. 

1 

ARMY RESDARCH~ABOIWTORY 

Accuracy and Railguns 

by Alexander E. Zielinski 

ARL-TR-2392 February 2001 

. 

Approved for public release, distribution is unlimited. 
r 

x 

The findings in this report are not to be construed as an official 

Department of the Army position unless so designated by other 

authorized documents. 

Citation of manufacturer’s or trade names does not constitute an 

official endorsement or approval of the use thereof. 

Destroy this report when it is no longer needed. Do not return 

it to the originator. 
Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5066 

ARL-TR-2392 February 2001 

Accuracy and Railguns 

Alexander E. Zielinski 

Weapons and Materials Research Directorate, ARL 

. 

Annroved for Dublic release: distribution is unlimited. 
Abstract 

Assessment of accuracy is dominated by a detailed experimental investigation of the 

launch and flight performance of a launcher and round. This assessment is commonly 

called a jump test. To evaluate the path of the round as it accelerates down the launcher, 

exits the barrel, and flies downrange to the target, single-shot firings are conducted. In 

the most recent test, integrated launch packages (ILPs) were launched at an exit velocity 

of 1,350 m/s. The test provides for the only set of accuracy data available in the world on 

EM gun-launched projectiles. The impact data show larger variability in the vertical 

direction than in the horizontal direction. Results from the jump test indicate that effects 

of the deviation of the launcher centerline (i.e., straightness) contribute significantly to 

the target impact dispersion. Substantial linear and angular rates at the muzzle are evident 

in the vertical direction. The contribution attributable to sabot discard is minimal in 

either plane. 

ii 
Table of Contents 

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V 

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 

1.1 Free-Flight Data and Analysis ............................................................................. 2 

1.2 Jump ..................................................................................................................... 2 

1.3 Linear Rates ......................................................................................................... 3 

1.4 Angular Rates ....................................................................................................... 6 

1.5 Dispersion ............................................................................................................ 6 

2. Technical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 

3. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..--- 9 

4. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..f.. 11 

Distribution List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .._............ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 

Report Documentation Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 

. . . 

111 
iv 
List of Figures 

Figure Paae 

1. Jump Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .._........................... 3 

2. Orthogonal X-ray Images From Shot 12 .................................................................... 4 

3. Jump Component Dispersions ................................................................................... 7 

4. Target Impact Dispersion as a Function of Launch Velocity ..................................... 7 

5. Measurement of the Deviation From the Bore Centerline ......................................... 8 

I I. 

V 
vi 
1. Introduction 

The earliest documented assessment of accuracy for electromagnetic gun-launched 

projectiles occurred in 1997 [l]. The primary objective of the test program, however, was to 

verify single-shot performance for the launcher and integrated launch package (ILP). During the 

course of testing a developmental approach allowed accuracy to be assessed simply due to the 

multitude of data acquired throughout the duration of the program. The initial results indicated 

that the largest disturbances were located in the vertical direction (i.e., the rail plane). The 

in-bore balloting loads created by the deviation of the bore centerline (i.e., straightness) 

contributed significantly to the round to round dispersion. Unfortunately, testing with this 

launcher was halted while attempting to demonstrate maximum performance. 

In the most recent and most comprehensive jump test, a capacitor bank was used to provide 

energy to the cannon caliber electromagnetic launcher [2]. The initial charge voltage was 7.2 kV 

and the muzzle switch, used to ensure zero current at projectile exit, was closed at 2.14 ms [3]. 

The average peak current for the jump test was 615 kA, +2 kA. The average launch velocity 

determined from the multistation flash x-ray images was 1,351 m/s, +lO m/s. Other electrical 

data acquired during the shot include the breech, launcher, and muzzle voltages. The voltage 

data and previous analysis indicate that the rear armature contact transitioned. While transition 

certainly plays an important role in ILP performance, the entire accuracy evaluation was 

conducted with a transitioned rear contact. 

