity(ft/s) X Error(in) Y Error(in) T

1 23 1/8 36 7/8 18 1/16 28 312 -5.0625 -8.875 2 23.25 36.75 20.5 33 1/8 313 -2.75 -3.625 3 23 3/8 36.75 24.25 26.25 311 0.875 -10.5 4 23 7/16 36.75 2.75 17 5/8 311 -20.6875 -19.125 5 23 7/16 36.75 41 39 308 17.5625 2.25 6 21 7/8 36 9/16 6 7/8 15 1/4 305 -15 -21.3125 7 22 36.25 22 5/8 7 1/8 309 0.625 -29.125 8 21 7/8 44.25 0.75 24 1/4 304 -21.125 -20 9 21 7/8 44.25 28 1/8 30 7/8 308 6.25 -13.375 

10 22 1/16 44.25 38 45 5/8 309 15.9375 1.375 11 22 3/16 44 1/8 41 3/8 22 3/8 305 19.1875 -21.75 12 22 1/4 44 15 1/2 14 1/8 304 -6.75 -29.875 13 22 1/8 44 27 3/4 16 5/8 307 5.625 -27.375 14 22 1/8 44 37 1/8 41 1/2 310 15 -2.5 15 22 1/4 43 7/8 19 1/2 25 313 -2.75 -18.875 16 22 1/2 43.75 33 37 5/8 310 10.5 -6.125 17 22 1/2 43.75 0 20 3/8 308 -22.5 -23.375 18 22 1/2 43.75 33 5/8 33 309 11.125 -10.75 19 22 9/16 43.75 32 3/4 37 1/4 310 10.1875 -6.5 20 22 9/16 43.75 11 7/8 8 7/8 303 -10.6875 -34.875 

Mean 308.45 0.278125 -15.215625 Standard Deviation 2.999561371 13.3174715 10.90971989 Azimuth Offset(deg) -0.016599363 Elevation Offset(deg) 0.908039693  pHit 50% pHit 75% pHit 90% pHit 95% pHit 99% # of shots (uncorrected) 2 3 4 5 7 # of shots (bias removed) 1 2 2 3 4 

18 
Range pHit 50% pHit 75% pHit 90% pHit95% pHit 99% pHit 50% cor. pHit 75% cor. pHit 90% cor. pHit 

 20 1 1 1 1 1 1 1 1  40 1 1 1 1 1 1 1 1  60 1 1 1 1 2 1 1 1  80 2 3 4 5 7 1 2 2 Range 20 40 60 80 pHit 50% 1 1 1 2 pHit 75% 1 1 1 3 pHit 90% 1 1 1 4 pHit 95% 1 1 1 5 pHit 99% 1 1 2 7 pHit 50% cor. 1 1 1 1 pHit 75% cor. 1 1 1 2 pHit 90% cor. 1 1 1 2 pHit 95% cor. 1 1 1 3 pHit 99% cor. 1 1 1 4

19 
20 

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24 

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