Aerodynamic and Flight Dynamic Characteristics of 

5.56-mm Ammunition: M855 

by Sidra I. Silton and Bradley E. Howell 

ARL-TR-5182 May 2010 

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Army Research Laboratory 

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ARL-TR-5182 May 2010 

Aerodynamic and Flight Dynamic Characteristics of 

5.56-mm Ammunition: M855 

Sidra I. Silton 

Weapons and Materials Research Directorate, ARL 

Bradley E. Howell

Data Matrix Solutions, Inc. 

Approved for public release; distribution is unlimited. 
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Aerodynamic and Flight Dynamic Characteristics of 5.56-mm Ammunition: 

M855 

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Sidra I. Silton and Bradley E. Howell*

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U.S. Army Research Laboratory 

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Project Manager for Maneuver Ammunition Systems 

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Picatinny Arsenal, NJ 

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PM-MAS 

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14. ABSTRACT 

An experimental program for the aerodynamic and flight dynamic characterization of current 5.56-mm small-caliber 

ammunition has been developed and executed to further enable the U.S. Army’s understanding of the ammunition. This report 

is focused on the M855 round, one of the most commonly used ammunitions for the M4 and M16A2 weapons. The 

aerodynamic characterization of the M855 round was accomplished at muzzle velocity as well as simulated downrange 

velocities out to 600 m. The resulting aerodynamic data will be used to update the U.S. Army’s aerodynamic model of M855 

ammunition to create improved modeling ability. A flight dynamic characterization, to include yaw limit cycle and Magnus 

moment instabilities, was accomplished at the same velocities. The predicted downrange yaw limit cycles were compared with 

previously obtained at-range yaw limit cycles with some success. 

15. SUBJECT TERMS

5.56-mm ammunition, M855, aerodynamic experimental facility 

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OF ABSTRACT 

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19a. NAME OF RESPONSIBLE PERSON

Sidra I. Silton 

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Unclassified

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iii

Contents 

List of Figures iv

List of Tables viii

Acknowledgments ix

1. Introduction 1

2. Experimental Setup 1

2.1 Ammunition Types ..........................................................................................................2

2.2 Indoor Spark Range Facility............................................................................................5

2.3 Launch Considerations ....................................................................................................6

2.3.1 Gun Barrel .............................................................................................................6

2.3.2 Charge Establishment ............................................................................................8

2.3.3 Launch Yaw Control .............................................................................................8

2.4 Data Analysis ................................................................................................................10

3. Results and Discussion 11

3.1 Flow Analysis ................................................................................................................11

3.2 Trajectory Analysis .......................................................................................................13

3.3 Spin Rates ......................................................................................................................19

3.4 Aerodynamic Coefficients .............................................................................................19

3.5 Dynamic Stability ..........................................................................................................29

4. Summary and Conclusions 43

5. References 44

Appendix A. Motion Plots 45

Appendix B. Complete Set of 6-Degrees-of-Freedom (6-DOF) Fits 65

Appendix C. Complete Set of Magnus Moment Plots 93

Distribution List 98 
iv

List of Figures 

Figure 1. Yaw behavior of small-caliber ammunition over its first 600 m of flight. ......................2

Figure 2. The 5.56-mm ammunition types tested in the current study. ..........................................3

Figure 3. Close-up picture of M855 ammunition discussed in this report. .....................................3

Figure 4. Dimensions of the M855 ammunition. ............................................................................4

Figure 5. Schematic of ARL’s AEF. ...............................................................................................5

Figure 6. Close view of a spark shadowgraph station in ARL’s AEF. ...........................................6

Figure 7. M16A2 weapon mounted in original hard mount and recoil mount. ..............................7

Figure 8. Angled cardboard setup for yaw induction. ....................................................................9

Figure 9. ARFDAS parameter identification process. ..................................................................10

Figure 10. Spark shadowgraph picture, shot 28096, station 40H, Mach 1.47. .............................11

Figure 11. Spark shadowgraph picture, shot 27353, station 15H, Mach 1.69. .............................12

Figure 12. Spark shadowgraph picture, shot 26833, station 15H, Mach 2.21. .............................12

Figure 13. Spark shadowgraph picture, shot 26598, station 45H, Mach 2.61. .............................12

Figure 14. Total aerodynamic coefficient definition relative to projectile. ..................................14

Figure 15. Pitch angle vs. range for round 28097 (M855 at Mach 1.47). .....................................14

Figure 16. Yaw angle vs. range for round 28097 (M855 at Mach 1.47). .....................................15

Figure 17. Pitch angle vs. yaw angle for round 28097 (M855 at Mach 1.47). .............................15

Figure 18. Total yaw vs. range for round 28097 (M855 at Mach 1.47). ......................................16

Figure 19. Roll angle vs. range for round 28097 (M855 at Mach 1.47). ......................................16

Figure 20. Spin vs. range for round 28097 (M855 at Mach 1.47). ...............................................17

Figure 21. Vertical position vs. range for round 28097 (M855 at Mach 1.47). ............................17

Figure 22. Lateral position vs. range for round 28097 (M855 at Mach 1.47). .............................18

Figure 23. Three-dimensional projectile motion through the range for round 28097 

(M855 at Mach 1.47). ..............................................................................................................18

Figure 24. Preliminary Magnus moment coefficient plot to determine groupings for 

nonlinear characteristics. ..........................................................................................................21

Figure 25. Total axial force coefficient vs. Mach number, group fits. .........................................21

Figure 26. Zero-yaw axial force coefficient vs. Mach number, group fits. ..................................22

Figure 27. Roll-damping coefficient vs. Mach number, group fits. .............................................23

Figure 28. Total pitching moment coefficient vs. Mach number, group fits. ...............................23

Figure 29. Linear pitching moment coefficient vs. Mach number, group fits. .............................24
v

Figure 30. Cubic pitching moment coefficient vs. Mach number, group fits. ..............................24

Figure 31. Normal force coefficient derivative vs. Mach number, group fits. .............................25

Figure 32. Normal force center of pressure vs. Mach number, group fits. ...................................26

Figure 33. Magnus moment coefficient derivative vs. Mach number, group fits. ........................27

Figure 34. Zero-yaw Magnus moment coefficient derivative vs. Mach number, group fits. .......27

Figure 35. Cubic Magnus moment coefficient derivative vs. Mach number, group fits. .............28

Figure 36. Pitch-damping moment coefficient vs. Mach number, group fits. ..............................28

Figure 37. Modal arm damping exponent definitions. ..................................................................29

Figure 38. Shot 27344 (Mach 1.69) showing F < 0 and S > 0. ..................................................29

Figure 39. Shot 27352 (Mach 1.70) showing F < 0and S < 0. ...................................................30

Figure 40. Modal arm damping exponents, Mach 1.15–1.20. ......................................................31

Figure 41. Modal arm damping exponents, Mach 1.45–1.49. ......................................................32

Figure 42. Modal arm damping exponents, Mach 1.65–1.73. ......................................................32

Figure 43. Modal arm damping exponents, Mach 2.17–2.25. ......................................................33

Figure 44. Modal arm damping exponents, Mach 2.60–2.63. ......................................................33

Figure 45. Modal arm damping exponents with matched spin, Mach 1.2. ...................................35

Figure 46. Modal arm damping exponents with matched spin, Mach 1.5. ...................................35

Figure 47. Modal arm damping exponents with matched spin, Mach 1.7. ...................................36

Figure 48. Magnus moment coefficient with stability bounds at Mach 1.18. ..............................37

Figure 49. Magnus moment coefficient with stability bounds at Mach 1.47. ..............................38

Figure 50. Magnus moment coefficient with stability bounds at Mach 1.48. ..............................38

Figure 51. Magnus moment coefficient with stability bounds at Mach 1.70. ..............................39

Figure 52. Magnus moment coefficient with matched spin stability bounds at Mach 1.18. ........39

Figure 53. Magnus moment coefficient with matched spin stability bounds at Mach 1.48. ........40

Figure 54. Magnus moment coefficient with matched spin stability bounds at Mach 1.7. ..........40

Figure 55. Yaw limit cycle: yaw vs. velocity. ..............................................................................41

Figure 56. The 6-DOF simulation to 600 m of the M855 projectile using experimentally 

determined aerodynamic coefficients. .....................................................................................42 

Figure A-1. Pitch angle vs. range for round 29271 (M855 at Mach 1.18). ..................................45

Figure A-2. Yaw angle vs. range for round 29271 (M855 at Mach 1.18). ...................................46

Figure A-3. Pitch angle vs. yaw angle for round 29271 (M855 at Mach 1.18). ...........................46

Figure A-4. Total yaw vs. range for round 29271 (M855 at Mach 1.18). ....................................47

Figure A-5. Roll angle vs. range for round 29271 (M855 at Mach 1.18). ....................................47

Figure A-6. Spin vs. range for round 29271 (M855 at Mach 1.18). .............................................48
vi

Figure A-7. Vertical position vs. range for round 29271 (M855 at Mach 1.18). .........................48

Figure A-8. Lateral position vs. range for round 29271 (M855 at Mach 1.18). ...........................49

Figure A-9. Three-dimensional projectile motion through the range for round 29271 

(M855 at Mach 1.18). ..............................................................................................................49

Figure A-10. Pitch angle vs. range for round 27353 (M855 at Mach 1.69). ................................50

Figure A-11. Yaw angle vs. range for round 27353 (M855 at Mach 1.69). .................................50

Figure A-12. Pitch angle vs. yaw angle for round 27353 (M855 at Mach 1.69). .........................51

Figure A-13. Total yaw vs. range for round 27353 (M855 at Mach 1.69). ..................................51

Figure A-14. Roll angle vs. range for round 27353 (M855 at Mach 1.69). ..................................52

Figure A-15. Spin vs. range for round 27353 (M855 at Mach 1.69). ...........................................52

Figure A-16. Vertical position vs. range for round 27353 (M855 at Mach 1.69). .......................53

Figure A-17. Lateral position vs. range for round 27353 (M855 at Mach 1.69). .........................53

Figure A-18. Three-dimensional projectile motion through the range for round 27353 

(M855 at Mach 1.69). ..............................................................................................................54

Figure A-19. Pitch angle vs. range for round 26833 (M855 at Mach 2.21). ................................54

Figure A-20. Yaw angle vs. range for round 26833 (M855 at Mach 2.21). .................................55

Figure A-21. Pitch angle vs. yaw angle for round 26833 (M855 at Mach 2.21). .........................55

Figure A-22. Total yaw vs. range for round 26833 (M855 at Mach 2.21). ..................................56

Figure A-23. Roll angle vs. range for round 26833 (M855 at Mach 2.21). ..................................56

Figure A-24. Spin vs. range for round 26833 (M855 at Mach 2.21). ...........................................57

Figure A-25. Vertical position vs. range for round 26833 (M855 at Mach 2.21). .......................57

Figure A-26. Lateral position vs. range for round 26833 (M855 at Mach 2.21). .........................58

Figure A-27. Three-dimensional projectile motion through the range for round 26833 

(M855 at Mach 2.21). ..............................................................................................................58

Figure A-28. Pitch angle vs. range for round 26597 (M855 at Mach 2.63). ................................59

Figure A-29. Yaw angle vs. range for round 26597 (M855 at Mach 2.63). .................................59

Figure A-30. Pitch angle vs. yaw angle for round 26597 (M855 at Mach 2.63). .........................60

Figure A-31. Total yaw vs. range for round 26597 (M855 at Mach 2.63). ..................................60

Figure A-32. Roll angle vs. range for round 26597 (M855 at Mach 2.63). ..................................61

Figure A-33. Spin vs. range for round 26597 (M855 at Mach 2.63). ...........................................61

Figure A-34. Vertical position vs. range for round 26597 (M855 at Mach 2.63). .......................62

Figure A-35. Lateral position vs. range for round 26597 (M855 at Mach 2.63). .........................62

Figure A-36. Three-dimensional projectile motion through the range for round 26597 

(M855 at Mach 2.63). ..............................................................................................................63
vii

Figure C-1. Magnus moment coefficient with stability bounds at Mach 1.68. ............................93

Figure C-2. Magnus moment coefficient with stability bounds at Mach 2.21. ............................93

Figure C-3. Magnus moment coefficient with stability bounds at Mach 2.24. ............................94

Figure C-4. Magnus moment coefficient with stability bounds at Mach 2.46. ............................94

Figure C-5. Magnus moment coefficient with stability bounds at Mach 2.62. ............................95
viii

List of Tables 

Table 1. M855 projectile physical parameters. ...............................................................................3

Table 2. Shots fired at each Mach number for M855 ammunition. ................................................5

Table 3. Nominal charge weights for M855. ..................................................................................8

Table 4. List of shots that used a yaw modifier. .............................................................................9

Table 5. Aerodynamic coefficients used in 6-DOF analysis. .......................................................13

Table 6. Other 6-DOF analysis parameters of interest. ................................................................13

Table 7. Probable error for final group fit analyses. .....................................................................19

Table 8. Multiple shot group fit aerodynamic coefficients. ..........................................................20

Table 9. Velocity matched spin rate as determined from PRODAS. ............................................34
ix

Acknowledgments 

The authors would like to thank the following U.S. Army Research Laboratory personnel: 

• Ronald Anderson for reading the spark range film images and digitizing the data; 

• Bernard Guidos and Ilmars Celmins for their input during technical review; 

• James Hall at the machine shop for spin pin insertion; 

• Robert Keppinger for measuring and recording projectile physical parameters; 

• Donald McClellan for film developing, setup, and vast experience; 

• Kenneth Paxton for film developing, setup, and data acquisition; 

• Tom Puckett for acting as test director and gunner; 

• Joyce Smith for reading the spark range film images and digitizing the data; 

• Gregory Watt for reading the spark range film images and digitizing the data; and 

• Dr. Paul Weinacht for providing the velocities associated with the downrange locations for 

each ammunition type and multiple discussions pertaining to the limit cycle/trim angle 

determinations. 

The authors would also like to thank Wayne Hathaway for his technical assistance in the initial 

analysis of the spark range data using the Aeroballistics Research Facility Data Analysis System 

reductions. 
x

INTENTIONALLY LEFT BLANK. 
1

1. Introduction 

The aerodynamic and flight dynamic characterization of ammunition is an essential element in 

any study for which the basic understanding of the projectile flight is desired. Over the past 

several years, there had been a renewed interested in small-caliber ammunition, specifically the 

5.56-mm ammunition. Although this caliber of ammunition has been used by the U.S. Army for 

many years, there is a limited amount of either aerodynamic or flight dynamic data available. 

In order to better understand the current generation of 5.56-mm ammunition, the Project 

Manager for Maneuver Ammunition Systems under the Program Executive Office for 

Ammunitions made the decision to fund the aerodynamic and flight dynamic characterization of 

many of the 5.56-mm ammunitions currently in use by the Soldier. This characterization, out to 

simulated ranges of 600 m, was undertaken by the Aerodynamics Branch at the U.S. Army 

Research Laboratory (ARL). As the testing was quite comprehensive (seven ammunition types), 

a series of reports will be presented to cover the findings. 

The current report presents the findings from the study completed on the M855 ammunition in 

the Aerodynamic Experimental Facility (AEF) at ARL. While the M855 ammunition had been 

previously tested and reported on by McCoy (1), a very limited number of rounds (seven total) 

were available for aerodynamic data. Slightly more data was obtained for the real-range yaw 

limit cycle tests (between 10 and 15 rounds at each range). Therefore, the current test was 

completed to supplement this original data, providing a more complete understanding of the 

ammunition. Of particular interest is the ability to predict the yaw limit cycle using simulated 

ranges, as real-range yaw limit cycle tests are costly. 

2. Experimental Setup 

The spark range test was designed to determine the aerodynamics and flight dynamics of the 

5.56-mm projectiles investigated over their first 600 m of flight. Prior to the test, the projectile’s 

physical properties, not including asymmetries, were measured. During the spark range test, the 

projectiles and flow field images were studied, and the spin rates of the projectiles were tracked. 

The subsequent analysis characterized the observed flight dynamics of each configuration and 

defined the aerodynamic model of each projectile at Mach numbers corresponding to the 

approximate velocities at the muzzle and 200, 400, and 600 m downrange. The velocities 

corresponding to these ranges were chosen based on the known flight behavior of small-caliber 

projectiles (figure 1), with each range of interest indicated by the small circle. The projectile 
2

Figure 1. Yaw behavior of small-caliber ammunition over its first 600 m of flight. 

exits the muzzle with some angular rate that causes yaw, hence the muzzle conditions. Due to 

the dynamic stability of the round, this yaw is known to damp out over the first 100–150 m of 

flight. It is desired to understand the projectile’s aerodynamic behavior once the projectile yaw 

has damped out (200-m velocity). Between 300 and 400 m, a dynamic instability begins to 

occur, causing the yaw to grow. The cause of this dynamic instability isn’t well understood, and 

a better aerodynamic characterization will always be helpful. By 600 m, a yaw limit cycle is 

believed to exist, and an aerodynamic characterization will help to better quantify the level. 

2.1 Ammunition Types 

Seven common 5.56-mm ammunition types were tested over the course of the study (figure 2): 

M193, M855, MK262, IMI, Sierra 69 gr, ATK 86 gr, and M995. The focus of this report is the 

M855 ammunition, specifically, the R011 reference lot (figure 3). The key dimensional and 

physical characteristics of the M855 ammunition are listed in table 1 and were obtained by 

measuring five projectiles and averaging the results. The reference diameter, d, corresponding to 

the maximum diameter of the projectile, is 5.69 mm. Figure 4 displays the key dimensions, in 

calibers, for the M855. The reader should note that the dimensions in figure 4 are not the same as 

those reported by McCoy (1), which were obtained by measuring the projectile on an optical 

comparator. The projectile physicals, however, are nearly identical. Most, but not all, of the 
3

Figure 2. The 5.56-mm ammunition types tested in 

the current study. 

Figure 3. Close-up picture of 

M855 ammunition 

discussed in this report. 

Table 1. M855 projectile physical parameters. 

Length (mm) 23.057 

Mass, m (g) 4.04 

Center of Gravity, XCG (mm from nose) 14.279 

Axial Moment of Inertia, I x (g-cm2) 0.1416 

Transverse Moment of Inertia, I y (g-cm2) 1.138 
4

Figure 4. Dimensions of the M855 ammunition. 

projectiles were fitted with a spin pin to allow for a spin analysis. The spin pins were 0.031-indiameter piano wire or solid steel pins inserted into the base of the projectile ~0.065 in off the 

centerline. The wire was inserted into the base of the projectile such that 0.050–0.060 in were 

exposed behind the projectile. The length of the exposed spin pin was recorded for each relevant 

shot. 