For evaluating launch dynamics, an aim point and intended line of flight (LoF) is essential; it 

was established using a boresight. The boresight is inserted in the muzzle end of the launcher 

and the crosshair in the eyepiece is marked on the downrange target. However, since the 

boresight is referenced to the bore surface, some misalignment and variability can exist because 

of the deviations of the bore centerline and surfaces. It was found that the standard deviation for 

the horizontal direction is 0.36 mil and 0.42 mil in the vertical direction. (One mil corresponds 

to 1 yd of deflection per 1,000 yd of range.) To reference the launcher LoF to the x-rays, a steel 

cable was attached at the breech, pulled through the launcher, and suspended over a pulley 

I 
5-m downrange. The pulley was aligned with the boresight crosshair. The cable, for indicating 

LoF, and beads, for referencing the subprojectile center of gravity (cg) location, were 

superimposed upon each x-ray. The LoF was corrected for misalignment with the boresight 

reading in the x-ray data reduction software. 

Yaw cards (cardboard targets) were consistently used to assess the free-flight aerodynamics 

of the projectile. Seven yaw cards were placed at measured intervals along the first 40 m of 

trajectory. New yaw cards were put up before each shot, and the yaw card located at 40 m was 

indicated with the boresight. The length of the subprojectile impact and the angular orientation 

relative to a vertical reference line were recorded. The pitch, yaw, and angle of attack (AoA) 

could then be determined from geometry. The maximum flight range was 222 m. 

1.1 Free-Flight Data and Analysis. The free-flight angular motion of the subprojectile was 

measured using the yaw cards placed along the flight path. The measured angular motion was 

then fitted to a theoretical model of the yawing motion, which is based on an analytical solution 

of the yawing motion of a rolling symmetric missile [l, 41. From the theoretical model, it is 

possible to extract information about the aerodynamic performance of the subprojectile and 

quantify the disturbances to the subprojectile during the launch and sabot discard. This 

establishes the initial conditions for the free-flight angular motion. This information is then used 

to evaluate aspects of the transitional ballistics which effect the accuracy and dispersion of the 

subprojectile. 

1.2 Jump. In this section, the series of six disturbances from shot start to target impact (TI) 

are discussed. Jump is a vector, the sum of whose horizontal and vertical components is equal to 

the linear deviation from the line of fire produced by forces acting on the ILP. These 

displacements are typically expressed in mils. The first component is the pointing angle (PA) of 

the muzzle at projectile exit. At the same time, the muzzle experiences a crossing velocity (CV) 

that is imposed upon the projectile. The third component is the angular deviation of the 

projectile cg motion (CG) relative to the instantaneous bore centerline at projectile exit. The 

next component is the net deviation attributable to sabot discard disturbances (SD). The fifth 
. 

. 

jump component is the aerodynamic jump (AJ). The final jump component is the displacement 

attributable to gravity (g) (GD). Each jump component has a variability associated with it. If the 

individual jump components are independent of each other (i.e., no cross-correlation) and the 

data are normally distributed (in a statistical sense), the square root of the sum of the individual 

jump dispersions squared should equal the target impact dispersion (TID). Differences are 

attributed to measurement errors and cross-correlation. A jump diagram is shown in Figure 1. 

For the accuracy assessment discussed here, the terms attributable to muzzle motion (PA and 

CV) are zero due to the relatively stiff launcher mounting. A thorough discussion of projectile 

jump and its measurement can be found in the literature [5]. 

Horizontal (mils) 

-2 

-2.5 i 

Figure 1. Jump Diagram. 

1.3 Linear Rates. Each of the jump components were deduced using a variety of existing 

transitional ballistic measurement techniques. The CG vector is determined from the location of 

. 

the subprojectile’s cg relative to the fiducial in the multistation orthogonal x-rays. A straight line 

is fit to the cg locations as a function of range for each plane and the slope of the line is the CG 

vector. The first three x-ray stations are used to determine the CG vector. The last three x-ray 

stations are used to determine the final deflection of the subprojectile’s trajectory prior to 

entering free flight. This deflection is determined from the slope of a straight line fit to the cg 

displacements from the final three x-ray stations. The SD jump occurs after the CG jump and 

prior to the subprojectile entering free flight. Hence, the SD vector is determined from the 
difference between the deflection measured from the last three x-rays and the deflection 

attributable to the CG vector. An example of the x-ray data for shot 12, with the downrange 

distances indicated, is shown in Figure 2. 

Figure 2. Orthogonal X-ray Images From Shot 12. 

