Paper: ASAT-13-AE-25 13th International Conference on AEROSPACE SCIENCES & AVIATION TECHNOLOGY, ASAT- 13, May 26 – 28, 2009, E-Mail: [email protected] Military Technical College, Kobry Elkobbah, Cairo, Egypt Tel : +(202) 24025292 – 24036138, Fax: +(202) 22621908 Ballistic Range Potential of Scaled Gun Barrels Firing Saboted Dart-Like Barrage Round Hatem H. Daken* Abstract: Providing the marines expeditionary and amphibious assault forces with long range surface fire support missions is one of the responsibilities of the U.S. Navy. Meeting the U.S. Marine Corps (USMC) Ship-To-Objective Maneuver (STOM) and Operational Maneuver From The Sea (OMFTS) requirements required the prediction of the maximum achievable ballistic ranges for a 100 lbs, 5″ diameter/12 calibers, GPS guided, dart-like barrage round when fired from 5″, 155mm, 8″, 10″, 12″, 14″, 16″, and 18″ bore barrels that are 64 and 200 calibers in length at maximum breech pressures of 448MPa (65Ksi) and 896MPa (130Ksi.) Keywords: SIMULINK, CONPRES, Interior Ballistics, Exterior Ballistics, Surface Fire Support 1. Nomenclature A Projectile Base Area, m2 BE Ballistic Efficiency, Equation 12 d Bore diameter, meter E Gas Internal Energy, MJ, Equation 7 i E Propellant Energy, MJ, Equation 6 p ER Expansion Ratio, Equation 11 I Propellant Impetus, Joule/kg K Gas Kinetic Energy, MJ, Equation 5 g K Projectile Kinetic Energy, MJ, Equation 4 p m Charge Mass, kg c m Projectile mass, kg p P Constant Breech Pressure, MPa c P Space Mean Pressure, MPa, Equation 8 P Base Pressure at Muzzle Exit, MPa, Equation 9 b PE Piezometric Efficiency, Equation 13 V Chamber Volume at Propellant Burn-out, m3, Equation 3 bf V Chamber Volume, m3 c V Free Chamber Volume accounting for Propellant Covolume, m3, Equation 1 cf V Free Gun Volume at Projectile Muzzle Exit, adjusting for Propellant mf Covolume, m3, Equation 2 U Projectile Muzzle Exit Velocity, m/sec m * Ph.D., Senior Structural Analysis Scientist/Engineer, Boeing Commercial Airplanes, The Boeing Company, Seattle, WA, USA (work was performed while working as the Principal Engineer, Defense Technology Inc., DTI, Arlington, VA, USA), [email protected] 1/16 Paper: ASAT-13-AE-25 x Projectile Travel at Propellant Burn-out, meter b x Projectile Travel at Muzzle Exit, meter, Equation 10 t  Ratio of Specific Heats  Propellant Covolume, m3/kg 2. Introduction The U.S. Navy’s Naval Surface Fire Support Systems (NSFS) Program Office PMS 529, which is currently reorganized into the Program Executive Office (PEO) for Integrated Warfare Systems (IWS) Code PEO IWS 3C, has developed visionary objectives for using shipboard gun systems to provide marines expeditionary and amphibious assault forces with long range surface fire support missions that entail suppression of enemy defenses and artillery, execution of quick response call fires, and interdiction of moving counter offensives in addition to executing traditional destruction fires, preparation fires, counter fires, suppression fires, and area neutralization fires. Validation of these objectives and meeting the USMC STOM/OMFTS requirements1,2, Figure 1, demanded modeling and simulating the range potential of a 100 lbs, 5″ diameter/12 calibers, GPS guided, dart-like barrage round, Figures 2 and 3, when fired from two sets of different caliber guns with barrel lengths of either 64 or 200 calibers, Figure 4, that operate at a maximum breech pressure of 448 MPa (65 Ksi). A future projection of this range potential was also performed when gun technology permitting a maximum breech pressure of 896 MPa (130 Ksi) becomes available. 