For each Mach number, a minimum of five data rounds across a spectrum of yaw levels was 

obtained. For the M855 ammunition, 38 rounds across five Mach numbers were used in the final 

analysis. Table 2 shows the Mach number used for the corresponding downrange location and 

the number of rounds included in the final analysis. Five Mach numbers were investigated for 

the M855 rather than the intended four because the Mach number originally chosen for the 

equivalent 600-m-downrange location (Mach 1.5) was found to correspond to the velocity at 

450 m downrange when a trajectory analysis with the revised drag data was accomplished. The 

decision was made that additional data at the lower Mach number was necessary for a complete 

characterization of the flight dynamics as this is the critical Mach number regime for yaw 

growth. As such, a follow-on test was conducted to obtain data rounds for analysis at Mach 1.2, 

the newly determined 600-m-downrange velocity. Additional rounds were used for charge 

establishment at the Mach numbers associated with the downrange location or designated as a 

warmer round for setup and range instrumentation calibration.
5

Table 2. Shots fired at each Mach number for 

M855 ammunition. 

Equivalent 

Location 

Mach 

No. 

No. of 

Shots 

Muzzle 2.6 5 

200 m 2.2 8 

400 m 1.7 8 

450 m 1.5 11 

600 m 1.2 6 

2.2 Indoor Spark Range Facility 

The firings were conducted in the ARL AEF (2). This facility is a 100-m-long spark 

shadowgraph facility designed to obtain aerodynamic coefficients from free-flight trajectory 

data. A schematic of the facility is shown in figure 5. 

Figure 5. Schematic of ARL’s AEF. 

There are 39 dual-plane, direct-image spark shadowgraph stations arranged in five groups, with 

the first station ~1.8 m from the muzzle of the gun (i.e., end of flash suppressor) for most of the 

current test. For the Mach 1.2 shots, the gun muzzle was 1.9 m from the first station. A close 

view of a shadowgraph station is shown in figure 6. As the projectile passes each station, an 

infrared sensor triggers the spark source that causes the projectile image to be captured on 

29.9-  35.6-cm (11-  14-in) film. The spark sources are connected to a computer so that the 

time when the spark source is triggered can be recorded. Each station is surveyed into a fiducial 

system that is simultaneously imaged onto the film with the projectile.
6

Figure 6. Close view of a spark shadowgraph station in ARL’s AEF. 

The film is developed after each shot and then read on a precision light table to produce the 

measured spatial coordinates (range, deflection, altitude) and angular orientation (pitch, yaw, 

roll) relative to an earth-fixed range coordinate system, all as a function of the spark time. 

The expected accuracy of the measured positions and angles is as follows: 

• position: 0.0003–0.0005 m, 

• pitch/yaw: 0.05°–0.10°, and 

• roll: 1.0°–5.0°. 

The measurement accuracy depends on the flow conditions and model contours. The accuracy 

of the roll orientation also depends on the distance between the model centerline and the radial 

position to the roll pin. For these 5.56-mm ammunition types, the accuracy is slightly less than 

the values just indicated. Even though the AEF was constructed in 1943, it remains the most 

accurate spark range in the world. 

2.3 Launch Considerations 

2.3.1 Gun Barrel 

The M16A2 weapon (figure 7) was secured into either a hard or recoil mount. Due to the 

requirements of other testing that used these ammunition types, the mount was modified as the 

testing progressed. For the Mach 1.2 shots, an M4 weapon was secured in the recoil mount. 
7

Figure 7. M16A2 weapon mounted in original hard mount and recoil mount. 

Neither mount appeared to affect the aerodynamics or flight dynamics of the projectile. Both 

weapon barrels had an interior bore diameter of 5.56 mm and a gun twist of 1 revolution in 

7 inches (1-in-7 twist). The difference between the weapons is that the M16A2 barrel is 20 in 

long, while the M4 barrel is only 16 in long. The shorter barrel made it easier to consistently 

obtain the lower velocity. The flash suppressor was used at all times on both weapons. The 

mounts allowed for adjustments in gun aim point to ensure projectile travel through the entire 

range and for easy barrel swap. Both mounts provided support under the barrel. Additionally, a 
8

20-lb shot bag was placed on top of the barrel to simulate a soldier holding the weapon (not 

shown in hard mount). Initially, the weapon was fired remotely using a lanyard on the trigger. 

This was modified to a hydraulic-controlled system to eliminate the possible jerking of the 

weapon due to the lanyard (again, this does not affect the aerodynamics of the projectile in flight 

but possibly produces more consistent launch dynamics). 

2.3.2 Charge Establishment 

A charge establishment study was conducted prior to firing the actual test in order to determine a 

nominal charge weight for each desired velocity. The primed cases were standard M855 

cartridge cases, and the standard WC844 powder was used for the higher velocities. For the 

lower velocities, it was necessary to use a faster burning powder (IMR 4198) to help ensure that 

consistent velocities were obtained. Additionally, at the lowest velocities, when the cartridges 

cases were only partially full, either tissue paper or 0.125-in-thick pink foam discs, 0.3125 inch 

in diameter, were used as ullage to provide for a more consistent powder burn. The approximate 

charge weights required to obtain the desired midrange velocities are shown in table 3. 

Table 3. Nominal charge weights for M855. 

Velocity Propellant Charge Weight 

(gr) 

Mach 2.6 WC844 26.1 

Mach 2.2 WC844 23.9 

Mach 1.7 IMR 4198 13.2 

Mach 1.5 IMR 4198 10.6 

Mach 1.2 IMR 4198 9.5 

2.3.3 Launch Yaw Control 

In order to obtain nonlinear aerodynamic coefficients, it is necessary to measure the flight 

dynamics across a characteristic spread of the anticipated flight yaw. To ensure a spread in yaw 

levels, a standard technique used in spark range testing is to produce variability in yaw with a 

yaw inducer. 

The range of first maximum yaw values varied between Mach numbers. For the M855, only the 

Mach 1.2 shots achieved the required spread of first maximum yaw without yaw induction. For 

the remainder of the downrange Mach numbers investigated, a yaw inducer was used to increase 

the launch yaw spread. During a previous study of 5.56-mm ammunition types, multiple halfmoon-type inducers were tried with minimal success. It was found that one or more pieces of 

cardboard, angled at 45° and spaced 1 in apart (when more than one sheet was used), provided 

the most consistent yaw induction (figure 8). Table 4 lists those shots that used a yaw modifier.
9

Figure 8. Angled cardboard setup for yaw induction. 

Table 4. List of shots that used a yaw modifier. 

Shot No. Mach No. 

Pieces of 

Cardboard 

26831 

2.2 

2 

26832 3 

26833 3 

26834 3 

27350 

1.7 

4 

27351 4 

27352 4 

27353 4 

28104 

1.5 

1 

28105 1 

28106 1 

28107 1 
10

2.4 Data Analysis 

Extraction of the aerodynamic coefficients and dynamic derivatives is the primary goal in 

analyzing the trajectories measured in the AEF spark range. The process is summarized in 

figure 9 and is accomplished with the Aeroballistics Research Facility Data Analysis System 

(ARFDAS) code (3). ARFDAS incorporates a standard linear theory analysis (4, 5) and a 

6-degrees-of-freedom (6-DOF) numerical integration technique (6). The 6-DOF routine 

incorporates the maximum likelihood method (MLM) to match the theoretical trajectory to the 

experimentally measured trajectory. The MLM is an iterative procedure that adjusts the 

aerodynamic coefficients to maximize a likelihood function. Using this likelihood function 

eliminates the inherent assumption in least squares theory that the magnitude of the measurement 

noise must be consistent between dynamic parameters (regardless of units). In general, the 

aerodynamic coefficients can be nonlinear functions of the angle of attack (AOA), Mach 

number, and aerodynamic roll angle. 

Figure 9. ARFDAS parameter identification process. 

ARFDAS represents a complete ballistics range data reduction system capable of analyzing 

symmetric and asymmetric bodies. Within ARFDAS, each data round was first analyzed 

individually; then, rounds were combined in appropriate Mach number groups for simultaneous 

analysis via the multiple fit capability. Multiple fits are also used to extract the nonlinear 

aerodynamic coefficients as a function of yaw and Mach number dependence.

6-DOF Dynamic Data 

t, x, y, z, 

ARFDAS 

Startup 

Linear Theory 

Analysis 

6DOF Symmetric 

Analysis 

Aerodynamic Forces and Moments vs. 

MachNo. & Angle of Attack & Roll Angle 

Physical 

Properties 

Fit Theoretical 

to Experimental 

Single & 

Multiple Fits 

Atmospheric 

Conditions 
11

As part of the data reduction, ARFDAS provides an estimate of the fast- and slow-mode 

damping estimates. Additionally, an estimate of the Magnus bounds from which any Magnus 

moment instability can be determined is also given. Both of these estimates are for the projectile 

spin rate in the given shot. Note the projectile is not spin-matched at muzzle exit for the 

downrange velocities as it is fired from an M16, not a high-twist barrel. Therefore, the 

nondimensional spin rate is below that which the projectile would experience in flight. 

3. Results and Discussion 

3.1 Flow Analysis 

Analyses of the spark shadowgraphs show minimal differences between the flow fields of the 

different velocities. Figures 10–13 show shadowgraphs for shots at Mach 1.47, 1.69, 2.21, and 

2.61, respectively. At all speeds, a shock wave stands just off the nose tip of the projectile, with 

the distance between the shock and the nose tip decreasing with increasing Mach number such 

that the shock looks almost attached at Mach 2.6. Additionally, the shock angle becomes smaller 

at higher Mach numbers, as expected. The turbulent wake flow evident behind the base remains 

consistent between Mach numbers. No shadowgraph is shown for shots at Mach 1.2 as it is very 

similar to that at Mach 1.47, only the shock angle further decreases. 

Figure 10. Spark shadowgraph picture, shot 28096, 

station 40H, Mach 1.47.
12

Figure 11. Spark shadowgraph picture, shot 27353, 

station 15H, Mach 1.69. 

Figure 12. Spark shadowgraph picture, shot 26833, 

station 15H, Mach 2.21. 

Figure 13. Spark shadowgraph picture, shot 26598, 

station 45H, Mach 2.61.
13

3.2 Trajectory Analysis 

The aerodynamic coefficients listed in table 5 were the set of fitted parameters in the 6-DOF 

analysis. Additional parameters of interest from the 6-DOF analysis are listed in table 6. The 

commonly used second-order aerodynamic expansions relating total, zero yaw, and yaw-induced 

coefficients for the nonlinear analysis are presented in reference 4. Figure 14 defines the total 

positive aerodynamic coefficients relative to the projectile. Note the pitch-damping coefficient is 

not shown. 

Table 5. Aerodynamic coefficients used in 6-DOF analysis. 

Variable Description 

CX Axial force coefficient 

X0 C Zero-yaw axial force coefficient 

X2 C Yaw axial force coefficient 

m C Overturning moment coefficient derivative 

 0

Cm Zero-yaw overturning moment coefficient derivative 

 3

Cm Cubic overturning moment coefficient derivative 

N C Normal force coefficient derivative 

m m C C q  Pitch-damping moment coefficient 

p Cl Roll-damping coefficient 

p Cn Magnus moment coefficient 

np C Magnus moment coefficient derivative 

p 0

Cn Zero-yaw Magnus moment coefficient derivative 

p 3

Cn Cubic Magnus moment coefficient derivative 

Table 6. Other 6-DOF analysis parameters of interest. 

Variable Description Units 

α (alpha bar) Total yaw Degrees 

max Maximum yaw Degrees 

δ Mean yaw Degrees 

2 δ Mean squared yaw Degrees squared 

 (phi) Roll angle Degrees 

 (theta) Pitch angle Degrees 

 (psi) Yaw angle Degrees 

XCP Normal force center of pressure Calibers 

PEx Probable error in x Meters 

PEyz Probable error in y-z Meters 

PE Probable error in  -  Degrees 

PE Probable error in  Degrees 
14

Figure 14. Total aerodynamic coefficient definition relative to projectile. 

From the film reading, the actual projectile motion is known (i.e., the raw data). During the 

ARFDAS reduction, the projectile motion based on the aerodynamic model, as determined by 

the 6-DOF fit for each round, is simulated. Figures 15–23 are a complete set of motion plots for 

shot 28097, an M855 projectile at Mach 1.47 (simulated 500-m range). In each figure, the 

circles represent the raw data and the solid line represents the 6-DOF fit. A complete set of 

motion plots is presented in appendix A for a representative round at each Mach number. 

Figure 15. Pitch angle vs. range for round 28097 (M855 at Mach 1.47).
15

Figure 16. Yaw angle vs. range for round 28097 (M855 at Mach 1.47). 

Figure 17. Pitch angle vs. yaw angle for round 28097 (M855 at Mach 1.47).
16

Figure 18. Total yaw vs. range for round 28097 (M855 at Mach 1.47). 

Figure 19. Roll angle vs. range for round 28097 (M855 at Mach 1.47).
17

Figure 20. Spin vs. range for round 28097 (M855 at Mach 1.47). 

Figure 21. Vertical position vs. range for round 28097 (M855 at Mach 1.47).
18

Figure 22. Lateral position vs. range for round 28097 (M855 at Mach 1.47). 

Figure 23. Three-dimensional projectile motion through the range for round 28097 (M855 at Mach 1.47).
19

The probable errors for the final ARFDAS multiple shot group fits at each Mach number are 

shown in table 7. The multiple fits were separated into high and low yaw groupings because the 

nonlinear characteristics of the projectiles were dependant on yaw. Some groups have a very 

limited yaw variation, thus making it difficult to determine the nonlinear coefficients. The group 

at Mach 2.46 was created using shots at Mach 2.6 and 2.25 to result in an average of Mach 2.46. 

The aerodynamic coefficients resulting from these fits (both individual and group) are able to 

reproduce the flight of the projectile observed in the range. 

Table 7. Probable error for final group fit analyses. 

Mach 

No. 2 (degree )

δ2

PEx

(m) 

PEyz

(m) 

PE

(degree) 

PE

(degree) 

2.62 2.97 0.0003 0.0004 0.3166 5.1636 

2.46 6.10 0.0003 0.0002 0.2661 7.1820 

2.24 6.27 0.0003 0.0002 0.2517 5.0596 

2.21 6.68 0.0004 0.0002 0.2752 6.3327 

1.68 28.08 0.0005 0.0003 0.2496 11.2821 

1.70 6.00 0.0005 0.0002 0.2304 6.2651 

1.47 10.61 0.0004 0.0001 0.2116 6.0615 

1.49 6.73 0.0004 0.0001 0.2405 4.4380 

1.18 13.04 0.0005 0.0001 0.2146 5.1990 

3.3 Spin Rates 

Spin rates were obtained as a function of range position from fits to the roll pin data, when 

available. When unavailable, due to lack of roll pin (as was the case for seven projectiles), the 

initial spin rate and roll-damping coefficient is prescribed using the results from the group fits at 

a similar Mach number. At each of the downrange velocities investigated, the projectile is in an 

underspun condition, i.e., it is spinning at a slower rate than it would be had it been launched at 

full spin and velocity and allowed to arrive at the downrange velocity with drag and roll 

damping. The underspun condition occurs because although the downrange velocity is 

approximately matched, the projectile is being launched from a standard M16A2 (or M4) barrel 

with a twist rate of 1-in-7. In order to match the spin that occurs at the downrange velocities, 

higher twist barrels would have to be used (e.g., 1-in-6, 1-in-5, etc.). Previous computational and 

experimental works (7, 8) have shown that small changes in spin rate, such as these, have 

minimal effect on the aerodynamic behavior of 5.56-mm projectiles. To date, the effect on the 

flight dynamic behavior has not been characterized. 

3.4 Aerodynamic Coefficients 

The results of the multiple shot group fits are presented, analyzed, and compared here. The 

aerodynamic coefficients obtained from the multiple shot group fits are listed in table 8. The 

results of all individual shots and multiple shot groups can be found in appendix B.
20

Table 8. Multiple shot group fit aerodynamic coefficients. 

Mach No. 2 δ X0 C X2 C Nα C α0

Cm α3Cm 0 npα C 3 npα C m m q α C +C p Cl

2.62 2.97 0.29 3a 2.93 2.45 –3a 0.32 0a –15.74 –0.026

2.46 6.1 0.33 3.82 2.89 2.53 –4a 0.19 0a –11.82 –0.026

2.23 6.13 0.32 2.31 2.92 2.54 –4.98 0.02 25.52 –11.43 –0.025

1.68 28.08 0.38 2.30 2.97 2.71 –1.98 0.07 8.08 –11.97 –0.028

1.47 13.29 0.40 4.37 2.87 2.76 –1.63 –0.20 22.13 –10.21 –0.030

1.18 13.04 0.45 3.36 2.72 2.81 11.77 –0.82 75.53 –8.54 –0.026 a

Indicates that value was prescribed in 6-DOF fit. 

The multiple fits for the aerodynamic coefficients were separated into high and low yaw 

groupings for each Mach number as some of the nonlinear coefficients (specifically, Magnus 

moment coefficient) varied depending on yaw levels. The nonlinear variation in p Cn was easy 

to recognize from the initial individual fits. By plotting p Cn against sin2(α) (figure 24), a 

change in the behavior of p Cn is noticeable at about  = 4.5° at Mach 1.5 and 1.7. For these 

Mach numbers, the high and low yaw groupings must be solved separately in order to obtain the 

best fit. Since the high yaw shots provided a better fit for the nonlinear coefficients, only those 

groupings are displayed in the table. This bimodal behavior was not apparent at any other Mach 

number. Therefore, only one grouping was created for the multiple fit in ARFDAS. There were 

enough good shots to create two groupings at Mach 2.2, even though the mean yaw was similar. 

The differences in aerodynamic coefficients between the two groups are the approximate error 

associated with that coefficient, and, therefore, only one set of coefficients is presented. 

Figure 25 shows the axial force coefficient as a function of Mach number for both the current test 

data and previous data from the earlier study conducted by Robert McCoy (1). Total axial force, 

defined as 

0 2

2 , C =C +C XX X δ (1) 

in which 2  is the value determined by ARFDAS for the group fit (converted to radians 

squared), appears to decrease slightly as the Mach number increases. The current test data 

coincides with McCoy’s values, and both data sets behave as expected. The small discrepancies 

between McCoy’s values and the current data set can easily be accounted for by using CX rather 

than McCoy’s CD, though they are approximately equal for the small angles found here. The 

axial forces decrease slightly as the Mach numbers increase out of the high drag transonic 

regime. The trend of zero-yaw axial force as a function of Mach number (figure 26) is quite 

similar to that of CX , indicating that similar yaw levels are achieved for all the shots. The small 

difference in value is accounted for by the yaw drag.
21

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 0.002 0.004 0.006 0.008 0.01 0.012

Sin2

(α)

Mach ~1.2

Mach ~1.5

Mach ~1.7

Mach ~2.2

Mach ~2.6

p n C

Figure 24. Preliminary Magnus moment coefficient plot to determine groupings for nonlinear characteristics. 

0

0.1

0.2

0.3

0.4

0.5

0.6

1 1.5 2 2.5 3

Mach Number

Test Data

M855-McCoy

X

C

Figure 25. Total axial force coefficient vs. Mach number, group fits.
22

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

Mach Number

0 X

C

Figure 26. Zero-yaw axial force coefficient vs. Mach number, group fits. 