Once the subprojectile enters fieeflight, it is subjected to aerodynamic forces which may 

further deflect the flight trajectory of the subprojectile. The deflection due to the aerodynamic 

forces can be decomposed into mean and fluctuating components. The mean component is 

referred to as aerodynamic jump and it is produced by the angular rates as the round enters free 

flight. These rates cause a linear deviation of the mean trajectory from the velocity vector the 

projectile has entering freeflight. The yaw card data is used to measure the free-flight angular 

rates. A reasonable approximation for AJ in mils [l] is given as 

AJ = -1000 WI. ----+Y . 

n-wll~ 

The subprojectile moment of inertia (IS, diameter (d), mass (m), and C,, were measured, 

whereas Ch was obtained from CFD computations. The angular rate (in rad/m), 6’, was 

determined for each plane, 3.1-m downrange (i.e., free flight) from the fits to the yaw card data. 

In addition to the mean deflection of the trajectory, the projectile’s swerving motion also has 

a fluctuating component, s, produced by the aerodynamic forces associated with the yawing 

motion of the round. These deflections are typically small and are usually not considered in a 

4 
jump test where the yaw card targets are many yaw cycles from the muzzle of the gun. Since the 

impact data used to evaluate the jump components in the present evaluation are taken after 

approximately ‘one cycle of yawing motion, the fluctuating part of the swerving motion is 

included. This term represents an additional displacement for each plane along the trajectory. 

The fluctuating part of the swerving motion can be determined by integrating the equations of 

motion using the predicted lift coefficient, C ~a, and the measured yawing motion. The resulting 

swerving motion is dampened periodically and is accounted for in the jump diagram by 

correcting the impact location. Fortuitously, s is close to a minimum at the 40-m yaw card which 

then minimizes the impact on the jump diagram. 

Finally, GD, which only appears as a vertical displacement, has been computed in mils from 

the launch velocity (V) and range (Z) as 

GD = lOOO= 

2v2 . 

(2) 

The target impact shown in Figure 1 has been corrected for both the fluctuating part of the 

swerving motion and the vertical displacement due to gravity. 

Once the jump vector diagram is assembled for each shot, each vector is referenced from the 

origin. The variability of the vectors for each component is then computed as the dispersion for 

the jump component. It is important to note that the summation of the jump vectors without 

cross-correlations should end at the impact location (i.e., closed). However, sources of 

measurement error should be accounted for in the analysis. (For example, the impact location is 

known relative to the bore centerline to within the variability of the boresight.) It is 

unreasonable to hold the impact location as an error-free datum. An error analysis was 

conducted on the measured data; the result indicates that for all shots, an average of 4 mm is 

needed in the horizontal direction and 15 mm in the vertical direction for the trajectory to be 

within the impact location determined by the boresight. Therefore, based on the boresight 

variability and x-ray measurement accuracy, the jump diagrams are considered “closed” for each 

5 
shot, and no additional vectors are added to the existing components to close with the measured 

target impact location. 

1.4 Angular Rates. The angular rates determined by the first three x-rays are indicative of 

the in-bore balloting forces acting on the ILP cg. The angular rates associated with free flight are 

also a result of the armature discard event and represent the final angular motion of the round. 

The free-flight angular rates are larger in the present jump test than the rates measured in 

previous tests [ 11. The average magnitude of the free-flight angular rate is 1.72’/m in the rail 

direction and 0.63’/m in the insulator direction. On average, the rates representative of in-bore 

balloting contribute 65% ‘toward the free-flight rates. Thus, the dominant factor driving AJ is 

due to in-bore balloting. Similar conclusions were reached in a prior experimental effort [ 11. 

1.5 Dispersion. In Figure 3, the dispersions for the CG, SD, and AJ jump components are 

plotted for the insulator (horizontal) and rail (vertical) directions. The component dispersions are 

larger in the rail direction than in the insulator direction. This trend was also observed in 

previous work [ 11. However, the dominant contribution in the rail direction is from the 

aerodynamic jump, while in the insulator direction it is attributable to in-bore balloting. As 

alluded to previously, the rates generated from the launcher contribute significantly to the 

dispersion. 

The horizontal and vertical TIDs, based on a linear summation of the jump vectors and no 

cross-correlation, are 0.62 and 2.07 mils and are quite reasonable compared to the TID measured 

at the 40-m yaw card target (0.64 and 2.73 mils). This agreement is encouraging since the 

calculations for the jump vectors do not rely on the target impact location data. 