3. Analysis Methodology The analysis consisted of the following interior and exterior ballistics tasks and subtasks: Interior Ballistics Shipboard Gun and Round Constraints Establishing values for the following system parameters: (1) maximum breech pressure; (2) maximum round G loading; (3) maximum muzzle exit pressure; (4) propellant composition; and (5) travel at burnout. The table below shows the parameters chosen. Table 1: Gun, Projectile, and Propellant Constraints Parameter Value Rationale 65 Ksi, Maximum Breech Pressure Customer specified 130 Ksi Maximum G Loading 12.5 KGs Customer Specified Max. Muzzle Exit Pressure Open Relaxed by Customer Propellant Composition EX99 Same as 5″/62 firing ERGM <64 Calibers Travel at Burnout Efficient use of propellant <200 Calibers Gun System Characteristics The CONPRESS interior ballistics model, illustrated in Figure 5, is used to compute the maximum muzzle velocity that satisfies the above constraints for each caliber. Additional characteristics needed are: (1) G loading; (2) charge mass, (3) chamber volume; (4) muzzle exit pressure; and (5) travel at propellant burnout. 2/16 Paper: ASAT-13-AE-25 CONPRESS3,4 is a constant pressure interior ballistics code that predicts the performance of a gun from its physical parameters, the masses of the propelling charge and projectile, and the thermochemical properties of the propellant. The CONPRESS code is a FORTRAN based computer program. It is described in References [3] and [4]. This code was adapted to Microsoft Excel. A snapshot of this model is shown in Figure 6. Excel’s Solver was used to find the maximum muzzle exit velocity, U , by changing the charge weight, m, and chamber m c volume, V , while ensuring that: (1) the G loading is less than or equal to 12500; (2) the travel c at propellant burn-out is less than or equal to the barrel length; and (3) the validation tests for m and x are passed. c b CONPRESS uses the following assumptions to calculate the energy imparted into the projectile by the gun: o The Lagrange gradient adequately describes the gas pressure and velocities in the gun. o The propellant burns in an ideal manner. (This means, it is instantaneously converted into gas.) o The burn rate of the propellant is controlled to provide a constant chamber pressure until burnout. o After burnout, the gas expands adiabatically. o The gas is polytropic. o The Nobel-Able equation of state is valid. o No energy loss occurs during the ballistic cycle. o The projectile base area equals the cross-sectional area of the tube. CONPRESS uses the following equations to compute its parameters. The conventions are explained in the nomenclature section: V V m (1) cf c c V V Ax m (2) mf c t c  m  m I 1+ c  c  2m   p  1 V   V (3) bf cf  m   1+ c   3m   p    P  V  V  Kp  c   Vbf Vcf  mf . bf   (4) 1 mc  -1 1 Vmf    2m   p  m K  c .K (5) g p 3m p 3/16 Paper: ASAT-13-AE-25 m I E  c (6) p -1 E E K K (7) i p g p E P i  1 (8) V mf P P  (9) b m 1 c 3m p V m V x  bf c c (10) b A V Ax ER  c t (11) V c K p BE (12) E i K p PE  (13) P Ax c t Once the maximum muzzle exit velocity is computed for each gun caliber, barrel length, and breech pressure, an exterior ballistics model using the lumped mass approach was developed. Exterior Ballistics This model was used to compute the maximum achievable range and optimum launch angle for each gun caliber, barrel length, and breech pressure set. The model entails the following modules; Drag Function This function was used to compute the total aerodynamic drag coefficient of the barrage round as a function of its flight Mach number and geometric characteristics using the McDrag5 model. The core of this model is illustrated in Figure 7. The Atmosphere This module uses the U.S. Standard Atmosphere6 database to calculate the air temperature, pressure, air density, and speed of sound for various geopotential flight altitudes. The database was extended for use at altitudes over 85 km. 4/16 Paper: ASAT-13-AE-25 4. Analysis Limitations Sabot Design The design of different caliber sabots, its volume, and weight calculations have the following limitations: o Designs were mainly intended to provide ballpark weight estimates of different caliber sabots and were not intended to be in-depth detailed minimum weight designs. o