The roll-damping coefficient, presented in figure 27, varies little with Mach number. With the 

exception of two low yaw groups at Mach 1.5 and 1.7, the coefficient only ranged from –0.025 

to –0.03. The difference in 

p

Cl at Mach 1.5 is quite small and can easily be attributed to 

experimental error. It is unclear at this time what could be the cause of the larger pCl for the 

lower yaw grouping at Mach 1.7. At this time, no further explanation beyond experimental error 

is feasible. 

Figure 28 shows the total pitching moment for the current test data and McCoy’s data. 

Agreement between the two data sets is quite good, with the difference well within experimental 

error. As the Mach number increases, the pitching moment gradually decreases. Figures 29 and 

30 illustrate the correlation of the linear pitching moment coefficient and cubic pitching moment 

coefficient vs. Mach number. While the linear pitching moment coefficient followed a similar 

trend as the overall pitching coefficient, the cubic pitching moment coefficient did not. It 

appears that the nonlinear pitching moment is relatively constant above Mach 1.5, with 

differences possibly due to variation in yaw levels. As the Mach number further decreases to 

Mach 1.2, there appears to be a drastic change in sign and magnitude for the nonlinear pitching 

moment. This indicates that the nonlinear behavior becomes a greater influence on the pitching 

moment as Mach 1 is approached, which is not unreasonable.
23

-0.035

-0.030

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

Mach Number

p l C

Figure 27. Roll-damping coefficient vs. Mach number, group fits. 

0

0.5

1

1.5

2

2.5

3

3.5

1 1.5 2 2.5 3

Mach Number

Test Data

855-McCoy

 m

C

Figure 28. Total pitching moment coefficient vs. Mach number, group fits.
24

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

Mach Number

0  m

C

Figure 29. Linear pitching moment coefficient vs. Mach number, group fits. 

-10.00

-5.00

0.00

5.00

10.00

15.00

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

Mach Number

3  m C

Figure 30. Cubic pitching moment coefficient vs. Mach number, group fits.
25

Figure 31 shows that the normal force coefficient does not vary significantly due to Mach 

number. However, groups at similar Mach numbers but different yaw levels did have varying 

results, though still within 10% (approximately the experimental error) of each other. A cubic 

normal force coefficient was investigated as a refinement of the normal force coefficient but was 

excluded from the final aerodynamic model for all shots because it did not improve the results. 

Therefore, N C is equal to 0

C . N

2.65

2.70

2.75

2.80

2.85

2.90

2.95

3.00

3.05

3.10

3.15

3.20

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

Mach Number

 N

C

Figure 31. Normal force coefficient derivative vs. Mach number, group fits. 

After N C and m C are determined, the normal force center of pressure, XCP, is determined by the 

following: 

. α

α

m

CP

N

C

c.g.– X = C (2) 

The results of equation 2 are plotted in figure 32. As the Mach number increases, the center of 

pressure very gradually shifts away from the center of gravity (c.g.).
26

0

0.2

0.4

0.6

0.8

1

1.2

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

Mach Number

C.G. - XCP

Figure 32. Normal force center of pressure vs. Mach number, group fits. 

As equation 3 states, p Cn can be separated into a linear and a nonlinear term. The best 

projectile design will have the linear term,  0 np C , as near 0 as possible. Figure 33 shows the total 

Magnus moment coefficient vs. Mach number for the current test data and data collected by 

McCoy (1). There are some differences between the data sets. The differences can easily be 

accounted for through the different reduction techniques (McCoy is based on linear theory only). 

The linear and cubic Magnus moment coefficients can be seen in figures 34 and 35, respectively. 

Not all of the linear coefficients are negative, but the values are close to 0 for each group. While 

the cubic term at the highest Mach number was prescribed as 0, ARFDAS did, on occasion, 

provide a better fit for a shot when the cubic term was allowed. Only at the lowest Mach 

numbers (and low yaw groupings at Mach 1.5 and 1.7) did the nonlinear component become 

significant. 

2

0 3

 p p p Cn  Cn  Cn . (3) 

Figure 36 shows the pitch-damping coefficient as a function of Mach number for McCoy’s data 

and the test data. Error bars indicate standard deviation predicted by ARFDAS and do not 

represent the bounds for the projectile. The positive pitch-damping coefficient for one of 

McCoy’s data points is attributed to it being in the transonic regime. The point’s proximity to 0 

most likely represents the fact that there is simply no damping and the shot has reached its yaw 

limit cycle.
27

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

1 1.5 2 2.5 3

Mach Number

Test Data

855 McCoy

p n C

Figure 33. Magnus moment coefficient derivative vs. Mach number, group fits. 

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

Mach Number

0 p n C

Figure 34. Zero-yaw Magnus moment coefficient derivative vs. Mach number, group fits.
28

0

10

20

30

40

50

60

70

80

90

100

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

Mach Number

3 p n C

Figure 35. Cubic Magnus moment coefficient derivative vs. Mach number, group fits. 

-20

-15

-10

-5

0

5

1 1.5 2 2.5 3

Mach Number

Test Data

855 McCoy

 m

m

C

C q 

Figure 36. Pitch-damping moment coefficient vs. Mach number, group fits.
29

3.5 Dynamic Stability 

From the motion analysis, it is possible to determine the modal arm damping exponents 

(figure 37). The value of F determines whether the nutation, or fast, arm damps. The value of 

S determines if the precession, or slow, arm damps. The values of F and S determined at each 

Mach number and angle only apply to the spin rates of the experiment. There are four possible 

combinations of F and S: F > 0 and S < 0, F < 0 and S > 0, F > 0 and S > 0, and F < 0 

and S < 0. Only two of these four combinations were found during the course of the analysis: 

F < 0 and S > 0 (figure 38) and F < 0 and S < 0 (figure 39). 

Figure 37. Modal arm damping exponent definitions. 

Figure 38. Shot 27344 (Mach 1.69) showing F < 0 and S > 0.
30

Figure 39. Shot 27352 (Mach 1.70) showing F < 0and S < 0. 

The damping coefficients are affected by the aerodynamic properties of the projectile. In fact, as 

outlined by McCoy (9) and converted to ARFDAS notation, these are 

, 2

1 2

2 4

      F S

P( T – H) λ =– H±

P–M

, (4) 

in which 

     

x

y

I pd P =

I V , (5) 

2

*

y

m

k

C

M   , (6) 

 

2

* *

* *

2 y

m m

L D k

C C

H C C q 



     , (7) 

and 

2

*

*

2 x

n

L

k

C

T C p



  , (8) 

in which 

2

2

x

x

I k =

md , 2

2

y

y

I

k =

md , V = velocity magnitude (m/s), and p = spin rate (rad/s). (9)

Alpha Bar (deg) 

X (m) 
31

The lift coefficient derivative, Lα C , and CD are related to Nα C and CX by 

cos sin  LN X α α C =C α C α (10) 

and 

cos sin  DX Nα C =C α C α . (11) 

The *

 indicates that the coefficient is multiplied by 

m

Sd

2

*   , (12) 

where  is the freestream density and S is the cross-sectional area (d2

/4). It is important to note 

that ARFDAS nondimensionalizes the aerodynamic coefficients by pd/2V, while McCoy 

nondimensionalizes them by pd/V. 

Plotting the damping exponents vs. AOA allows one to better determine the dynamic stability of 

the round for a given Mach number. Figures 40–44 display the damping exponents at each of the 

Mach numbers. Nutation is damped at all five Mach numbers. At Mach 1.2, for the angles of 

attack observed in this test, precession is undamped (figure 40). The damping exponents for the 

slow mode do approach 0 at 4°, indicating a yaw limit cycle likely exists. Figures 41 and 42 

show that precession is only damped for yaw angles greater than roughly 2.5° at Mach 1.5 and 

1.7. With that information, it can be stated that a yaw limit cycle of ~2.5° exists at a simulated 

range of 400 m due to a slow-mode instability, with an eventual yaw limit-cycle of slightly more 

than 4° at a simulated range of 600 m. At Machs 2.2 and 2.6 (figures 43 and 44, respectively), 

the precession and the nutation damping exponents are both negative, indicating that any initial 

yaw should damp out and remained damped over the first 200 m of flight. 

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Mean Angle of Attack, Deg

Damping Exponent, /

m

Nutation at Mach

1.15-1.20

Precession at Mach

1.15-1.20

Figure 40. Modal arm damping exponents, Mach 1.15–1.20.
32

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0123456

Mean Angle of Attack, Deg

Damping Exponent, /m

Nutation at Mach 1.45-1.49

Precession at Mach 1.45-1.49

Figure 41. Modal arm damping exponents, Mach 1.45–1.49. 

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

01234567

Mean Angle of Attack, Deg

Damping Exponent, /m

Nutation at Mach 1.65-1.73

Precession at Mach 1.65-1.73

Figure 42. Modal arm damping exponents, Mach 1.65–1.73.
33

-0.04

-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0 0.5 1 1.5 2 2.5 3 3.5 4

Mean Angle of Attack, Deg

Damping Exponent, /m

Nutation at Mach 2.17-2.25

Precession at Mach 2.17-2.25

Figure 43. Modal arm damping exponents, Mach 2.17–2.25. 

-0.05

-0.045

-0.04

-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0 0.5 1 1.5 2 2.5 3

Mean Angle of Attack, Deg

Damping Exponent, /m

Nutation at Mach 2.60-2.63

Precession at Mach 2.60-2.63

Figure 44. Modal arm damping exponents, Mach 2.60–2.63.
34

However, these damping exponents are determined using the spin rate due to the twist of the 

barrel rather than the spin rate that would be experienced by the projectile were it allowed to spin 

down from muzzle velocity and spin to the desired velocity. Using the CX and p Cl values 

determined by the 6-DOF fits, a trajectory simulation was accomplished using the Projectile 

Rocket Ordnance Design and Analysis System (PRODAS) (10) to determine the approximate 

spin rates at the downrange distances corresponding to the velocities tested and listed in table 9. 

The values of F and S can then be recalculated from equation 4 for each shot once P in 

equation 5 is updated using the corresponding spin values in table 9. As mentioned previously, 

the aerodynamic coefficients have been found to be minimally affected by these changes in spin 

(7, 8). Since dynamic stability was not of concern at the 200-m distance (F and S were already 

negative, even for the lower spin rate), the reanalysis was confined to the 400-, 500-, and 600-m 

velocities. For the Mach numbers and angles of attack present in the range test, increasing the 

nondimensional spin decreases the values of the damping exponents, indicating that the rounds 

are more stable. At Mach 1.2, the limit cycle appears to be reduced to below 4°, as the one shot 

having this mean angle appears to just become stable or at least neutrally stable with S ≈ 0 

(figure 45). The stability of the rounds at Machs 1.5 and 1.7 also appears to be increased. At 

Mach 1.5 (figure 46), most of the rounds show dynamic stability (F and S < 0). However, two 

of the rounds show neutral stability, indicating that a yaw limit cycle likely exists; it is just at 

yaw levels below those present in this study. This is confirmed at Mach 1.7 (figure 47), where 

slightly smaller yaw levels were observed, as the shots with the lowest yaw levels still have 

S > 0, although with a smaller magnitude.

Table 9. Velocity matched spin rate as determined 

from PRODAS. 

Downrange 

Distance 

(m) 

Mach No. Spin 

(rad/s) 

200 2.24 30,171 

400 1.7 27,319

500 1.5 26,138 

600 1.2 24,448 
35

Figure 45. Modal arm damping exponents with matched spin, Mach 1.2. 

Figure 46. Modal arm damping exponents with matched spin, Mach 1.5.
36

Figure 47. Modal arm damping exponents with matched spin, Mach 1.7. 

An additional method to describe dynamic stability is to plot p Cn as a function of AOA, with the 

expansion 

pp p 0 3

3 CC C nn n     δ δ , (13) 

(with δ in radians) and then overlaying the nutation boundary and the precession boundary. The 

nutation boundary and the precession boundary can be found by setting equation 4 equal to 0 and 

solving each portion for p Cn . In this case, the values used were solved for using ARFDAS (2) 

for each individual shot, with the average value used to represent each group. This provides the 

slope of the line to be plotted. Typically, the nutation boundary represents the maximum value 

of p Cn that can exist at a particular Mach number and AOA in order to retain a damped nutation 

arm. Similarly, the precession boundary represents the minimum value of p Cn that can exist at a 

particular Mach number and AOA in order to retain a damped precession arm. The region of 

dynamic stability (i.e., angles of attack for which both arms are damped) lies below the nutation 

boundary and above the precession boundary. In that case, the AOA where p Cn and the 

precession boundary intersect is considered the limit cycle for that Mach number. This is 

predicated on the requirement that the nutation boundary has a larger slope than the precession 

boundary.
37

Figures 48–51 include the stability bounds determined directly from the range data (underspun 

condition). Figure 48 displays the Magnus moment and stability bounds for a group of shots 

with an average Mach number of 1.18. The slow arm is undamped for yaw levels less than 4.5°. 

Figures 49 and 50 represent the Magnus moment and stability bounds of two groups with 

average Mach numbers of 1.47 and 1.48, respectively. At Mach 1.47, the Magnus moment 

coefficient is within its bounds for the entire yaw range shown. It is important to note that the 

average yaw for the shots in that group was 3.6°, making the accuracy of the plot at yaw values 

<2° uncertain. At Mach 1.48, however, precession was undamped at yaw levels smaller than 2°. 

The average yaw for the shots in the Mach 1.48 group was only 2.5°, thus providing a better 

indicator of stability at smaller yaw levels. Similarly, figure 51 shows that at Mach 1.7, 

precession was undamped at yaw angles less than 3°. This indicates that at Mach 1.18, small 

yaw levels will grow to around 4.5°, and at Machs 1.48 and 1.7, small yaw levels will grow until 

they reach ~2° and ~3°, respectively. It is possible, however, that at Machs 1.48 and 1.7, the 

slow arm damping exponent is 0, rather than positive, at low yaw angles since the Magnus 

moment is only slightly outside of its bounds and other groups at similar speeds are shown to be 

within the stability bounds. For all other Mach numbers, the Magnus coefficient was within the 

stability bounds. p Cn plots at different Mach numbers can be found in appendix C. The findings 

of the Magnus bounds are consistent with the limit cycles predicted using the damping 

frequencies. 

Figure 48. Magnus moment coefficient with stability bounds at Mach 1.18.
38

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 0.5 1 1.5 2 2.5 3 3.5 4

Nutation Bound

Precession Bound

Magnus Moment Coefficient



0   F

S  0  p n C

Average Yaw for 

Group was 3.6°

Figure 49. Magnus moment coefficient with stability bounds at Mach 1.47. 

-0.02

-0.01

0

0.01

0.02

0.03

0 0.5 1 1.5 2 2.5 3

Nutation Bound

Precession Bound

Magnus Moment Coefficient



0   F

S  0 

p n C

Average Yaw for 

Group was 2.5°

Figure 50. Magnus moment coefficient with stability bounds at Mach 1.48. 
39

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Nutation Bound

Precession Bound

Magnus Moment Coefficient



S  0

 0  F

p n C

Figure 51. Magnus moment coefficient with stability bounds at Mach 1.70. 

As was the case with the damping frequencies, the Magnus bounds are also solved for assuming 

muzzle spin rates rather than the actual downrange spin rates. Using the downrange spin rates 

predicted by the trajectory calculations, a second set of “at range” Magnus bounds was 

calculated using equation 4 set to 0 and an updated P value. These “at range” Magnus bounds 

lay outside the original Magnus bounds, indicating a larger stability region. Figures 52–54 show 

the same Magnus moment coefficient plots vs. mean AOA, as were shown in figures 48–51 (the 

Mach 1.47 plot is not included as that case was already shown to be stable). The extended 

stability region that occurs with matched spin is immediately apparent; the yaw limit cycle is 

decreased by ~0.5° for these three Mach numbers. While this may not seem significant, the yaw 

limit cycle experienced by the round may affect its terminal performance. 

Figure 52. Magnus moment coefficient with matched spin stability bounds at Mach 1.18.
40

Figure 53. Magnus moment coefficient with matched spin stability bounds at Mach 1.48. 

Figure 54. Magnus moment coefficient with matched spin stability bounds at Mach 1.7. 
41

A final method to estimate the simulated range limit cycle at each Mach number is to interrogate 

the total yaw fit obtained from the ARFDAS solution to extract the average total yaw for each 

shot during the last 2–3 m of flight. Figure 55 shows the yaw limit cycle as determined by this 

method. Also included in the plot is data from work previously done by McCoy (1). While the 

recent data at muzzle spin indicates that a significant limit cycle may appear as early as 600 m/s, 

McCoy’s data indicates that the yaw limit cycle does not occur until 400 m/s. This discrepancy 

is likely due to the rounds in the current test being in an underspun condition (spin is lower than 

expected for the velocity), causing the round to be less stable than it would be under actual 

conditions. However, as the round continues to slow down, the magnitude of the limit cycle 

predicted by the simulated range experiments nearly matches that found by McCoy at range. 

This indicates that while the simulated range experiments may not accurately predict at what 

velocity the limit cycle begins to appear, they do accurately predict the limit cycle once it is 

known to exist. 

0.00E+00

2.00E+00

4.00E+00

6.00E+00

8.00E+00

1.00E+01

1.20E+01

0 100 200 300 400 500 600 700 800 900 1000

Average Velocity (m/s)

Yaw (deg)

Test DataIndividual Shots

855-McCoy

Figure 55. Yaw limit cycle: yaw vs. velocity. 

The main purpose of conducting any aerodynamic testing is to create a complete aerodynamic 

database for future use in simulating trajectories that have nonstandard initial conditions or to 

determine the effect of weather (i.e., winds, temperature, etc.). To this end, it important to 

ensure that the aerodynamic coefficients predicted by the simulated range experiments also 

produce that known downrange behavior. As this is one of the few rounds for which “at range” 

limit cycle data is available, this prediction capability is investigated. 

Using the experimentally obtained aerodynamic coefficients, the existing M855 aerodynamic 

database in PRODAS was updated. The trajectory simulation available within PRODAS was 

used to verify that the yaw limit cycles observed in the range could be reproduced at each of the 
42

downrange Mach numbers to ensure that all of the aerodynamic coefficients were accurately 

determined. The next step was to allow the model to simulate the real range test to see how the 

results agreed with what McCoy (1) observed. The results of this simulation were not expected, 

and no significant limit cycle was observed (figure 56). PRODAS accurately predicted the 

damping of the initial yaw. However, there appears to be very little yaw growth (still less than 1°) 

at 600 m. Very little yaw growth is occurring because the slow-mode (un)damping remains quite 

small, even at 600 m, as found in the current range test. Without a significant event occurring, it 

would take a very long distance for a limit cycle such as that seen by McCoy to develop. In the 

current testing, it is likely that the significant event causing the yaw growth was the initial launch 

rates. It is unclear at this time why the real-range experiments were showing a limit cycle, while 

none are predicted. One possibility would be the existence of a small mass asymmetry. 

However, the Aerodynamics Branch at ARL does not possess the correct instrumentation to 

verify whether or not a mass asymmetry exists. Additional analyses and studies would need to 

be completed in order to further address this issue. 