The impact data used to determine the TID was obtained 40-m downrange. The impact data 

are corrected for the misalignment in the LoF due to boresight errors. Shown in Figure 4 is the 

TID as a function of launch velocity. Data from previous work on a similar ILP [l], as well as 

that from a similar-caliber, conventionally-launched munition are also included. The dashed 

6 
4 “[“’ ,,-, “,,: ,,,,,, _ __ ,, ,... ^ _.” ,,,,. -,,“-~ ” _-.,, “,“, -x”,, -,...,- _.“. 1”‘: 

. 

3.5 .I 1 8 Sabot Discard (SD) 1 

3 ‘1 1 flCenterof Gravey(CG) 

IIl-XLXX,-t” ,,,,1111 ‘ 

Rail Direction 

Figure 3, Jump Component ~is~e~si~~s. 

1200 1400 1600 1800 2000 

MuzzleVelocity (rds) 

Figure 4. Target Impact Dispersion as a Function of Launch Velocity. 

lines are extrapolations of the measured data beyond 1,500 m/s. The TID appears to increase 

linearly with velocity at a rate of 1.4 milskrnk. Despite the seemingly linear relationship, 

further commentary is not warranted since the prior data used an identical launcher with a 

different centerline. 

The correlation of launcher straightness with accuracy and dispersion is not new [6, 71. The 

angular rates and variability of the CG jump vector suggest that railgun straightness may be 
correlated with accuracy and dispersion. The deviation from the bore centerline is measured as a 

function of launcher length for the recent assessment and is shown in Figure 5. The vertical 

component of the CG vector is in agreement with the trend of the centerline in the rail direction 

at the muzzle. All of the ILPs exit the launcher oriented upwards. However, the same 

correlation is not evident in the insulator direction. Nonetheless, producing a smoother 

centerline will certainly contribute to smaller angular and linear rates. 

A 

:. 

: ._.--*s ._---... .’ -. L Up or 

Right 

I 

1 

2.5 

Leff or 

Down 

-. - . . -. . Insulator Direction (Horizontal) 

-600 l - Rail Direction (Vertical) 

Travel (m) 

Figure 5. Measurement of the Deviation From the Bore Centerline. 

2. Technical Issues 

The linear and angular rates produced by the launcher appear to be the major contributor to 

the TID. The dominant linear rate for both planes was produced by the launcher (CG). The 

linear rates were effectively managed using a less stiff front armature contact compared to that 

measured in previous results [ 11. 

The angular rates produced by the launcher contribute significantly toward the free-flight 

rates. These rates manifest themselves as a linear displacement in aerodynamic jump (AJ). 

These rates are managed in the subprojectile by the pitching moment coefficient. The goal of 

further enhancing accuracy is then to balance the contribution of the linear and angular rates 

through armature and subprojectile design changes so that the combined contribution toward TID 

is minimized. While this trade-off can be accomplished analytically, obtaining a balance 

8 
depends on the rates generated by the launcher; therefore, it can best be quantified only through 

experiments. 

The deviation from the bore centerline (i.e., straightness) has been measured on 

electromagnetic railguns [g-lo]. However, relatively little has been done to collectively assess, 

quantify, and corroborate the causal relationships. Moreover, even less has been done to address 

the unique details of railgun centerlines both in terms of manufacturability and accuracy 

requirements. 

3. Conclusions 

Accuracy as related to railguns was assessed in a limited number of tests. The most 

significant contributor to dispersion was found to be correlated with in-bore dynamics associated 

with the deviation from the bore centerline. It is recommended that this characteristic of the 

launcher be addressed with respect to manufacturability, as its origination is unclear. Also, the 

possibility of alternate and/or higher accuracy measurement techniques should be explored. 

Other contributors to accuracy not previously addressed include a launcher mount in which 

the muzzle pointing angle (MP) and crossing velocity (CV) are not zero. The relative effect of 

armature contact transition and gouging can be readily assessed in separate experiments. Finally, 

multishot dynamics should be addressed along with consequences for extending bore life. 

9 
10 
1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

4. References 

Zielinski, A. E., P. Weinacht, D. W. Webb, and K. P. Soencksen. “An Investigation of the 

Ballistic Performance for an Electromagnetic Gun-Launched Projectile.” ARL-TR-1361, 

U.S. Army Research Laboratory, Aberdeen Proving Ground, MD, June 1997. 