The lower specific weights of advanced and innovative materials (ceramics, composites, and thermoplastics) were not addressed since cost minimization was a main consideration. CONPRESS - Constant Breech Pressure Interior Ballistics Model o Assumes a barrel with no well-defined chamber or transition region. o Provides an absolute measure of maximum muzzle velocity performance. McDrag Function and Coefficients This model assumes: o Zero degree angle of attack. o No conning motion. o Nose first flight. o Errors in estimating drag coefficients for supersonic, transonic, and subsonic speeds are 3%, 11%, and 6%, respectively. 5. Results Sabot Design A sabot was designed for each gun caliber. Each of these sabots, with the exception of the 5″ gun sabot, is composed of three main elements: o Pusher plate made of carbon steel (density 7.87 gram/cm3) o 4-Segment sabot made of aluminum (density 2.7 gram/cm3). Each segment is reinforced with two-0.25” thick ribs shaped as circular segments. o Nosecone made of fire retardant nylon (density 1.3 gram/cm3) that provides an interface to the fuse setter. The 5″ gun sabot entails the 4 sabot segments and the nosecone, but no pusher plate. The following table summarized the weights of individual elements and the total package weight reflecting weight savings after design refinements for each gun caliber. 5/16 Paper: ASAT-13-AE-25 Table 2: Sabot Weights Pusher Plate Nose Cone Sabot Weight Package Weight Gun Caliber Weight Weight [Kg] 5″ 22.11 0.00 3.37 25.48 155 mm 40.77 3.14 3.37 47.27 8″ 71.41 5.10 3.37 79.88 10" 93.73 7.70 3.37 104.79 12” 115.05 10.84 3.37 129.26 14” 133.92 14.52 3.37 151.81 16" 149.91 18.74 3.37 172.02 18” 162.46 23.5 3.37 189.33 Interior ballistics Maximum G loading was constrained to 12.5 KGs and travel at burnout was constrained to occur before muzzle exit. The model was run twice for each gun caliber, for breech pressures of 65 and 130 Ksi. The following tables summarize the main results of the different CONPRESS runs. Figures 8 through 10 depict the major parameters computed from the interior ballistics model. Table 3: Interior Ballistic Characteristics of 64-Caliber Guns Muzzle Exit Kinetic Energy G Loading Charge Mass Gun Caliber Velocity [m/sec] [MJ] [Gs] [kg] [inch [mm] 65 Ksi 130 Ksi 65 Ksi 130 Ksi 65 Ksi 130 Ksi 65 Ksi 130 Ksi 5.0 127.0 999 1296 23 38 6399 11093 39 67 6.1 155.0 1135 1450 29 48 6846 11634 67 111 8.0 203.2 1364 1697 42 65 7748 12500 132 224 10.0 254.0 1597 1918 57 83 8859 12500 222 441 12.0 304.8 1792 2091 73 99 9735 12500 336 717 14.0 355.6 1962 2237 87 113 10532 12500 468 1058 16.0 406.4 2112 2362 101 127 11280 12500 616 1462 18.0 457.2 2248 2473 115 139 12013 12500 780 1931 Table 4: Interior Ballistic Characteristics of 64-Caliber Guns (continued) Muzzle Exit Travel at Burnout Chamber Volume Gun Caliber Pressure [MPa] [cm] [caliber] [liter] [inch [mm] 65 Ksi 130 Ksi 65 Ksi 130 Ksi 65 Ksi 130 Ksi 65 Ksi 130 Ksi 5.0 127.0 273 406 670 594 52.73 46.81 48 82 6.1 155.0 240 341 777 675 50.11 43.56 81 136 8.0 203.2 188 261 92 820 45.40 40.35 161 273 10.0 254.0 142 216 1026 1088 40.83 42.84 271 538 12.0 304.8 109 169 1103 1270 36.19 41.68 410 875 14.0 355.6 85 131 1152 1410 32.40 39.66 570 1291 16.0 406.4 67 103 1183 1521 29.13 37.41 752 1784 18.0 457.2 53 81 1202 1611 26.29 35.24 951 2356 6/16 Paper: ASAT-13-AE-25 Table 5: Interior Ballistic Characteristics of 200-Caliber Guns Muzzle Exit Kinetic Energy G Loading Charge Mass Gun Caliber Velocity [m/sec] [MJ] [Gs] [kg] [inch [mm] 65 Ksi 130 Ksi 65 Ksi 130 Ksi 65 Ksi 130 Ksi 65 Ksi 130 Ksi 5.0 127.0 1506 1846 51 77 4946 8061 92 146 8.0 203.2 1920 2262 84 116 5567 8820 282 422 10.0 254.0 2161 2494 105 141 6163 9694 451 655 12.0 304.8 2353 2674 126 162 6655 10426 653 930 Table 6: Interior Ballistic Characteristics of 200-Caliber Guns (continued) Muzzle Exit Travel at Burnout Chamber Volume Gun Caliber Pressure [MPa] [cm] [caliber] [liter] [inch [mm] 65 Ksi 