Figure 56. The 6-DOF simulation to 600 m of the M855 projectile using experimentally determined 

aerodynamic coefficients. 
43

4. Summary and Conclusions 

An experimental test was completed for the aerodynamic and flight dynamic characterization of 

the M855 reference round from the muzzle to a simulated range of ~600 m. Data was collected 

at five different launch Mach numbers over the simulated 600 m of flight. There were 38 shots 

for which data was collected, including 5 shots near Mach 2.6, 8 near Mach 2.2, 8 near Mach 1.7, 

11 near Mach 1.5, and 6 near Mach 1.2. With the exception of three shots at Mach 1.5 and four 

shots at Mach 1.2, all of the shots had spin pins for the characterization of spin, specifically, roll 

damping. At each of the downrange velocities investigated, the projectile is in an underspun 

condition. 

Pitching and yawing motion were well determined at all Mach numbers. This allowed linear and 

nonlinear aerodynamic coefficients to be obtained with sufficient accuracy. The resulting 

aerodynamic coefficients and dynamic derivatives can be used to improve the predictive 

capabilities of flight models with confidence. Coefficients for axial force, pitching moment, 

Magnus moment, and pitch damping were all found to have values similar to those obtained from 

previous tests, validating both sets of results. For future tests, a larger range of initial yaw values 

at the higher Mach numbers would be useful in determining if there is a cubic Magnus moment 

coefficient. 

The round was determined to be dynamically stable at all Mach numbers tested through analysis 

of the Magnus moment coefficient, stability bounds, and modal arm damping exponents. 

Analysis of the data for determination of yaw limit cycle at simulated ranges produced mixed 

results. While the current test found that a yaw limit cycle did exist, it was predicted to occur 

significantly earlier than for the real-range test. Current results indicate that yaw limit cycle of 

~2° begins to occur at a simulated range of 400 m, eventually reaching 4° at 600 m, while the 

real-range testing indicated that a similar yaw limit cycle didn’t occur until 600 m. Completing 

the stability analysis using matched spin showed that the yaw limit cycle could be reduced by as 

much as 0.5°. Additionally, this second analysis showed that the yaw limit cycle may not begin 

until further downrange than predicted by the simulated ranges in the underspun condition. This 

indicates that if the limit cycle of a particular round is of concern, the extra step should be taken 

to complete the second stability analysis using matched spin. 

With a complete set of aerodynamic coefficients, an updated aerodynamic model was created. 

This model will allow a better understanding of the flight dynamics of the projectile and better 

matching capabilities as improvements to the round are made. 
44

5. References 

1. McCoy, R. L. Aerodynamic and Flight Dynamic Characteristics of the New Family of 

5.56MM NATO Ammunition; BRL Report No. 3467; U.S. Army Ballistics Research 

Laboratory: Aberdeen Proving Ground, MD, October 1985. 

2. Braun, W. F. The Free Flight Aerodynamic Range; BRL Report No. 1048; U.S. Army 

Ballistics Research Laboratory: Aberdeen Proving Ground, MD, July 1958. 

3. Arrow Tech Associates. ARFDAS: Ballistic Range Data Analysis System; User and 

Technical Manual. South Burlington, VT, May 1997. 

4. Murphy, C. H. Free-Flight Motion of Symmetric Missiles; BRL Report 1216; U.S. Army 

Ballistics Research Laboratory: Aberdeen Proving Ground, MD, July 1963. 

5. Murphy, C. H. Data Reduction for Free-Flight Spark Ranges; BRL Report 900; U.S. Army 

Ballistics Research Laboratory: Aberdeen Proving Ground, MD, February 1954. 

6. Hathaway, W. H.; Whyte, R. H. Aeroballistic Research Facility Free-Flight Data Analysis 

Using the Maximum Likelihood Method; AFATL-TR-79-98; Arrow Tech Associates: South 

Burlington, VT, December 1979. 

7. Weinacht, P. Validation and Prediction of the Effect of Rifling Grooves on Small-Caliber 

Ammunition Performance. AIAA Atmospheric Flight Mechanics Conference and Exhibit, 

AIAA-2006-6010, Keystone, CO, August 2006. 

8. Silton, S.; Webb, D. Experimental Determination of the Effect of Rifling Grooves on the 

Aerodynamics of Small Caliber Projectiles. AIAA Atmospheric Flight Mechanics 

Conference and Exhibit, AIAA-2006-6009, Keystone, CO, August 2006. 

9. McCoy, R. L. Modern Exterior Ballistics: The Launch and Flight Dynamics of Symmetric 

Projectiles. Schiffer Publishing: Atglen, PA, 1999; pp 233, 306, 308. 

10. ArrowTech Associates. PRODAS User’s Manual, Burlington, VT, 2007. 
45

Appendix A. Motion Plots 

A complete set of motion plots is presented for a chosen shot to represent each Mach number. 

On each plot, the line indicates the six degrees of freedom fit and the solid circles are the 

experimental data. In figures A-1–A-9, the motion plots for a shot at Mach 1.18 are presented. 

Figures A-10–A-18 show the motion plots at Mach 1.69, and figures A-19–A-27 are the motions 

plots for a shot fired at Mach 2.21. Finally, figures A-28–A-36 show the motion plots Mach 

2.63. The complete set of sample motion plots at Mach 1.5 is shown in the main body of the 

text. 

Figure A-1. Pitch angle vs. range for round 29271 (M855 at Mach 1.18).
46

Figure A-2. Yaw angle vs. range for round 29271 (M855 at Mach 1.18). 

Figure A-3. Pitch angle vs. yaw angle for round 29271 (M855 at Mach 1.18).
47

Figure A-4. Total yaw vs. range for round 29271 (M855 at Mach 1.18). 

Figure A-5. Roll angle vs. range for round 29271 (M855 at Mach 1.18).
48

Figure A-6. Spin vs. range for round 29271 (M855 at Mach 1.18). 

Figure A-7. Vertical position vs. range for round 29271 (M855 at Mach 1.18).
49

Figure A-8. Lateral position vs. range for round 29271 (M855 at Mach 1.18). 

Figure A-9. Three-dimensional projectile motion through the range for round 29271 (M855 at Mach 1.18).
50

Figure A-10. Pitch angle vs. range for round 27353 (M855 at Mach 1.69). 

Figure A-11. Yaw angle vs. range for round 27353 (M855 at Mach 1.69).
51

Figure A-12. Pitch angle vs. yaw angle for round 27353 (M855 at Mach 1.69). 

Figure A-13. Total yaw vs. range for round 27353 (M855 at Mach 1.69).
52

Figure A-14. Roll angle vs. range for round 27353 (M855 at Mach 1.69). 

Figure A-15. Spin vs. range for round 27353 (M855 at Mach 1.69).
53

Figure A-16. Vertical position vs. range for round 27353 (M855 at Mach 1.69). 

Figure A-17. Lateral position vs. range for round 27353 (M855 at Mach 1.69).
54

Figure A-18. Three-dimensional projectile motion through the range for round 27353 (M855 at Mach 1.69). 

Figure A-19. Pitch angle vs. range for round 26833 (M855 at Mach 2.21).
55

Figure A-20. Yaw angle vs. range for round 26833 (M855 at Mach 2.21). 

Figure A-21. Pitch angle vs. yaw angle for round 26833 (M855 at Mach 2.21).
56

Figure A-22. Total yaw vs. range for round 26833 (M855 at Mach 2.21). 

Figure A-23. Roll angle vs. range for round 26833 (M855 at Mach 2.21).
57

Figure A-24. Spin vs. range for round 26833 (M855 at Mach 2.21). 

Figure A-25. Vertical position vs. range for round 26833 (M855 at Mach 2.21).
58

Figure A-26. Lateral position vs. range for round 26833 (M855 at Mach 2.21). 

Figure A-27. Three-dimensional projectile motion through the range for round 26833 (M855 at Mach 2.21).
59

Figure A-28. Pitch angle vs. range for round 26597 (M855 at Mach 2.63). 

Figure A-29. Yaw angle vs. range for round 26597 (M855 at Mach 2.63).
60

Figure A-30. Pitch angle vs. yaw angle for round 26597 (M855 at Mach 2.63). 

Figure A-31. Total yaw vs. range for round 26597 (M855 at Mach 2.63).
61

Figure A-32. Roll angle vs. range for round 26597 (M855 at Mach 2.63). 

Figure A-33. Spin vs. range for round 26597 (M855 at Mach 2.63).
62

Figure A-34. Vertical position vs. range for round 26597 (M855 at Mach 2.63). 

Figure A-35. Lateral position vs. range for round 26597 (M855 at Mach 2.63).
63

Figure A-36. Three-dimensional projectile motion through the range for round 26597 (M855 at Mach 2.63).
64

INTENTIONALLY LEFT BLANK.
65

Appendix B. Complete Set of 6-Degrees-of-Freedom (6-DOF) Fits

 

This appendix appears in its original form, without editorial change. 
66

 M16A2 M855 LR M1.7++ roll pins  6 DOF Summary Output (08-AUG-08 09:42:10)  ---------------------------------------------------------------------------------------------------------------- Ref. Ref. Ref.Mach Mach Max Angle | Standard Er Shot Number Date Time CG Length Number Number DBSQ of Attack | X Y-Z Angle  (mm) (mm) (deg2) (deg) | (m) (m) (deg)  ---------------------------------------------------------------------------------------------------------------- 27350 28-FEB-08 16:31:50 14.27 23.06 1.65 1.664 32.000 14.5 0.0005 0.0002 0.188  27351 28-FEB-08 16:32:24 14.27 23.06 1.65 1.678 29.530 12.1 0.0002 0.0002 0.203  27344 25-FEB-08 10:58:42 14.27 23.06 1.70 1.686 3.210 2.2 0.0001 0.0001 0.157  27346 25-FEB-08 11:17:01 14.27 23.06 1.70 1.687 3.142 2.4 0.0001 0.0001 0.197  27353 25-FEB-08 12:42:18 14.27 23.06 1.70 1.689 13.180 7.7 0.0003 0.0002 0.271  27352 28-FEB-08 16:32:48 14.27 23.06 1.70 1.702 37.140 15.0 0.0005 0.0003 0.159  27347 06-AUG-08 14:13:50 14.30 23.06 1.70 1.723 2.121 1.8 0.0006 0.0001 0.185  27345 25-FEB-08 11:04:18 14.27 23.06 1.70 1.725 4.512 3.1 0.0002 0.0001 0.201  26827 25-FEB-08 09:10:47 14.27 23.06 2.15 2.172 3.236 3.5 0.0002 0.0002 0.200  26833 28-FEB-08 16:34:01 14.27 23.06 2.20 2.212 9.357 6.8 0.0002 0.0002 0.231  26834 25-FEB-08 10:46:04 14.27 23.06 2.20 2.215 14.450 8.7 0.0003 0.0002 0.254  26826 25-FEB-08 10:09:05 14.27 23.06 2.20 2.224 0.734 1.9 0.0001 0.0002 0.236  26831 25-FEB-08 09:53:08 14.27 23.06 2.25 2.230 6.353 5.0 0.0002 0.0002 0.179  26828 28-FEB-08 16:34:18 14.27 23.06 2.25 2.248 2.174 2.8 0.0002 0.0001 0.155  26829 28-FEB-08 16:34:30 14.27 23.06 2.25 2.250 1.739 2.9 0.0002 0.0001 0.150  26832 25-FEB-08 09:54:42 14.27 23.06 2.25 2.252 7.421 6.1 0.0002 0.0001 0.208  26591 28-FEB-08 16:34:41 14.27 23.06 2.60 2.612 1.235 2.5 0.0002 0.0001 0.203  26598 28-FEB-08 16:34:54 14.27 23.06 2.60 2.613 6.653 6.2 0.0003 0.0006 0.306  26590 25-FEB-08 08:19:35 14.27 23.06 2.60 2.617 2.046 3.3 0.0003 0.0002 0.275  26597 28-FEB-08 16:35:07 14.27 23.06 2.65 2.631 4.481 4.9 0.0002 0.0003 0.248  26592 28-FEB-08 16:35:16 14.27 23.06 2.65 2.632 0.630 1.7 0.0002 0.0002 0.252 
67

 M16A2 M855 LR M1.7++ roll pins  6 DOF Summary Output (08-AUG-08 09:42:10)  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Error  Shot Number Number DBSQ CX CNa CYpa Cma Cmq Cnpa Clp CXM | X(m) Angle( ABARM CX2 CNa3 CYpa3 Cma3 Cmq2 Cnpa3 Cnpa5 IX/IY CmaM | Y-Z(m) Roll( ---------------------------------------------------------------------------------------------------------------- 27350 1.664 32.0 0.387 3.110 -1.00 2.739 -12.7 0.14 -0.0273 -0.12 0.0005 0.18 14.5 2.300 0.000 0.00 -2.4 0.0 5.1 0. 0.1201 0.00 0.0002 6.21 27351 1.678 29.5 0.384 3.095 -1.00 2.738 -9.9 0.13 -0.0286 -0.07 0.0002 0.20 12.1 2.300 0.000 0.00 -3.6 0.0 0.0 0. 0.1218 0.00 0.0002 11.65 27344 1.686 3.2 0.374 2.941 -1.00 2.677 -6.4 -0.82 -0.0320 -0.10 0.0001 0.15 2.2 4.930 0.000 0.00 -2.5 0.0 109.0 0. 0.1204 -0.43 0.0001 5.84 27346 1.687 3.1 0.372 2.884 -1.00 2.656 -4.7 -0.50 -0.0327 -0.10 0.0001 0.19 2.4 2.300 0.000 0.00 -2.5 0.0 0.0 0. 0.1200 -0.33 0.0001 5.98 27353 1.689 13.2 0.371 2.973 -1.00 2.708 -9.4 -0.01 -0.0303 -0.13 0.0003 0.27 7.7 4.930 0.000 0.00 0.0 0.0 0.0 0. 0.1220 0.00 0.0002 6.83 27352 1.702 37.1 0.385 3.190 -1.00 2.709 -12.1 0.24 -0.0278 -0.15 0.0005 0.15 15.0 2.300 0.000 0.00 -2.9 0.0 0.0 0. 0.1216 0.00 0.0003 8.70 27347 1.723 2.1 0.379 2.704 -1.00 2.745 -2.0 -0.62 -0.0469 -0.13 0.0006 0.18 1.8 3.803 0.000 0.00 0.0 0.0 0.0 0. 0.1235 -0.46 0.0001 6.93 27345 1.725 4.5 0.368 2.722 -1.00 2.662 -7.6 -0.64 -0.0323 -0.10 0.0002 0.20 3.1 4.930 0.000 0.00 -2.5 0.0 109.0 0. 0.1200 -0.48 0.0001 6.57 26827 2.172 3.2 0.328 2.893 -1.00 2.493 -8.0 -0.22 -0.0247 -0.07 0.0002 0.20 3.5 3.414 0.000 0.00 -4.0 0.0 0.0 0. 0.1191 0.00 0.0002 7.63 26833 2.212 9.4 0.332 2.958 -1.00 2.521 -12.2 0.19 -0.0255 -0.05 0.0002 0.23 6.8 3.000 0.000 0.00 -4.0 0.0 0.0 0. 0.1237 0.00 0.0002 4.98 26834 2.215 14.4 0.325 2.960 -1.00 2.514 -13.8 -0.14 -0.0241 -0.01 0.0003 0.25 8.7 2.310 0.000 0.00 -2.8 0.0 46.9 0. 0.1241 0.00 0.0002 6.70
68

 M16A2 M855 LR M1.7++ roll pins  6 DOF Summary Output (08-AUG-08 09:42:10)  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Error  Shot Number Number DBSQ CX CNa CYpa Cma Cmq Cnpa Clp CXM | X(m) Angle( ABARM CX2 CNa3 CYpa3 Cma3 Cmq2 Cnpa3 Cnpa5 IX/IY CmaM | Y-Z(m) Roll( ---------------------------------------------------------------------------------------------------------------- 26826 2.224 0.7 0.321 3.000 -1.00 2.548 -11.0 0.20 -0.0238 -0.04 0.0001 0.23 1.9 3.000 0.000 0.00 -4.0 0.0 0.0 0. 0.1214 0.00 0.0002 7.02 26831 2.230 6.4 0.318 2.962 -1.00 2.554 -8.9 0.06 -0.0269 -0.05 0.0002 0.17 5.0 2.880 0.000 0.00 -4.0 0.0 0.0 0. 0.1238 0.00 0.0002 5.19 26828 2.248 2.2 0.325 3.000 -1.00 2.510 -8.2 -0.29 -0.0251 -0.07 0.0002 0.15 2.8 3.000 0.000 0.00 -4.0 0.0 0.0 0. 0.1225 0.00 0.0001 4.55 26829 2.250 1.7 0.328 3.160 -1.00 2.534 -11.9 -0.05 -0.0353 -0.06 0.0002 0.15 2.9 3.000 0.000 0.00 -4.0 0.0 0.0 0. 0.1230 0.00 0.0001 4.67 26832 2.252 7.4 0.317 2.951 -1.00 2.581 -10.2 0.11 -0.0247 -0.05 0.0002 0.20 6.1 3.414 0.000 0.00 -10.0 0.0 0.0 0. 0.1235 0.00 0.0001 3.88 26591 2.612 1.2 0.298 2.627 -1.00 2.413 -13.1 0.17 -0.0297 -0.06 0.0002 0.20 2.5 3.000 0.000 0.00 -4.0 0.0 0.0 0. 0.1233 0.00 0.0001 5.26 26598 2.613 6.7 0.294 3.006 -1.00 2.507 -22.8 0.47 -0.0205 -0.06 0.0003 0.30 6.2 3.000 0.000 0.00 -7.2 0.0 0.0 0. 0.1261 0.00 0.0006 4.31 26590 2.617 2.0 0.304 2.801 -1.00 2.404 -12.6 0.15 -0.0295 -0.06 0.0003 0.27 3.3 3.000 0.000 0.00 -4.0 0.0 0.0 0. 0.1227 0.00 0.0002 4.47 26597 2.631 4.5 0.293 2.886 -1.00 2.429 -11.4 0.26 -0.0246 -0.03 0.0002 0.24 4.9 1.000 0.000 0.00 -4.0 0.0 0.0 0. 0.1236 0.00 0.0003 5.16 26592 2.632 0.6 0.292 3.000 -1.00 2.457 -11.0 0.20 -0.0258 -0.06 0.0002 0.25 1.7 3.000 0.000 0.00 -4.0 0.0 0.0 0. 0.1227 0.00 0.0002 6.56
69