Zielinski, A. E., and M. Werst. “Cannon-Caliber Electromagnetic Launcher.” IEEE 

Transactions on Magnetics, vol. 33, no. 1, January 1997. 

Zielinski, A., and P. Weinacht. “Improved Integrated Launch Package Ballistic 

Perfomrance.” IEEE Transactions on Magnetics, January 1999. 

Murphy, C. H. “Free-Flight Motion of Symmetric Missiles.” BRL-TR-1216, U.S. Army 

Ballistic Research Laboratory, Aberdeen Proving Ground, MD, July 1963. 

Bornstein, J., I. Celmins, P. Plostins, and E. M. Schmidt. “Techniques for the Measurement 

of Tank Cannon Jump.” BRL-MR-37 15, U.S. Army Ballistic Research Laboratory, 

Aberdeen Proving Ground, MD, December 1988. 

Garner, J., M. Bundy, D. Webb, and B. Patton. “Variation in Muzzle Pointing Angle and 

Shot- Impact of a M242 Chain Gun.” ARL-TR-785, U.S. Army Research Laboratory, 

Aberdeen Proving Ground, MD, July 1995. 

Bundy, M., and B. Patton. “Variation in Shot Impacts Due to a Controlled Bending of a 

Gun Tub. “ ARL-TR-1190, U.S. Army Research Laboratory, Aberdeen Proving Ground, 

MD, September 1996. 

Burton, L. “A Comparison of In-Bore Projectile Motion From an Electromagnetic Railgun 

vs. That of a Conventional Cannon Barrel.” ARL-TR-295, U.S. Army Research Laboratory, 

Aberdeen Proving Ground, MD, October 1993. 

Burton, L. “In-Bore Dynamic Response Analysis of a SLEKE I Projectile Fired From the 

Single Shot Gun (SSG) Railgun.” ARL-TR-470, U.S. Army Research Laboratory, 

Aberdeen Proving Ground, MD, July 1994. 

10. Burton, L. “A RASCAL In-Bore Dynamic Analysis of the Task B and Task C 

Electromagnetic Railguns.” ARL-TR-726, U.S. Army Research Laboratory, Aberdeen 

Proving Ground, MD, April 1995. 

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. PERFORMING ORGANIZATION NAME(S) AND ADDRESS 8. PERFORMING ORGANIZATION 

J.S. Army Research Laboratory REPORT NUMBER 

IT-l-N: AMSRL-WM-BC ARL-TR-2392 

Aberdeen Proving Ground, MD 21005-5069 

I. SPONSORING/MONITORING AGENCY NAMES(S) AND ADDRESS 10.SPONSORINGIMONITORlNG 

AGENCY REPORT NUMBER 

1. SUPPLEMENTARY NOTES 

2a. DlSTRlBUTlON/AVAlL4BlLlM STATEMENT 12b. DISTRIBUTION CODE 

ipproved for public release; distribution is unlimited. 

3. ABSTRACT(Maximum 200 words) 

Assessment of accuracy is dominated by a detailed experimental investigation of the launch and flight performance o 

t launcher and round. This assessment is commonly called a jump test. To evaluate the path of the round as i 

accelerates down the launcher, exits the barrel, and flies downrange to the target, single-shot firings are conducted. II 

he most recent test, integrated launch packages (ILPs) were launched at an exit velocity of 1,350 m/s. The test provide: 

:or the only set of accuracy data available in the world on EM gun-launched projectiles. The impact data show large 

rariability in the vertical direction than in the horizontal direction. Results from the jump test indicate that effects of the 

deviation of the launcher centerline (i.e., straightness) contribute significantly to the target impact dispersion. Substantia 

inear and angular rates at the muzzle are evident in the vertical direction. The contribution attributable to sabot discarc 

s minimal in either plane. 

14. SUBJECT TERMS 15. NUMBER OF PAGES 

:ailguq accuracy, jump test, straightness, centerline 18 

18. PRICE CODE 

17. SECURITY CLASSIFICATION 18. SECURllY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT 

OF REPORT OF THIS PAGE OF ABSTRACT 

UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED UL 

NSN 7540-01-280-5500 17 

Standard Form 298 (Rev. 2-89) 

Prescribed by ANSI Std. 239-18 298-102 
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1. ARL Report Number/Author ARL-TR-2392 (Zielinski) Date of Report Pebmary 2001 

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