 M16A2 M855 LR M1.7++ roll pins  6 DOF Summary Output (08-AUG-08 09:42:10)  ---------------------------------------------------------------------------------------------------------------- Ref. Mach Mach Max Angle | Standard Error  Shot Numbers Date Time Number Number DBSQ of Attack | X Y-Z Angle Rol (deg2) (deg) | (m) (m) (deg) (deg ---------------------------------------------------------------------------------------------------------------- 27350 27351 11-JUN-07 10:38:29 1.700 1.683 28.08 14.87 0.0005 0.0003 0.250 11.28 27353 27352  27350 27351 22-FEB-08 13:58:59 1.700 1.683 28.35 14.96 0.0009 0.0004 0.455 16.53 27352 27353  27346 27344 06-AUG-08 12:38:32 1.700 1.697 6.00 7.58 0.0005 0.0002 0.230 6.26 27353 27345  27345 27347 02-APR-08 09:59:34 1.700 1.705 3.18 3.03 0.0003 0.0001 0.219 6.31 27346 27344  26827 26833 11-JUN-07 10:38:50 2.250 2.211 6.68 8.45 0.0004 0.0002 0.275 6.33 26826 26834  26831  26827 26829 22-FEB-08 12:40:56 2.200 2.223 5.38 6.88 0.0009 0.0007 0.213 5.34 26831 26832  26833  26826 26828 22-FEB-08 13:05:14 2.200 2.234 6.13 8.46 0.0006 0.0002 0.227 5.57 26831 26832  26834  26831 26829 11-JUL-08 11:23:48 2.200 2.239 6.24 8.50 0.0004 0.0002 0.244 5.06 26828 26832  26834  26597 26592 11-JUN-07 10:39:11 2.200 2.461 6.10 8.47 0.0003 0.0002 0.266 7.18 26590 26834  26833  26590 26591 22-FEB-08 15:04:47 2.650 2.621 2.96 6.02 0.0003 0.0003 0.276 5.15 26592 26598  26597  26591 26598 11-JUN-07 10:39:21 2.650 2.621 2.97 5.98 0.0003 0.0004 0.317 5.16 26590 26592  26597 
70

 M16A2 M855 LR M1.7++ roll pins  6 DOF Summary Output (08-AUG-08 09:42:10)  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Erro Shot Numbers Number DBSQ CX CNa CYpa Cma Cmq Cnpa Clp | X(m) Angle ABARM CX2 CNa3 CYpa3 Cma3 Cmq2 Cnpa3 CXm | Y-Z(m) Roll CX4 CNa5 Cma5 Cmq4 Cnpa5 CmaM |  ---------------------------------------------------------------------------------------------------------------- 27350 27351 1.683 28.1 0.383 2.970 -1.00 2.720 -12.0 0.07 -0.0303 0.0005 0.249 27353 27352 14.9 2.297 0.000 0.00 -1.978 0.0 8.10 -0.0766 0.0003 11.280 0.00 0.00 0.0 0. 0. -0.294  27350 27351 1.683 28.4 0.384 3.198 -1.00 2.684 -11.4 0.15 -0.0286 0.0009 0.454 27352 27353 15.0 2.208 0.000 0.00 0.000 0.0 0.00 -0.1040 0.0004 16.530 0.00 0.00 0.0 0. 0. 0.000  27346 27344 1.697 6.0 0.372 3.136 -1.00 2.658 -9.9 -0.62 -0.0317 0.0005 0.230 27353 27345 7.6 3.788 0.000 0.00 9.861 0.0 95.00 -0.0861 0.0002 6.265 0.00 0.00 0.0 0. 0. -0.642  27345 27347 1.705 3.2 0.375 3.000 -1.00 2.665 -6.1 -0.59 -0.0367 0.0003 0.219 27346 27344 3.0 2.300 0.000 0.00 -2.500 0.0 0.00 -0.1023 0.0001 6.311 0.00 0.00 0.0 0. 0. -0.371  26827 26833 2.211 6.7 0.320 2.886 -1.00 2.530 -11.5 0.15 -0.0249 0.0004 0.275 26826 26834 8.5 4.270 0.000 0.00 -5.263 0.0 0.00 -0.0768 0.0002 6.333 26831 0.00 0.00 0.0 0. 0. 0.000  26827 26829 2.223 5.4 0.325 0.335 -1.00 0.000 -14.6 0.48 -0.0274 0.0009 0.213 26831 26832 6.9 3.414303.928 0.00 -4.000 0.0 0.00 -0.0603 0.0007 5.344 26833 0.00 0.00 0.0 0. 0. 0.000  26826 26828 2.234 6.1 0.322 2.918 -1.00 0.000 -11.4 0.02 -0.0249 0.0006 0.227 26831 26832 8.5 2.310 0.000 0.00 -4.979 0.0 25.52 -0.0221 0.0002 5.573 26834 0.00 0.00 0.0 0. 0. 0.000  26831 26829 2.239 6.2 0.323 3.079 -1.00 2.545 -11.2 0.02 -0.0272 0.0004 0.244 26828 26832 8.5 3.000 0.000 0.00 -6.835 0.0 21.64 -0.0572 0.0002 5.064 26834 0.00 0.00 0.0 0. 0. 0.000  26597 26592 2.461 6.1 0.307 2.891 -1.00 2.469 -11.8 0.19 -0.0268 0.0003 0.266 26590 26834 8.5 3.824 0.000 0.00 -4.000 0.0 0.00 -0.0687 0.0002 7.182 26833 0.00 0.00 0.0 0. 0. -0.224  26590 26591 2.621 3.0 0.299 3.010 -1.00 0.000 -15.4 0.29 -0.0260 0.0003 0.276 26592 26598 6.0 3.000 0.000 0.00 -4.000 0.0 1.10 -0.0632 0.0003 5.159 26597 0.00 0.00 0.0 0. 0. 0.000  26591 26598 2.621 3.0 0.296 2.928 -1.00 2.449 -15.7 0.32 -0.0260 0.0003 0.316 26590 26592 6.0 3.000 0.000 0.00 -3.000 0.0 0.00 -0.0617 0.0004 5.164 26597 0.00 0.00 0.0 0. 0. 0.000
71

 6 DOF Summary Output  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Error  Shot Number Number DBSQ CX CNa CYpa Cma Cmq Cnpa Clp CXM | X(m) Angle( ABARM CX2 CNa3 CYpa3 Cma3 Cmq2 Cnpa3 Cnpa5 IX/IY CmaM | Y-Z(m) Roll( ---------------------------------------------------------------------------------------------------------------- 27350 1.664 32.0 0.387 3.110 -1.00 2.739 -12.7 0.14 -0.0273 -0.12 0.0005 0.18 ( 0.1%)( 1.4%) (*) ( 0.1%)( 3.6%)(38.4%) ( 0.3%)( 4.8%)  14.5 2.300 0.000 0.00 -2.4 0.0 5.1 0. 0.1201 0.00 0.0002 6.21 (*) (*) (*) ( 8.3%) (*) (33.4%) (*) ( 0.0%) (*)  ---------------------------------------------------------------------------------------------------------------- 27351 1.678 29.5 0.384 3.095 -1.00 2.738 -9.9 0.13 -0.0286 -0.07 0.0002 0.20 ( 0.0%)( 0.8%) (*) ( 0.2%)( 4.6%)(34.8%) ( 0.5%)( 3.6%)  12.1 2.300 0.000 0.00 -3.6 0.0 0.0 0. 0.1218 0.00 0.0002 11.65 (*) (*) (*) (10.2%) (*) (*) (*) ( 0.0%) (*)  ---------------------------------------------------------------------------------------------------------------- 27344 1.686 3.2 0.374 2.941 -1.00 2.677 -6.4 -0.82 -0.0320 -0.10 0.0001 0.15 ( 0.0%)( 1.9%) (*) ( 0.2%)(37.8%)(16.2%) ( 0.4%)( 1.6%)  2.2 4.930 0.000 0.00 -2.5 0.0 109.0 0. 0.1204 -0.43 0.0001 5.84 (*) (*) (*) (*) (*) (*) (*) ( 0.1%)(28.8%)  ---------------------------------------------------------------------------------------------------------------- 27346 1.687 3.1 0.372 2.884 -1.00 2.656 -4.7 -0.50 -0.0327 -0.10 0.0001 0.19 ( 0.0%)( 1.6%) (*) ( 0.2%)(43.9%)(28.9%) ( 0.2%)( 1.1%)  2.4 2.300 0.000 0.00 -2.5 0.0 0.0 0. 0.1200 -0.33 0.0001 5.98 (*) (*) (*) (*) (*) (*) (*) ( 0.1%)(36.0%)  ---------------------------------------------------------------------------------------------------------------- 27353 1.689 13.2 0.371 2.973 -1.00 2.708 -9.4 -0.01 -0.0303 -0.13 0.0003 0.27 ( 0.0%)( 1.3%) (*) ( 0.1%)(10.9%) (-) ( 0.3%) (*)  7.7 4.930 0.000 0.00 0.0 0.0 0.0 0. 0.1220 0.00 0.0002 6.83 (*) (*) (*) (*) (*) (*) (*) ( 0.0%) (*)  ---------------------------------------------------------------------------------------------------------------- 27352 1.702 37.1 0.385 3.190 -1.00 2.709 -12.1 0.24 -0.0278 -0.15 0.0005 0.15 ( 0.1%)( 1.4%) (*) ( 0.1%)( 2.8%)(14.2%) ( 0.4%)( 4.2%)  15.0 2.300 0.000 0.00 -2.9 0.0 0.0 0. 0.1216 0.00 0.0003 8.70 (*) (*) (*) ( 4.7%) (*) (*) (*) ( 0.0%) (*)  ---------------------------------------------------------------------------------------------------------------- 27347 1.723 2.1 0.379 2.704 -1.00 2.745 -2.0 -0.62 -0.0469 -0.13 0.0006 0.18 ( 0.0%)( 6.1%) (*) ( 0.2%) (-) (27.1%) ( 0.2%) (*)  1.8 3.803 0.000 0.00 0.0 0.0 0.0 0. 0.1235 -0.46 0.0001 6.93 (*) (*) (*) (*) (*) (*) (*) ( 0.1%)(28.4%)  ----------------------------------------------------------------------------------------------------------------
72

 27345 1.725 4.5 0.368 2.722 -1.00 2.662 -7.6 -0.64 -0.0323 -0.10 0.0002 0.20 ( 0.0%)( 2.1%) (*) ( 0.2%)(21.4%)(19.9%) ( 0.3%)( 1.5%)  3.1 4.930 0.000 0.00 -2.5 0.0 109.0 0. 0.1200 -0.48 0.0001 6.57 (*) (*) (*) (*) (*) (*) (*) ( 0.1%)(20.6%)  ---------------------------------------------------------------------------------------------------------------- 26827 2.172 3.2 0.328 2.893 -1.00 2.493 -8.0 -0.22 -0.0247 -0.07 0.0002 0.20 ( 0.0%)( 2.4%) (*) ( 0.2%)(18.5%)(61.4%) ( 0.4%) (*)  3.5 3.414 0.000 0.00 -4.0 0.0 0.0 0. 0.1191 0.00 0.0002 7.63 (*) (*) (*) (*) (*) (*) (*) ( 0.0%) (*)  ---------------------------------------------------------------------------------------------------------------- 26833 2.212 9.4 0.332 2.958 -1.00 2.521 -12.2 0.19 -0.0255 -0.05 0.0002 0.23 ( 0.0%)( 1.1%) (*) ( 0.1%)( 7.3%)(44.7%) ( 0.3%)( 3.0%)  6.8 3.000 0.000 0.00 -4.0 0.0 0.0 0. 0.1237 0.00 0.0002 4.98 (*) (*) (*) (*) (*) (*) (*) ( 0.0%) (*)  ---------------------------------------------------------------------------------------------------------------- 26834 2.215 14.4 0.325 2.960 -1.00 2.514 -13.8 -0.14 -0.0241 -0.01 0.0003 0.25 ( 0.0%)( 1.3%) (*) ( 0.3%)( 6.9%)(67.1%) ( 0.4%)(20.9%)  8.7 2.310 0.000 0.00 -2.8 0.0 46.9 0. 0.1241 0.00 0.0002 6.70 (*) (*) (*) (37.4%) (*) (20.9%) (*) ( 0.0%) (*)  ---------------------------------------------------------------------------------------------------------------- 26826 2.224 0.7 0.321 3.000 -1.00 2.548 -11.0 0.20 -0.0238 -0.04 0.0001 0.23 ( 0.0%) (*) (*) ( 0.5%) (*) (*) ( 0.4%)( 2.8%)  1.9 3.000 0.000 0.00 -4.0 0.0 0.0 0. 0.1214 0.00 0.0002 7.02 (*) (*) (*) (*) (*) (*) (*) ( 0.1%) (*)  ---------------------------------------------------------------------------------------------------------------- 26831 2.230 6.4 0.318 2.962 -1.00 2.554 -8.9 0.06 -0.0269 -0.05 0.0002 0.17 ( 0.0%)( 1.2%) (*) ( 0.1%)(12.0%) (-) ( 0.3%)( 2.9%)  5.0 2.880 0.000 0.00 -4.0 0.0 0.0 0. 0.1238 0.00 0.0002 5.19 (*) (*) (*) (*) (*) (*) (*) ( 0.0%) (*)  ---------------------------------------------------------------------------------------------------------------- 26828 2.248 2.2 0.325 3.000 -1.00 2.510 -8.2 -0.29 -0.0251 -0.07 0.0002 0.15 ( 0.0%) (*) (*) ( 0.2%)(10.9%)(12.7%) ( 0.2%)( 2.2%)  2.8 3.000 0.000 0.00 -4.0 0.0 0.0 0. 0.1225 0.00 0.0001 4.55 (*) (*) (*) (*) (*) (*) (*) ( 0.0%) (*)  ---------------------------------------------------------------------------------------------------------------- 26829 2.250 1.7 0.328 3.160 -1.00 2.534 -11.9 -0.05 -0.0353 -0.06 0.0002 0.15 ( 0.0%)( 2.1%) (*) ( 0.2%)(12.8%) (-) ( 0.2%)( 1.7%)  2.9 3.000 0.000 0.00 -4.0 0.0 0.0 0. 0.1230 0.00 0.0001 4.67 (*) (*) (*) (*) (*) (*) (*) ( 0.1%) (*)  ----------------------------------------------------------------------------------------------------------------
73

 6 DOF Summary Output  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Error  Shot Number Number DBSQ CX CNa CYpa Cma Cmq Cnpa Clp CXM | X(m) Angle( ABARM CX2 CNa3 CYpa3 Cma3 Cmq2 Cnpa3 Cnpa5 IX/IY CmaM | Y-Z(m) Roll( ---------------------------------------------------------------------------------------------------------------- 26832 2.252 7.4 0.317 2.951 -1.00 2.581 -10.2 0.11 -0.0247 -0.05 0.0002 0.20 ( 0.0%)( 0.9%) (*) ( 0.3%) (*) (39.5%) ( 0.2%)( 3.0%)  6.1 3.414 0.000 0.00 -10.0 0.0 0.0 0. 0.1235 0.00 0.0001 3.88 (*) (*) (*) (18.1%) (*) (*) (*) ( 0.0%) (*)  ---------------------------------------------------------------------------------------------------------------- 26591 2.612 1.2 0.298 2.627 -1.00 2.413 -13.1 0.17 -0.0297 -0.06 0.0002 0.20 ( 0.0%)( 3.9%) (*) ( 0.3%)(16.5%) (-) ( 0.2%)( 2.3%)  2.5 3.000 0.000 0.00 -4.0 0.0 0.0 0. 0.1233 0.00 0.0001 5.26 (*) (*) (*) (*) (*) (*) (*) ( 0.1%) (*)  ---------------------------------------------------------------------------------------------------------------- 26598 2.613 6.7 0.294 3.006 -1.00 2.507 -22.8 0.47 -0.0205 -0.06 0.0003 0.30 ( 0.1%)( 2.7%) (*) ( 0.5%)( 9.6%)(26.6%) ( 0.3%)( 5.7%)  6.2 3.000 0.000 0.00 -7.2 0.0 0.0 0. 0.1261 0.00 0.0006 4.31 (*) (*) (*) (54.3%) (*) (*) (*) ( 0.1%) (*)  ---------------------------------------------------------------------------------------------------------------- 26590 2.617 2.0 0.304 2.801 -1.00 2.404 -12.6 0.15 -0.0295 -0.06 0.0003 0.27 ( 0.0%)( 3.5%) (*) ( 0.3%)(18.3%) (-) ( 0.2%)( 2.9%)  3.3 3.000 0.000 0.00 -4.0 0.0 0.0 0. 0.1227 0.00 0.0002 4.47 (*) (*) (*) (*) (*) (*) (*) ( 0.1%) (*)  ---------------------------------------------------------------------------------------------------------------- 26597 2.631 4.5 0.293 2.886 -1.00 2.429 -11.4 0.26 -0.0246 -0.03 0.0002 0.24 ( 0.0%)( 2.1%) (*) ( 0.3%)(13.5%)(51.4%) ( 0.3%)( 6.0%)  4.9 1.000 0.000 0.00 -4.0 0.0 0.0 0. 0.1236 0.00 0.0003 5.16 (*) (*) (*) (*) (*) (*) (*) ( 0.1%) (*)  ---------------------------------------------------------------------------------------------------------------- 26592 2.632 0.6 0.292 3.000 -1.00 2.457 -11.0 0.20 -0.0258 -0.06 0.0002 0.25 ( 0.0%) (*) (*) ( 0.6%) (*) (*) ( 0.3%)( 2.5%)  1.7 3.000 0.000 0.00 -4.0 0.0 0.0 0. 0.1227 0.00 0.0002 6.56 (*) (*) (*) (*) (*) (*) (*) ( 0.1%) (*)  ----------------------------------------------------------------------------------------------------------------
74

 6 DOF Summary Output  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Erro Shot Numbers Number DBSQ CX CNa CYpa Cma Cmq Cnpa Clp | X(m) Angle ABARM CX2 CNa3 CYpa3 Cma3 Cmq2 Cnpa3 CXm | Y-Z(m) Roll CX4 CNa5 Cma5 Cmq4 Cnpa5 CmaM |  ---------------------------------------------------------------------------------------------------------------- 27350 27351 1.683 28.1 0.383 2.970 -1.00 2.720 -12.0 0.07 -0.0303 0.0005 0.249 (*) ( 0.8%) (*) ( 0.1%)( 2.4%)(42.0%) (*)  27353 27352 14.9 2.297 0.000 0.00 -1.978 0.0 8.10 -0.0766 0.0003 11.280 (*) (*) (*) ( 9.8%) (*) (12.3%)( 3.6%)  0.00 0.00 0.0 0. 0. -0.294  (*) (*) (*) (*) (*) (12.8%)  ---------------------------------------------------------------------------------------------------------------- 27350 27351 1.683 28.4 0.384 3.198 -1.00 2.684 -11.4 0.15 -0.0286 0.0009 0.454 ( 0.1%)( 1.3%) (*) ( 0.1%)( 4.8%)(37.2%)( 0.4%)  27352 27353 15.0 2.208 0.000 0.00 0.000 0.0 0.00 -0.1040 0.0004 16.530 ( 2.3%) (*) (*) (*) (*) (*) ( 3.0%)  0.00 0.00 0.0 0. 0. 0.000  (*) (*) (*) (*) (*) (*)  ---------------------------------------------------------------------------------------------------------------- 27346 27344 1.697 6.0 0.372 3.136 -1.00 2.658 -9.9 -0.62 -0.0317 0.0005 0.230 (*) ( 1.4%) (*) ( 0.1%)( 7.6%)( 9.7%) (*)  27353 27345 7.6 3.788 0.000 0.00 9.861 0.0 95.00 -0.0861 0.0002 6.265 (*) (*) (*) ( 9.4%) (*) ( 6.6%) (*)  0.00 0.00 0.0 0. 0. -0.642  (*) (*) (*) (*) (*) ( 8.1%)  ---------------------------------------------------------------------------------------------------------------- 27345 27347 1.705 3.2 0.375 3.000 -1.00 2.665 -6.1 -0.59 -0.0367 0.0003 0.219 (*) (*) (*) ( 0.1%)(17.9%)( 4.2%) (*)  27346 27344 3.0 2.300 0.000 0.00 -2.500 0.0 0.00 -0.1023 0.0001 6.311 (*) (*) (*) (*) (*) (*) ( 1.0%)  0.00 0.00 0.0 0. 0. -0.371  (*) (*) (*) (*) (*) (16.5%)  ---------------------------------------------------------------------------------------------------------------- 26827 26833 2.211 6.7 0.320 2.886 -1.00 2.530 -11.5 0.15 -0.0249 0.0004 0.275 (*) ( 1.0%) (*) ( 0.2%)( 4.9%)(33.2%) (*)  26826 26834 8.5 4.270 0.000 0.00 -5.263 0.0 0.00 -0.0768 0.0002 6.333 (*) (*) (*) (14.5%) (*) (*) ( 1.6%)  26831 0.00 0.00 0.0 0. 0. 0.000  (*) (*) (*) (*) (*) (*)  ---------------------------------------------------------------------------------------------------------------- 26827 26829 2.223 5.4 0.325 0.335 -1.00 0.000 -14.6 0.48 -0.0274 0.0009 0.213 (*) (26.3%) (*) (*) ( 2.7%)( 7.1%) (*) 
75

 26831 26832 6.9 3.414303.928 0.00 -4.000 0.0 0.00 -0.0603 0.0007 5.344 (*) ( 5.0%) (*) (*) (*) (*) (*)  26833 0.00 0.00 0.0 0. 0. 0.000  (*) (*) (*) (*) (*) (*)  ---------------------------------------------------------------------------------------------------------------- 26826 26828 2.234 6.1 0.322 2.918 -1.00 0.000 -11.4 0.02 -0.0249 0.0006 0.227 (*) ( 1.1%) (*) (*) ( 4.2%) (-) (*)  26831 26832 8.5 2.310 0.000 0.00 -4.979 0.0 25.52 -0.0221 0.0002 5.573 (*) (*) (*) (*) (*) (17.6%) (*)  26834 0.00 0.00 0.0 0. 0. 0.000  (*) (*) (*) (*) (*) (*)  ---------------------------------------------------------------------------------------------------------------- 26831 26829 2.239 6.2 0.323 3.079 -1.00 2.545 -11.2 0.02 -0.0272 0.0004 0.244 (*) ( 1.0%) (*) ( 0.1%)( 4.6%) (-) (*)  26828 26832 8.5 3.000 0.000 0.00 -6.835 0.0 21.64 -0.0572 0.0002 5.064 (*) (*) (*) (10.0%) (*) (21.6%)( 2.1%)  26834 0.00 0.00 0.0 0. 0. 0.000  (*) (*) (*) (*) (*) (*)  ---------------------------------------------------------------------------------------------------------------- 26597 26592 2.461 6.1 0.307 2.891 -1.00 2.469 -11.8 0.19 -0.0268 0.0003 0.266 (*) ( 0.8%) (*) ( 0.1%)( 4.7%)(26.2%) (*)  26590 26834 8.5 3.824 0.000 0.00 -4.000 0.0 0.00 -0.0687 0.0002 7.182 (*) (*) (*) (*) (*) (*) ( 1.3%)  26833 0.00 0.00 0.0 0. 0. -0.224  (*) (*) (*) (*) (*) ( 5.6%)  ---------------------------------------------------------------------------------------------------------------- 26590 26591 2.621 3.0 0.299 3.010 -1.00 0.000 -15.4 0.29 -0.0260 0.0003 0.276 (*) ( 1.2%) (*) (*) ( 6.4%)(28.1%) (*)  26592 26598 6.0 3.000 0.000 0.00 -4.000 0.0 1.10 -0.0632 0.0003 5.159 (*) (*) (*) (*) (*) (-) (*)  26597 0.00 0.00 0.0 0. 0. 0.000  (*) (*) (*) (*) (*) (*)  ---------------------------------------------------------------------------------------------------------------- 26591 26598 2.621 3.0 0.296 2.928 -1.00 2.449 -15.7 0.32 -0.0260 0.0003 0.316 (*) ( 1.4%) (*) ( 0.2%)( 7.1%)(27.1%) (*)  26590 26592 6.0 3.000 0.000 0.00 -3.000 0.0 0.00 -0.0617 0.0004 5.164 (*) (*) (*) (*) (*) (*) ( 1.7%)  26597 0.00 0.00 0.0 0. 0. 0.000  (*) (*) (*) (*) (*) (*)  ----------------------------------------------------------------------------------------------------------------
76

 M16A2 M855 LR M1.7++ roll pins  6 DOF Summary (ARL Format) (08-AUG-08 09:42:10)  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Error  Shot Number Number DBSQ CD0 CLA0 CYPA CMA CMQ CMPA CLP CXM | X(m) Angle( YAW CD2 CLA3 CYPA3 CMA3 CMQ2 CMPA3 CMPA5 IX/IY CMAM | Y-Z(m) Roll( ---------------------------------------------------------------------------------------------------------------- 27350 1.664 32.0 0.387 2.72 -0.50 2.74 -6.3 0.07 -0.0137 -0.12 0.0005 0.18 5.7 5.4 -2.3 0.0 -2.4 0.0 2.6 0. 0.1201 0.00 0.0002 6.21 27351 1.678 29.5 0.384 2.71 -0.50 2.74 -4.9 0.07 -0.0143 -0.07 0.0002 0.20 5.4 5.4 -2.3 0.0 -3.6 0.0 0.0 0. 0.1218 0.00 0.0002 11.65 27344 1.686 3.2 0.374 2.57 -0.50 2.68 -3.2 -0.41 -0.0160 -0.10 0.0001 0.15 1.8 7.9 -4.9 0.0 -2.5 0.0 54.5 0. 0.1204 -0.43 0.0001 5.84 27346 1.687 3.1 0.372 2.51 -0.50 2.66 -2.3 -0.25 -0.0163 -0.10 0.0001 0.19 1.8 5.2 -2.3 0.0 -2.5 0.0 0.0 0. 0.1200 -0.33 0.0001 5.98 27353 1.689 13.2 0.371 2.60 -0.50 2.71 -4.7 0.00 -0.0151 -0.13 0.0003 0.27 3.6 7.9 -4.9 0.0 0.0 0.0 0.0 0. 0.1220 0.00 0.0002 6.83 27352 1.702 37.1 0.385 2.80 -0.50 2.71 -6.0 0.12 -0.0139 -0.15 0.0005 0.15 6.1 5.5 -2.3 0.0 -2.9 0.0 0.0 0. 0.1216 0.00 0.0003 8.70 27347 1.723 2.1 0.379 2.33 -0.50 2.74 -1.0 -0.31 -0.0235 -0.13 0.0006 0.18 1.5 6.5 -3.8 0.0 0.0 0.0 0.0 0. 0.1235 -0.46 0.0001 6.93 27345 1.725 4.5 0.368 2.35 -0.50 2.66 -3.8 -0.32 -0.0161 -0.10 0.0002 0.20 2.1 7.6 -4.9 0.0 -2.5 0.0 54.5 0. 0.1200 -0.48 0.0001 6.57 26827 2.172 3.2 0.328 2.56 -0.50 2.49 -4.0 -0.11 -0.0124 -0.07 0.0002 0.20 1.8 6.3 -3.4 0.0 -4.0 0.0 0.0 0. 0.1191 0.00 0.0002 7.63 26833 2.212 9.4 0.332 2.63 -0.50 2.52 -6.1 0.09 -0.0127 -0.05 0.0002 0.23 3.1 6.0 -3.0 0.0 -4.0 0.0 0.0 0. 0.1237 0.00 0.0002 4.98 26834 2.215 14.4 0.325 2.64 -0.50 2.51 -6.9 -0.07 -0.0121 -0.01 0.0003 0.25 3.8 5.3 -2.3 0.0 -2.8 0.0 23.5 0. 0.1241 0.00 0.0002 6.70
77

 M16A2 M855 LR M1.7++ roll pins  6 DOF Summary (ARL Format) (08-AUG-08 09:42:10)  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Error  Shot Number Number DBSQ CD0 CLA0 CYPA CMA CMQ CMPA CLP CXM | X(m) Angle( YAW CD2 CLA3 CYPA3 CMA3 CMQ2 CMPA3 CMPA5 IX/IY CMAM | Y-Z(m) Roll( ---------------------------------------------------------------------------------------------------------------- 26826 2.224 0.7 0.321 2.68 -0.50 2.55 -5.5 0.10 -0.0119 -0.04 0.0001 0.23 0.9 6.0 -3.0 0.0 -4.0 0.0 0.0 0. 0.1214 0.00 0.0002 7.02 26831 2.230 6.4 0.318 2.64 -0.50 2.55 -4.4 0.03 -0.0134 -0.05 0.0002 0.17 2.5 5.8 -2.9 0.0 -4.0 0.0 0.0 0. 0.1238 0.00 0.0002 5.19 26828 2.248 2.2 0.325 2.67 -0.50 2.51 -4.1 -0.15 -0.0125 -0.07 0.0002 0.15 1.5 6.0 -3.0 0.0 -4.0 0.0 0.0 0. 0.1225 0.00 0.0001 4.55 26829 2.250 1.7 0.328 2.83 -0.50 2.53 -5.9 -0.02 -0.0176 -0.06 0.0002 0.15 1.3 6.2 -3.0 0.0 -4.0 0.0 0.0 0. 0.1230 0.00 0.0001 4.67 26832 2.252 7.4 0.317 2.63 -0.50 2.58 -5.1 0.06 -0.0123 -0.05 0.0002 0.20 2.7 6.4 -3.4 0.0 -10.0 0.0 0.0 0. 0.1235 0.00 0.0001 3.88 26591 2.612 1.2 0.298 2.33 -0.50 2.41 -6.6 0.09 -0.0148 -0.06 0.0002 0.20 1.1 5.6 -3.0 0.0 -4.0 0.0 0.0 0. 0.1233 0.00 0.0001 5.26 26598 2.613 6.7 0.294 2.71 -0.50 2.51 -11.4 0.23 -0.0102 -0.06 0.0003 0.30 2.6 6.0 -3.0 0.0 -7.2 0.0 0.0 0. 0.1261 0.00 0.0006 4.31 26590 2.617 2.0 0.304 2.50 -0.50 2.40 -6.3 0.08 -0.0148 -0.06 0.0003 0.27 1.4 5.8 -3.0 0.0 -4.0 0.0 0.0 0. 0.1227 0.00 0.0002 4.47 26597 2.631 4.5 0.293 2.59 -0.50 2.43 -5.7 0.13 -0.0123 -0.03 0.0002 0.24 2.1 3.9 -1.0 0.0 -4.0 0.0 0.0 0. 0.1236 0.00 0.0003 5.16 26592 2.632 0.6 0.292 2.71 -0.50 2.46 -5.5 0.10 -0.0129 -0.06 0.0002 0.25 0.8 6.0 -3.0 0.0 -4.0 0.0 0.0 0. 0.1227 0.00 0.0002 6.56
78

 M16A2 M855 LR M1.7++ roll pins  6 DOF Summary (ARL Format) (08-AUG-08 09:42:10)  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Erro Shot Numbers Number DBSQ CD0 CLA0 CYPA CMA CMQ CMPA CLP | X(m) Angle Yaw CD2 CLA3 CYPA3 CMA3 CMQ2 CMPA3 CXm | Y-Z(m) Roll CDR CLR CMA5 CMQ4 CMPA5 CmaM |  ---------------------------------------------------------------------------------------------------------------- 27350 27351 1.683 28.1 0.383 2.59 -0.50 2.72 -6.0 0.04 -0.0151 0.0005 0.249 27353 27352 5.3 5.3 -2.3 0.0 -2.0 0.0 4.05 -0.0766 0.0003 11.280 0.426 2.554 0.0 0. 0. -0.294  27350 27351 1.683 28.4 0.384 2.81 -0.50 2.68 -5.7 0.08 -0.0143 0.0009 0.454 27352 27353 5.3 5.4 -2.2 0.0 0.0 0.0 0.00 -0.1040 0.0004 16.530 0.429 2.781 0.0 0. 0. 0.000  27346 27344 1.697 6.0 0.372 2.76 -0.50 2.66 -5.0 -0.31 -0.0159 0.0005 0.230 27353 27345 2.4 6.9 -3.8 0.0 9.9 0.0 47.50 -0.0861 0.0002 6.265 0.385 2.754 0.0 0. 0. -0.642  27345 27347 1.705 3.2 0.375 2.63 -0.50 2.67 -3.0 -0.29 -0.0183 0.0003 0.219 27346 27344 1.8 5.3 -2.3 0.0 -2.5 0.0 0.00 -0.1023 0.0001 6.311 0.380 2.622 0.0 0. 0. -0.371  26827 26833 2.211 6.7 0.320 2.57 -0.50 2.53 -5.7 0.08 -0.0125 0.0004 0.275 26826 26834 2.6 7.2 -4.3 0.0 -5.3 0.0 0.00 -0.0768 0.0002 6.333 26831 0.334 2.554 0.0 0. 0. 0.000  26827 26829 2.223 5.4 0.325 0.01 -0.50 0.00 -7.3 0.24 -0.0137 0.0009 0.213 26831 26832 2.3 3.7 300.3 0.0 -4.0 0.0 0.00 -0.0603 0.0007 5.344 26833 0.332 0.501 0.0 0. 0. 0.000  26826 26828 2.234 6.1 0.322 2.60 -0.50 0.00 -5.7 0.01 -0.0124 0.0006 0.227 26831 26832 2.5 5.2 -2.3 0.0 -5.0 0.0 12.76 -0.0221 0.0002 5.573 26834 0.332 2.588 0.0 0. 0. 0.000  26831 26829 2.239 6.2 0.323 2.76 -0.50 2.54 -5.6 0.01 -0.0136 0.0004 0.244 26828 26832 2.5 6.1 -3.0 0.0 -6.8 0.0 10.82 -0.0572 0.0002 5.064 26834 0.334 2.748 0.0 0. 0. 0.000  26597 26592 2.461 6.1 0.307 2.58 -0.50 2.47 -5.9 0.10 -0.0134 0.0003 0.266 26590 26834 2.5 6.7 -3.8 0.0 -4.0 0.0 0.00 -0.0687 0.0002 7.182 26833 0.320 2.574 0.0 0. 0. -0.224  26590 26591 2.621 3.0 0.299 2.71 -0.50 0.00 -7.7 0.14 -0.0130 0.0003 0.276 26592 26598 1.7 6.0 -3.0 0.0 -4.0 0.0 0.55 -0.0632 0.0003 5.159 26597 0.304 2.707 0.0 0. 0. 0.000  26591 26598 2.621 3.0 0.296 2.63 -0.50 2.45 -7.9 0.16 -0.0130 0.0003 0.316 26590 26592 1.7 5.9 -3.0 0.0 -3.0 0.0 0.00 -0.0617 0.0004 5.164 26597 0.301 2.628 0.0 0. 0. 0.000
79

 M16A2 M855 LR M1.7++ roll pins  6 DOF Summary (ARL Format) (08-AUG-08 09:42:10)  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Erro Shot Numbers Number DBSQ CD0 CLA0 CYPA CMA CMQ CMPA CLP | X(m) Angle Yaw CD2 CLA3 CYPA3 CMA3 CMQ2 CMPA3 CXm | Y-Z(m) Roll CDR CLR CMA5 CMQ4 CMPA5 CmaM |  ---------------------------------------------------------------------------------------------------------------- M16A2 M855 LR M1.5 roll pins  6 DOF Summary Output (11-JUL-08 10:23:41)  ---------------------------------------------------------------------------------------------------------------- Ref. Ref. Ref.Mach Mach Max Angle | Standard Er Shot Number Date Time CG Length Number Number DBSQ of Attack | X Y-Z Angle  (mm) (mm) (deg2) (deg) | (m) (m) (deg)  ---------------------------------------------------------------------------------------------------------------- 29270 08-JUL-08 16:03:04 14.30 23.06 1.15 1.151 13.090 4.2 0.0004 0.0002 0.173  29266 09-JUL-08 08:31:25 14.30 23.06 1.15 1.157 6.372 3.7 0.0012 0.0003 0.194  29271 08-JUL-08 10:28:05 14.30 23.06 1.20 1.180 13.900 5.8 0.0005 0.0002 0.172  29268 08-JUL-08 11:25:56 14.30 23.06 1.20 1.186 10.110 4.1 0.0007 0.0002 0.195  29267 08-JUL-08 11:24:32 14.30 23.06 1.20 1.188 16.020 7.3 0.0005 0.0002 0.194  29269 08-JUL-08 11:35:00 14.30 23.06 1.20 1.201 12.390 5.8 0.0004 0.0002 0.204  28106 14-FEB-08 14:14:37 14.27 23.06 1.45 1.457 8.963 5.1 0.0001 0.0001 0.162  28099 14-FEB-08 14:14:38 14.27 23.06 1.45 1.458 8.675 5.4 0.0001 0.0001 0.138  28092 11-MAR-08 10:36:32 14.27 23.06 1.45 1.459 6.820 3.5 0.0001 0.0001 0.196  28096 25-FEB-08 14:12:16 14.27 23.06 1.45 1.467 9.598 6.3 0.0001 0.0001 0.144  28097 14-FEB-08 14:14:41 14.27 23.06 1.45 1.473 5.459 4.1 0.0001 0.0001 0.162  28104 25-FEB-08 14:17:16 14.27 23.06 1.45 1.473 23.300 10.6 0.0003 0.0001 0.224  28098 14-FEB-08 14:14:43 14.27 23.06 1.50 1.485 2.705 2.1 0.0001 0.0001 0.166  28105 14-FEB-08 14:14:44 14.27 23.06 1.50 1.485 16.330 8.2 0.0001 0.0001 0.178  28107 25-FEB-08 13:45:23 14.27 23.06 1.50 1.488 8.774 6.0 0.0002 0.0001 0.148  28093 11-MAR-08 10:34:23 14.27 23.06 1.50 1.490 2.801 2.7 0.0001 0.0002 0.157  28094 11-MAR-08 10:41:41 14.27 23.06 1.50 1.490 3.546 3.0 0.0001 0.0001 0.158 
80

 M16A2 M855 LR M1.5 roll pins  6 DOF Summary Output (11-JUL-08 10:23:41)  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Error  Shot Number Number DBSQ CX CNa CYpa Cma Cmq Cnpa Clp CXM | X(m) Angle( ABARM CX2 CNa3 CYpa3 Cma3 Cmq2 Cnpa3 Cnpa5 IX/IY CmaM | Y-Z(m) Roll( ---------------------------------------------------------------------------------------------------------------- 29270 1.151 13.1 0.446 2.791 -1.00 2.847 -11.0 -1.21 -0.0231 -0.06 0.0004 0.17 4.2 5.198 0.000 0.00 0.0 0.0 159.4 0. 0.1224 0.00 0.0002 8.18 29266 1.157 6.4 0.450 2.309 -1.00 2.823 -1.8 -1.31 -0.0270 -0.14 0.0012 0.19 3.7 5.226 0.000 0.00 0.0 0.0 179.4 0. 0.1199 0.00 0.0003 0.00 29271 1.180 13.9 0.438 2.721 -1.00 2.811 -9.1 -0.90 -0.0286 -0.14 0.0005 0.17 5.8 5.326 0.000 0.00 9.7 0.0 97.4 0. 0.1217 0.00 0.0002 8.53 29268 1.186 10.1 0.444 2.731 -1.00 2.861 -6.5 -0.62 -0.0270 -0.11 0.0007 0.19 4.1 5.356 0.000 0.00 0.0 0.0 0.0 0. 0.1212 0.00 0.0002 0.00 29267 1.188 16.0 0.440 2.739 -1.00 2.878 -8.8 -0.67 -0.0270 -0.17 0.0005 0.19 7.3 5.361 0.000 0.00 2.8 0.0 56.7 0. 0.1219 0.00 0.0002 0.00 29269 1.201 12.4 0.441 2.642 -1.00 2.784 -8.8 -0.97 -0.0270 -0.13 0.0004 0.20 5.8 5.422 0.000 0.00 17.7 0.0 119.4 0. 0.1223 0.00 0.0002 0.00 28106 1.457 9.0 0.399 2.868 -1.00 2.734 -7.4 -0.24 -0.0283 -0.16 0.0001 0.16 5.1 4.467 0.000 0.00 0.0 0.0 0.0 0. 0.1192 0.00 0.0001 8.39 28099 1.458 8.7 0.413 2.911 -1.00 2.734 -8.3 -0.24 -0.0258 -0.17 0.0001 0.13 5.4 4.482 0.000 0.00 0.0 0.0 0.0 0. 0.1202 0.00 0.0001 3.96 28092 1.459 6.8 0.420 2.858 -1.00 2.810 -9.2 -0.51 -0.0300 -0.13 0.0001 0.19 3.5 4.477 0.000 0.00 0.0 0.0 0.0 0. 0.1205 0.00 0.0001 0.00 28096 1.467 9.6 0.407 2.850 -1.00 2.699 -9.9 -0.20 -0.0324 -0.16 0.0001 0.14 6.3 4.430 0.000 0.00 0.0 0.0 21.0 0. 0.1188 0.00 0.0001 10.13 28097 1.473 5.5 0.396 2.906 -1.00 2.824 -10.9 -0.20 -0.0276 -0.16 0.0001 0.16 4.1 4.402 0.000 0.00 0.0 0.0 0.0 0. 0.1228 0.00 0.0001 4.42
81

 M16A2 M855 LR M1.5 roll pins  6 DOF Summary Output (11-JUL-08 10:23:41)  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Error  Shot Number Number DBSQ CX CNa CYpa Cma Cmq Cnpa Clp CXM | X(m) Angle( ABARM CX2 CNa3 CYpa3 Cma3 Cmq2 Cnpa3 Cnpa5 IX/IY CmaM | Y-Z(m) Roll( ---------------------------------------------------------------------------------------------------------------- 28104 1.473 23.3 0.394 2.945 -1.00 2.792 -9.8 0.03 -0.0307 -0.22 0.0003 0.22 10.6 4.422 0.000 0.00 0.0 0.0 0.0 0. 0.1218 0.00 0.0001 6.75 28098 1.485 2.7 0.403 3.021 -1.00 2.824 -19.1 -0.40 -0.0339 -0.15 0.0001 0.16 2.1 4.352 0.000 0.00 0.0 0.0 0.0 0. 0.1230 0.00 0.0001 4.86 28105 1.485 16.3 0.392 2.923 -1.00 2.763 -9.0 -0.05 -0.0301 -0.16 0.0001 0.17 8.2 4.366 0.000 0.00 0.0 0.0 0.0 0. 0.1212 0.00 0.0001 6.69 28107 1.488 8.8 0.398 3.049 -1.00 2.799 -8.8 -0.24 -0.0295 -0.14 0.0002 0.14 6.0 4.400 0.000 0.00 0.0 0.0 21.0 0. 0.1216 0.00 0.0001 5.54 28093 1.490 2.8 0.396 3.002 -1.00 2.798 -10.1 -0.36 -0.0300 -0.15 0.0001 0.15 2.7 4.355 0.000 0.00 0.0 0.0 0.0 0. 0.1198 0.00 0.0002 0.00 28094 1.490 3.5 0.406 3.002 -1.00 2.793 -15.7 -0.26 -0.0270 -0.13 0.0001 0.15 3.0 4.335 0.000 0.00 0.0 0.0 0.0 0. 0.1204 0.00 0.0001 0.00
82

 M16A2 M855 LR M1.5 roll pins  6 DOF Summary Output (11-JUL-08 10:23:41)  ---------------------------------------------------------------------------------------------------------------- Ref. Mach Mach Max Angle | Standard Error  Shot Numbers Date Time Number Number DBSQ of Attack | X Y-Z Angle Rol (deg2) (deg) | (m) (m) (deg) (deg ---------------------------------------------------------------------------------------------------------------- 29270 29271 08-JUL-08 11:38:22 1.200 1.181 13.04 7.27 0.0005 0.0002 0.215 5.19 29267 29269  29268  28099 28092 12-JUL-07 12:20:44 1.450 1.466 10.61 10.61 0.0004 0.0001 0.212 6.06 28096 28097  28104  28106 28107 09-JUL-08 13:31:41 1.500 1.474 13.29 10.54 0.0004 0.0001 0.172 7.58 28096 28104  28105  28096 28106 20-FEB-08 09:39:57 1.500 1.476 6.03 6.29 0.0007 0.0002 0.166 6.19 28097 28094  28093  28098 28093 09-JUL-08 13:44:14 1.450 1.477 6.45 6.29 0.0006 0.0001 0.164 5.89 28107 28096  28099  28098 28105 12-JUL-07 12:46:30 1.500 1.488 6.73 8.24 0.0004 0.0002 0.241 4.43 28107 28093  28094 
83

 M16A2 M855 LR M1.5 roll pins  6 DOF Summary Output (11-JUL-08 10:23:41)  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Erro Shot Numbers Number DBSQ CX CNa CYpa Cma Cmq Cnpa Clp | X(m) Angle ABARM CX2 CNa3 CYpa3 Cma3 Cmq2 Cnpa3 CXm | Y-Z(m) Roll CX4 CNa5 Cma5 Cmq4 Cnpa5 CmaM |  ---------------------------------------------------------------------------------------------------------------- 29270 29271 1.181 13.0 0.449 2.718 -1.00 2.812 -8.6 -0.82 -0.0260 0.0005 0.214 29267 29269 7.3 3.360 0.000 0.00 11.816 0.0 75.87 -0.1371 0.0002 5.199 29268 0.00 0.00 0.0 0. 0. 0.000  28099 28092 1.466 10.6 0.404 2.852 -1.00 0.000 -10.9 -0.29 -0.0295 0.0004 0.211 28096 28097 10.6 4.422 0.000 0.00 0.000 0.0 31.07 -0.1608 0.0001 6.062 28104 0.00 0.00 0.0 0. 0. 0.000  28106 28107 1.474 13.3 0.402 2.869 -1.00 0.000 -10.2 -0.20 -0.0302 0.0004 0.171 28096 28104 10.5 4.366 0.000 0.00 -1.632 0.0 22.13 -0.1523 0.0001 7.587 28105 0.00 0.00 0.0 0. 0. 0.000  28096 28106 1.476 6.0 0.399 2.606 -1.00 0.000 -11.6 -0.32 -0.0373 0.0007 0.165 28097 28094 6.3 4.355 0.000 0.00 0.000 0.0 66.16 -0.1055 0.0002 6.193 28093 0.00 0.00 0.0 0. 0. 0.000  28098 28093 1.477 6.5 0.400 3.133 -1.00 0.000 -10.4 -0.49 -0.0308 0.0006 0.164 28107 28096 6.3 6.809 0.000 0.00 0.000 0.0 86.59 -0.2014 0.0001 5.899 28099 0.00 0.00 0.0 0. 0. 0.000  28098 28105 1.488 6.7 0.404 3.105 -1.00 2.780 -10.2 -0.39 -0.0373 0.0004 0.240 28107 28093 8.2 4.335 0.000 0.00 0.000 0.0 48.17 -0.1426 0.0002 4.438 28094 0.00 0.00 0.0 0. 0. 0.000 
84

 6 DOF Summary Output  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Error  Shot Number Number DBSQ CX CNa CYpa Cma Cmq Cnpa Clp CXM | X(m) Angle( ABARM CX2 CNa3 CYpa3 Cma3 Cmq2 Cnpa3 Cnpa5 IX/IY CmaM | Y-Z(m) Roll( ---------------------------------------------------------------------------------------------------------------- 29270 1.151 13.1 0.446 2.791 -1.00 2.847 -11.0 -1.21 -0.0231 -0.06 0.0004 0.17 ( 0.1%)( 2.1%) (*) ( 0.1%)(15.4%)(11.1%) ( 0.5%) (*)  4.2 5.198 0.000 0.00 0.0 0.0 159.4 0. 0.1224 0.00 0.0002 8.18 (*) (*) (*) (*) (*) (18.9%) (*) ( 0.1%) (*)  ---------------------------------------------------------------------------------------------------------------- 29266 1.157 6.4 0.450 2.309 -1.00 2.823 -1.8 -1.31 -0.0270 -0.14 0.0012 0.19 ( 0.1%)( 9.9%) (*) ( 0.2%) (*) ( 9.6%) (*) ( 7.6%)  3.7 5.226 0.000 0.00 0.0 0.0 179.4 0. 0.1199 0.00 0.0003 0.00 (*) (*) (*) (*) (*) (22.3%) (*) ( 0.1%) (*)  ---------------------------------------------------------------------------------------------------------------- 29271 1.180 13.9 0.438 2.721 -1.00 2.811 -9.1 -0.90 -0.0286 -0.14 0.0005 0.17 ( 0.1%)( 3.1%) (*) ( 0.5%)(12.6%)(16.0%) ( 0.4%) (*)  5.8 5.326 0.000 0.00 9.7 0.0 97.4 0. 0.1217 0.00 0.0002 8.53 (*) (*) (*) (32.7%) (*) (29.6%) (*) ( 0.1%) (*)  ---------------------------------------------------------------------------------------------------------------- 29268 1.186 10.1 0.444 2.731 -1.00 2.861 -6.5 -0.62 -0.0270 -0.11 0.0007 0.19 ( 0.1%)( 3.9%) (*) ( 0.1%)(19.1%)(15.0%) (*) (*)  4.1 5.356 0.000 0.00 0.0 0.0 0.0 0. 0.1212 0.00 0.0002 0.00 (*) (*) (*) (*) (*) (*) (*) ( 0.0%) (*)  ---------------------------------------------------------------------------------------------------------------- 29267 1.188 16.0 0.440 2.739 -1.00 2.878 -8.8 -0.67 -0.0270 -0.17 0.0005 0.19 ( 0.1%)( 2.7%) (*) ( 0.2%)(10.1%)(15.7%) (*) ( 2.6%)  7.3 5.361 0.000 0.00 2.8 0.0 56.7 0. 0.1219 0.00 0.0002 0.00 (*) (*) (*) (45.4%) (*) (21.8%) (*) ( 0.0%) (*)  ---------------------------------------------------------------------------------------------------------------- 29269 1.201 12.4 0.441 2.642 -1.00 2.784 -8.8 -0.97 -0.0270 -0.13 0.0004 0.20 ( 0.1%)( 2.9%) (*) ( 0.6%)(14.4%)(18.9%) (*) ( 3.1%)  5.8 5.422 0.000 0.00 17.7 0.0 119.4 0. 0.1223 0.00 0.0002 0.00 (*) (*) (*) (23.5%) (*) (33.0%) (*) ( 0.1%) (*)  ---------------------------------------------------------------------------------------------------------------- 28106 1.457 9.0 0.399 2.868 -1.00 2.734 -7.4 -0.24 -0.0283 -0.16 0.0001 0.16 ( 0.0%)( 1.2%) (*) ( 0.1%)(12.1%)(33.1%) ( 0.4%)( 0.8%)  5.1 4.467 0.000 0.00 0.0 0.0 0.0 0. 0.1192 0.00 0.0001 8.39 (*) (*) (*) (*) (*) (*) (*) ( 0.0%) (*)  ----------------------------------------------------------------------------------------------------------------
85

 28099 1.458 8.7 0.413 2.911 -1.00 2.734 -8.3 -0.24 -0.0258 -0.17 0.0001 0.13 ( 0.0%)( 1.0%) (*) ( 0.1%)( 9.6%)(30.7%) ( 0.3%)( 0.7%)  5.4 4.482 0.000 0.00 0.0 0.0 0.0 0. 0.1202 0.00 0.0001 3.96 (*) (*) (*) (*) (*) (*) (*) ( 0.0%) (*)  ---------------------------------------------------------------------------------------------------------------- 28092 1.459 6.8 0.420 2.858 -1.00 2.810 -9.2 -0.51 -0.0300 -0.13 0.0001 0.19 ( 0.0%)( 1.5%) (*) ( 0.2%)(19.2%)(24.5%) (*) ( 1.1%)  3.5 4.477 0.000 0.00 0.0 0.0 0.0 0. 0.1205 0.00 0.0001 0.00 (*) (*) (*) (*) (*) (*) (*) ( 0.1%) (*)  ---------------------------------------------------------------------------------------------------------------- 28096 1.467 9.6 0.407 2.850 -1.00 2.699 -9.9 -0.20 -0.0324 -0.16 0.0001 0.14 ( 0.0%)( 1.1%) (*) ( 0.1%)( 7.4%)(35.5%) ( 0.4%)( 0.8%)  6.3 4.430 0.000 0.00 0.0 0.0 21.0 0. 0.1188 0.00 0.0001 10.13 (*) (*) (*) (*) (*) (*) (*) ( 0.0%) (*)  ---------------------------------------------------------------------------------------------------------------- 28097 1.473 5.5 0.396 2.906 -1.00 2.824 -10.9 -0.20 -0.0276 -0.16 0.0001 0.16 ( 0.0%)( 1.3%) (*) ( 0.1%)(11.1%)(54.0%) ( 0.2%)( 0.7%)  4.1 4.402 0.000 0.00 0.0 0.0 0.0 0. 0.1228 0.00 0.0001 4.42 (*) (*) (*) (*) (*) (*) (*) ( 0.0%) (*)  ---------------------------------------------------------------------------------------------------------------- 28104 1.473 23.3 0.394 2.945 -1.00 2.792 -9.8 0.03 -0.0307 -0.22 0.0003 0.22 ( 0.1%)( 1.3%) (*) ( 0.1%)( 7.1%) (-) ( 0.3%)( 1.4%)  10.6 4.422 0.000 0.00 0.0 0.0 0.0 0. 0.1218 0.00 0.0001 6.75 (*) (*) (*) (*) (*) (*) (*) ( 0.0%) (*)  ---------------------------------------------------------------------------------------------------------------- 28098 1.485 2.7 0.403 3.021 -1.00 2.824 -19.1 -0.40 -0.0339 -0.15 0.0001 0.16 ( 0.0%)( 1.9%) (*) ( 0.3%)(21.4%)(41.2%) ( 0.2%)( 0.8%)  2.1 4.352 0.000 0.00 0.0 0.0 0.0 0. 0.1230 0.00 0.0001 4.86 (*) (*) (*) (*) (*) (*) (*) ( 0.2%) (*)  ---------------------------------------------------------------------------------------------------------------- 28105 1.485 16.3 0.392 2.923 -1.00 2.763 -9.0 -0.05 -0.0301 -0.16 0.0001 0.17 ( 0.0%)( 0.6%) (*) ( 0.1%)( 7.5%) (-) ( 0.3%)( 0.7%)  8.2 4.366 0.000 0.00 0.0 0.0 0.0 0. 0.1212 0.00 0.0001 6.69 (*) (*) (*) (*) (*) (*) (*) ( 0.0%) (*)  ---------------------------------------------------------------------------------------------------------------- 28107 1.488 8.8 0.398 3.049 -1.00 2.799 -8.8 -0.24 -0.0295 -0.14 0.0002 0.14 ( 0.0%)( 1.2%) (*) ( 0.1%)( 8.9%)(32.9%) ( 0.3%)( 1.0%)  6.0 4.400 0.000 0.00 0.0 0.0 21.0 0. 0.1216 0.00 0.0001 5.54 (*) (*) (*) (*) (*) (*) (*) ( 0.0%) (*)  ----------------------------------------------------------------------------------------------------------------
86

 6 DOF Summary Output  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Error  Shot Number Number DBSQ CX CNa CYpa Cma Cmq Cnpa Clp CXM | X(m) Angle( ABARM CX2 CNa3 CYpa3 Cma3 Cmq2 Cnpa3 Cnpa5 IX/IY CmaM | Y-Z(m) Roll( ---------------------------------------------------------------------------------------------------------------- 28093 1.490 2.8 0.396 3.002 -1.00 2.798 -10.1 -0.36 -0.0300 -0.15 0.0001 0.15 ( 0.0%)( 2.3%) (*) ( 0.2%)(20.3%)(42.8%) (*) ( 1.1%)  2.7 4.355 0.000 0.00 0.0 0.0 0.0 0. 0.1198 0.00 0.0002 0.00 (*) (*) (*) (*) (*) (*) (*) ( 0.1%) (*)  ---------------------------------------------------------------------------------------------------------------- 28094 1.490 3.5 0.406 3.002 -1.00 2.793 -15.7 -0.26 -0.0270 -0.13 0.0001 0.15 ( 0.0%)( 1.6%) (*) ( 0.2%)(13.3%)(47.7%) (*) ( 0.8%)  3.0 4.335 0.000 0.00 0.0 0.0 0.0 0. 0.1204 0.00 0.0001 0.00 (*) (*) (*) (*) (*) (*) (*) ( 0.1%) (*)  ----------------------------------------------------------------------------------------------------------------
87

 6 DOF Summary Output  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Erro Shot Numbers Number DBSQ CX CNa CYpa Cma Cmq Cnpa Clp | X(m) Angle ABARM CX2 CNa3 CYpa3 Cma3 Cmq2 Cnpa3 CXm | Y-Z(m) Roll CX4 CNa5 Cma5 Cmq4 Cnpa5 CmaM |  ---------------------------------------------------------------------------------------------------------------- 29270 29271 1.181 13.0 0.449 2.718 -1.00 2.812 -8.6 -0.82 -0.0260 0.0005 0.214 (*) ( 1.3%) (*) ( 0.2%)( 6.1%)( 5.8%) (*)  29267 29269 7.3 3.360 0.000 0.00 11.816 0.0 75.87 -0.1371 0.0002 5.199 (*) (*) (*) ( 7.9%) (*) ( 8.2%) (*)  29268 0.00 0.00 0.0 0. 0. 0.000  (*) (*) (*) (*) (*) (*)  ---------------------------------------------------------------------------------------------------------------- 28099 28092 1.466 10.6 0.404 2.852 -1.00 0.000 -10.9 -0.29 -0.0295 0.0004 0.211 (*) ( 1.0%) (*) (*) ( 4.2%)(14.5%) (*)  28096 28097 10.6 4.422 0.000 0.00 0.000 0.0 31.07 -0.1608 0.0001 6.062 (*) (*) (*) (*) (*) ( 6.2%)( 0.8%)  28104 0.00 0.00 0.0 0. 0. 0.000  (*) (*) (*) (*) (*) (*)  ---------------------------------------------------------------------------------------------------------------- 28106 28107 1.474 13.3 0.402 2.869 -1.00 0.000 -10.2 -0.20 -0.0302 0.0004 0.171 (*) ( 0.7%) (*) (*) ( 3.0%)(14.6%) (*)  28096 28104 10.5 4.366 0.000 0.00 -1.632 0.0 22.13 -0.1523 0.0001 7.587 (*) (*) (*) (19.5%) (*) ( 7.0%) (*)  28105 0.00 0.00 0.0 0. 0. 0.000  (*) (*) (*) (*) (*) (*)  ---------------------------------------------------------------------------------------------------------------- 28096 28106 1.476 6.0 0.399 2.606 -1.00 0.000 -11.6 -0.32 -0.0373 0.0007 0.165 (*) ( 2.2%) (*) (*) ( 4.8%)(14.6%) (*)  28097 28094 6.3 4.355 0.000 0.00 0.000 0.0 66.16 -0.1055 0.0002 6.193 (*) (*) (*) (*) (*) (10.4%) (*)  28093 0.00 0.00 0.0 0. 0. 0.000  (*) (*) (*) (*) (*) (*)  ----------------------------------------------------------------------------------------------------------------
88

 28098 28093 1.477 6.5 0.400 3.133 -1.00 0.000 -10.4 -0.49 -0.0308 0.0006 0.164 (*) ( 1.7%) (*) (*) ( 4.7%)( 9.4%) (*)  28107 28096 6.3 6.809 0.000 0.00 0.000 0.0 86.59 -0.2014 0.0001 5.899 (*) (*) (*) (*) (*) ( 6.8%) (*)  28099 0.00 0.00 0.0 0. 0. 0.000  (*) (*) (*) (*) (*) (*)  ---------------------------------------------------------------------------------------------------------------- 28098 28105 1.488 6.7 0.404 3.105 -1.00 2.780 -10.2 -0.39 -0.0373 0.0004 0.240 (*) ( 1.1%) (*) ( 0.1%)( 6.7%)(15.6%) (*)  28107 28093 8.2 4.335 0.000 0.00 0.000 0.0 48.17 -0.1426 0.0002 4.438 (*) (*) (*) (*) (*) ( 8.9%)( 0.9%)  28094 0.00 0.00 0.0 0. 0. 0.000  (*) (*) (*) (*) (*) (*)  ----------------------------------------------------------------------------------------------------------------
89

 M16A2 M855 LR M1.5 roll pins  6 DOF Summary (ARL Format) (11-JUL-08 10:23:41)  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Error  Shot Number Number DBSQ CD0 CLA0 CYPA CMA CMQ CMPA CLP CXM | X(m) Angle( YAW CD2 CLA3 CYPA3 CMA3 CMQ2 CMPA3 CMPA5 IX/IY CMAM | Y-Z(m) Roll( ---------------------------------------------------------------------------------------------------------------- 29270 1.151 13.1 0.446 2.34 -0.50 2.85 -5.5 -0.60 -0.0116 -0.06 0.0004 0.17 3.6 8.0 -5.2 0.0 0.0 0.0 79.7 0. 0.1224 0.00 0.0002 8.18 29266 1.157 6.4 0.450 1.86 -0.50 2.82 -0.9 -0.65 -0.0135 -0.14 0.0012 0.19 2.5 7.5 -5.2 0.0 0.0 0.0 89.7 0. 0.1199 0.00 0.0003 0.00 29271 1.180 13.9 0.438 2.28 -0.50 2.81 -4.6 -0.45 -0.0143 -0.14 0.0005 0.17 3.7 8.0 -5.3 0.0 9.7 0.0 48.7 0. 0.1217 0.00 0.0002 8.53 29268 1.186 10.1 0.444 2.29 -0.50 2.86 -3.2 -0.31 -0.0135 -0.11 0.0007 0.19 3.2 8.1 -5.4 0.0 0.0 0.0 0.0 0. 0.1212 0.00 0.0002 0.00 29267 1.188 16.0 0.440 2.30 -0.50 2.88 -4.4 -0.34 -0.0135 -0.17 0.0005 0.19 4.0 8.1 -5.4 0.0 2.8 0.0 28.4 0. 0.1219 0.00 0.0002 0.00 29269 1.201 12.4 0.441 2.20 -0.50 2.78 -4.4 -0.48 -0.0135 -0.13 0.0004 0.20 3.5 8.1 -5.4 0.0 17.7 0.0 59.7 0. 0.1223 0.00 0.0002 0.00 28106 1.457 9.0 0.399 2.47 -0.50 2.73 -3.7 -0.12 -0.0142 -0.16 0.0001 0.16 3.0 7.3 -4.5 0.0 0.0 0.0 0.0 0. 0.1192 0.00 0.0001 8.39 28099 1.458 8.7 0.413 2.50 -0.50 2.73 -4.1 -0.12 -0.0129 -0.17 0.0001 0.13 2.9 7.4 -4.5 0.0 0.0 0.0 0.0 0. 0.1202 0.00 0.0001 3.96 28092 1.459 6.8 0.420 2.44 -0.50 2.81 -4.6 -0.25 -0.0150 -0.13 0.0001 0.19 2.6 7.3 -4.5 0.0 0.0 0.0 0.0 0. 0.1205 0.00 0.0001 0.00 28096 1.467 9.6 0.407 2.44 -0.50 2.70 -4.9 -0.10 -0.0162 -0.16 0.0001 0.14 3.1 7.3 -4.4 0.0 0.0 0.0 10.5 0. 0.1188 0.00 0.0001 10.13 28097 1.473 5.5 0.396 2.51 -0.50 2.82 -5.4 -0.10 -0.0138 -0.16 0.0001 0.16 2.3 7.3 -4.4 0.0 0.0 0.0 0.0 0. 0.1228 0.00 0.0001 4.42
90

 M16A2 M855 LR M1.5 roll pins  6 DOF Summary (ARL Format) (11-JUL-08 10:23:41)  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Error  Shot Number Number DBSQ CD0 CLA0 CYPA CMA CMQ CMPA CLP CXM | X(m) Angle( YAW CD2 CLA3 CYPA3 CMA3 CMQ2 CMPA3 CMPA5 IX/IY CMAM | Y-Z(m) Roll( ---------------------------------------------------------------------------------------------------------------- 28104 1.473 23.3 0.394 2.55 -0.50 2.79 -4.9 0.02 -0.0153 -0.22 0.0003 0.22 4.8 7.4 -4.4 0.0 0.0 0.0 0.0 0. 0.1218 0.00 0.0001 6.75 28098 1.485 2.7 0.403 2.62 -0.50 2.82 -9.6 -0.20 -0.0169 -0.15 0.0001 0.16 1.6 7.4 -4.4 0.0 0.0 0.0 0.0 0. 0.1230 0.00 0.0001 4.86 28105 1.485 16.3 0.392 2.53 -0.50 2.76 -4.5 -0.02 -0.0151 -0.16 0.0001 0.17 4.0 7.3 -4.4 0.0 0.0 0.0 0.0 0. 0.1212 0.00 0.0001 6.69 28107 1.488 8.8 0.398 2.65 -0.50 2.80 -4.4 -0.12 -0.0147 -0.14 0.0002 0.14 3.0 7.4 -4.4 0.0 0.0 0.0 10.5 0. 0.1216 0.00 0.0001 5.54 28093 1.490 2.8 0.396 2.61 -0.50 2.80 -5.1 -0.18 -0.0150 -0.15 0.0001 0.15 1.7 7.4 -4.4 0.0 0.0 0.0 0.0 0. 0.1198 0.00 0.0002 0.00 28094 1.490 3.5 0.406 2.60 -0.50 2.79 -7.9 -0.13 -0.0135 -0.13 0.0001 0.15 1.9 7.3 -4.3 0.0 0.0 0.0 0.0 0. 0.1204 0.00 0.0001 0.00
91

 M16A2 M855 LR M1.5 roll pins  6 DOF Summary (ARL Format) (11-JUL-08 10:23:41)  ---------------------------------------------------------------------------------------------------------------- Mach | Standard Erro Shot Numbers Number DBSQ CD0 CLA0 CYPA CMA CMQ CMPA CLP | X(m) Angle Yaw CD2 CLA3 CYPA3 CMA3 CMQ2 CMPA3 CXm | Y-Z(m) Roll CDR CLR CMA5 CMQ4 CMPA5 CmaM |  ---------------------------------------------------------------------------------------------------------------- 29270 29271 1.181 13.0 0.449 2.27 -0.50 2.81 -4.3 -0.41 -0.0130 0.0005 0.214 29267 29269 3.6 6.1 -3.4 0.0 11.8 0.0 37.94 -0.1371 0.0002 5.199 29268 0.473 2.250 0.0 0. 0. 0.000  28099 28092 1.466 10.6 0.404 2.45 -0.50 0.00 -5.5 -0.14 -0.0147 0.0004 0.211 28096 28097 3.3 7.3 -4.4 0.0 0.0 0.0 15.53 -0.1608 0.0001 6.062 28104 0.427 2.429 0.0 0. 0. 0.000  28106 28107 1.474 13.3 0.402 2.47 -0.50 0.00 -5.1 -0.10 -0.0151 0.0004 0.171 28096 28104 3.6 7.2 -4.4 0.0 -1.6 0.0 11.07 -0.1523 0.0001 7.587 28105 0.430 2.443 0.0 0. 0. 0.000  28096 28106 1.476 6.0 0.399 2.21 -0.50 0.00 -5.8 -0.16 -0.0186 0.0007 0.165 28097 28094 2.5 7.0 -4.4 0.0 0.0 0.0 33.08 -0.1055 0.0002 6.193 28093 0.411 2.196 0.0 0. 0. 0.000  28098 28093 1.477 6.5 0.400 2.73 -0.50 0.00 -5.2 -0.25 -0.0154 0.0006 0.164 28107 28096 2.5 9.9 -6.8 0.0 0.0 0.0 43.29 -0.2014 0.0001 5.899 28099 0.419 2.717 0.0 0. 0. 0.000  28098 28105 1.488 6.7 0.404 2.70 -0.50 2.78 -5.1 -0.19 -0.0186 0.0004 0.240 28107 28093 2.6 7.4 -4.3 0.0 0.0 0.0 24.09 -0.1426 0.0002 4.438 28094 0.419 2.689 0.0 0. 0. 0.000 
92 

INTENTIONALLY LEFT BLANK. 
93 

Appendix C. Complete Set of Magnus Moment Plots 

Figures C-1–C-5 illustrate the Magnus moment and stability bounds of several groups with Mach 

numbers ranging from 1.68 to 2.62. At each of these Mach numbers, p Cn remains within the 

stability bounds over the range of angles of attack tested, indicating that a Magnus moment 

instability is not likely present at these Mach numbers. Plots displaying the Magnus moment and 

stability bounds at Machs 1.18, 1.47, 1.48, and 1.7, showing a possible Magnus moment 

instability, can be found in the main body of the report. As Mach 1.7 shows an instability and 

Mach 1.68 does not, it is likely that the round is neutrally stable near Mach 1.7 in the underspun 

condition. 

 at Mach 1.68

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

01234567

Nutation Bound

Precession Bound

Magnus Moment Coefficient



S  0 

0   F

n p C

p n C

Figure C-1. Magnus moment coefficient with stability bounds at Mach 1.68. 

 at Mach 2.21

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

012345678

Nutation Bound

Precession Bound

Magnus Moment Coefficient



S  0

 0  F

n p C

Figure C-2. Magnus moment coefficient with stability bounds at Mach 2.21.
94 

 at Mach 2.24

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

012345678

Nutation Bound

Precession Bound

Magnus Moment Coefficient



0   F

S  0

np C

Figure C-3. Magnus moment coefficient with stability bounds at Mach 2.24. 

 at Mach 2.46

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 0.5 1 1.5 2 2.5 3 3.5 4

Nutation Bound

Precession Bound

Magnus Moment Coefficient



S  0

 0  F

n p C

p n C

Figure C-4. Magnus moment coefficient with stability bounds at Mach 2.46.
95 

 at Mach 2.62

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 0.5 1 1.5 2 2.5 3 3.5 4

Nutation Bound

Precession Bound

Magnus Moment Coefficient



 0  F

S  0

np C

p n C

Figure C-5. Magnus moment coefficient with stability bounds at Mach 2.62.
NO. OF 

COPIES ORGANIZATION

96 

 1 DEFENSE TECHNICAL 

 (PDF INFORMATION CTR 

 only) DTIC OCA 

 8725 JOHN J KINGMAN RD 

 STE 0944 

 FORT BELVOIR VA 22060-6218 

 1 DIRECTOR 

 US ARMY RESEARCH LAB 

 IMNE ALC HRR 

 2800 POWDER MILL RD 

 ADELPHI MD 20783-1197 

 1 DIRECTOR 

 US ARMY RESEARCH LAB 

 RDRL CIM L 

 2800 POWDER MILL RD 

 ADELPHI MD 20783-1197 

 1 DIRECTOR 

 US ARMY RESEARCH LAB 

 RDRL CIM P 

 2800 POWDER MILL RD 

 ADELPHI MD 20783-1197 

 1 DIRECTOR 

 US ARMY RESEARCH LAB 

 RDRL D 

 2800 POWDER MILL RD 

 ADELPHI MD 20783-1197 

ABERDEEN PROVING GROUND

 1 DIR USARL 

 RDRL CIM G (BLDG 4600) 
NO. OF NO. OF 

COPIES ORGANIZATION COPIES ORGANIZATION

97

 1 COMMANDER 

 US ARMY MATL CMD 

 AMXMI INT 

 9301 CHAPEK RD 

 FORT BELVOIR VA 22060-5527 

1 PRODUCT MGR 

SML AND ME CAL AMMO 

 SFAE AMO MAS SMC 

 LTC WOODS 

 BLDG 354 

 PICATINNY ARSENAL NJ 

 07806-5000 

 4 APM 

 SML AND ME CAL AMMO 

 SFAE AMO MAS SMC 

 R KOWALSKI 

 F HANZL 

 P RIGGS 

 G DEROSA 

 BLDG 354 

 PICATINNY ARSENAL NJ 

 07806-5000 

 1 US ARMY ARDEC 

 AMSRD AAR AEM T 

 M NICOLICH 

 BLDG 65S 

 PICATINNY ARSENAL NJ 

 07806-5000 

 1 US ARMY ARDEC 

 AMSRD AAR AEM L 

 D VO 

 BLDG 65 S 

 PICATINNY ARSENAL NJ 

 07806-5000 

 1 US ARMY ARDEC 

 AMSRD AAR AEM S 

 S MUSALLI 

 BLDG 65S 

 PICATINNY ARSENAL NJ 

 07806-5000 

 1 US ARMY ARDEC 

 AMSRD AAR EMB 

 R CARR 

 BLDG 1 

 PICATINNY ARSENAL NJ 

 07806-5000 

 1 US ARMY ARDEC 

 AMSRD AAR AEM L 

 R SAYER 

 BLDG 65 

 PICATINNY ARSENAL NJ 

 07806-5000 

 1 US ARMY ARDEC 

 AMSRD AAR AEW D 

 M MINISI 

 BLDG 65N 

 PICATINNY ARSENAL NJ 

 07806-5000 

 2 US ARMY ARDEC 

 AMSRD AAR AIJ 

 V SCHISSLER 

 K SPIEGEL 

 BLDG 65 

 PICATINNY ARSENAL NJ 

 07806-5000 

 3 US ARMY ARDEC 

 AMSRD AAR AEM I 

 J MIDDLETON 

 BLDG 65N 

 PICATINNY ARSENAL NJ 

 07806-5000 

 1 COMMANDER 

 US ARMY ARDEC 

 AMSRD AAR ATD 

 B MACHAK 

 BLDG 1 

 PICATINNY ARSENAL NJ 

 07806-5000 

 1 US ARMY ARDEC 

 AMSTA AAR AEW A (D) 

 M CHIEFA 

 BLDG 1 

 PICATINNY ARSENAL NJ 

 07806-5000 

 1 US ARMY ARDEC 

 AMSTA AR FSP G 

 M SCHIKSNIS 

 BLDG 1 

 PICATINNY ARSENAL NJ 

 07806-5000 
NO. OF NO. OF 

COPIES ORGANIZATION COPIES ORGANIZATION

98

 1 US ARMY ARDEC 

 AMSTA AR FSP G 

 D CARLUCCI 

 BLDG 1 

 PICATINNY ARSENAL NJ 

 07806-5000 

 14 COMMANDER 

 US ARMY TACOM ARDEC 

 AMSRD AAR AEM A 

 C LIVECCHIA 

 J GRAU 

 B WONG 

 A FARINA 

 G MALEJKO 

 E VAZQUEZ 

 W TOLEDO 

 L YEE 

 R TROHANOWSKY 

 S HAN 

 W KOENIG 

 S CHUNG 

 C WILSON 

 T RECCHIA 

 BLDG 95 

 PICATINNY ARSENAL NJ 07806-5000 

ABERDEEN PROVING GROUND

 4 COMMANDER 

 US ARMY ATC 

 G NIEWENHOUSE 

 G POWERS 

 T HUMISTON 

 J AYERS 

 BLDG 400 

 APG MD 21005 

 4 COMMANDER 

 US ARMY TACOM ARDEC 

 AMSRD AR AEF D 

 R LIESKE 

 J MATTS 

 A SOWA 

 J FONNER 

 BLDG 305 

 APG MD 21005 

 29 DIR USARL 

 RDRL HRS B 

 T FRY 

 RDRL SLB D 

 R KINSLER 

 RDRL WM 

 P PLOSTINS 

 RDRL WMB D 

 B FORCH 

 RDRL WML 

 J NEWILL 

 M ZOLTOSKI 

 RDRL WML A 

 C MERMAGEN 

 W OBERLE 

 J SOUTH 

 S WANSACK 

 D WEBB 

 RDRL WML E 

 I CELMINS 

 G COOPER 

 J DESPIRITO 

 F FRESCONI 

 J GARNER 

 B GUIDOS 

 K HEAVEY 

 B HOWELL 

 J SAHU 

 S SILTON 

 P WEINACHT 

 RDRL WML F 

 D LYON 

 RDRL WML H 

 C CANDLAND 

 T EHLERS 

 L MAGNESS 

 RDRL WMM F 

 R CARTER 

 RDRL WMP 

 P BAKER 

 RDRL WMS 

 T ROSENBERGER