130 Ksi 65 Ksi 130 Ksi 65 Ksi 130 Ksi 65 Ksi 130 Ksi 5.0 127.0 160 202 1684 1386 132.63 109.15 113 178 8.0 203.2 91 104 2116 1648 104.14 81.09 344 514 10.0 254.0 62 68 2231 1680 87.85 66.15 550 799 12.0 304.8 44 47 2291 1686 75.17 55.33 797 1136 Exterior Ballistics The following tables summarize the main results of the different runs of the exterior ballistics model. Figures 11 through 16 illustrate these results versus the gun caliber for the two barrel lengths and breech pressures: Table 7: Exterior Ballistic Performance of 64-Caliber Guns Max Range Firing Angle Range Increase Gun Caliber [mile] [degree] [mile] % [inch] [mm] 65 Ksi 130 Ksi 65 Ksi 130 Ksi 5.0 127.0 32 67 52 51 35 108.23 6.1 155.0 46 91 52 50 45 98.04 8.0 203.2 77 137 51 49 60 77.16 10.0 254.0 118 185 49 48 67 57.07 12.0 304.8 157 227 49 48 70 44.30 14.0 355.6 195 265 48 47 69 35.52 16.0 406.4 232 300 48 47 68 29.09 18.0 457.2 268 332 47 47 64 23.97 7/16 Paper: ASAT-13-AE-25 Table 8: Exterior Ballistic Performance of 200-Caliber Guns Max Range Firing Angle Range Increase Gun Caliber [mile] [degree] [inch] [mm] 65 Ksi 130 Ksi 65 Ksi 130 Ksi [mile] % 5.0 127.0 101 169 50 48 68 67.09 8.0 203.2 185 271 48 47 86 46.43 10.0 254.0 245 338 48 47 93 38.20 12.0 304.8 297 395 47 47 97 32.80 6. Conclusions The 200-caliber gun barrels offer definite advantages over the 64-caliber barrels in terms of its: (1) longer range potential; (2) efficient propellant usage and economy for the smaller bore diameters; (3) lower projectile G loads, and (4) lower muzzle exit pressures. This analysis focused only on the range potential of a ballistic round fired from different gun calibers with different barrel lengths and breech pressures. Cancellation of Raytheon’s rocket-assisted EX171 Extended Range Guided Munition (ERGM) program, the vague destiny of Zona’s (Zona Technology Inc.) Arizona Glider (AG) gliding projectile, and the very expensive cost of the cruise missile left us with no other options to analyze for meeting the USMC STOM/OPFTS requirements. 7. References [1] Milligan, M., “U.S. Marine Corps Naval Surface Fire Support Requirements,” Marine Corps Combat Development Command (MCCDC), 7th International Artillery and Indirect Fire Symposium & Exhibition, 17-19 June 2002, http://www.dtic.mil/ndia/2002artillery/milligan.pdf [2] Hause, 7th International Artillery and Indirect Fire Symposium & Exhibition, 17-19 June 2002, http://www.dtic.mil/ndia/2002artillery/hause.pdf [3] Oberle, W. F., “Constant Breech Pressure Interior Ballistics Code CONPRESS: Theory and User’s Manual,” Technical Report ARL-TR-199, US Army Research Laboratory, Aberdeen Proving Ground, MD, 1993, http://www.dtic.mil/cgi- bin/GetTRDoc?AD=ADA275491&Location=U2&doc=GetTRDoc.pdf. [4] Norton, S. A., “CONPRESS in Mathcad: Implementation of the CONPRESS Constant Pressure Interior Ballistics Code as a Mathcad Live Scratchpad Document,” Defense Technology, Incorporated, Arlington, VA, 1996. [5] MacCoy, R. L., “MC Drag – A Computer Program for Estimating the Drag Coefficients of Projectiles,” Technical Report ARBRL-TR-02293, US Army Armament Research and Development Command, Ballistics Research Laboratory, Aberdeen Proving Ground, MD, 1981, http://www.ada.ru/guns/ballistic/bc/McCoy.pdf [6] National Geophysical Data Center, National Oceanic and Atmospheric Administration, Boulder, CO, 1976. [7] Wilson, G. et al, “AOT Gun,” Applied Ordnance Technology, 39th NDIA Guns & Ammunition Conference Baltimore, MD April 2004, www.dtic.mil/ndia/2004guns/fri/aot.ppt [8] Adams, M. et al, “Advanced Modular Gun: Developing Tomorrow’s Weapon Systems with Today’s Technology,” Applied Ordnance Technology and NSWC Dahlgren, 41st NDIA Gun and Missile Systems Conference Sacramento, CA March 2006, http://www.dtic.mil/ndia/2006garm/tuesday/coladonato.pdf 8/16 Paper: ASAT-13-AE-25 Figure 1: The USMC Requirements for Naval Surface Fire Support Figure 2: The 5”/12 Calibers, 100 lbs, Dart-Like Barrage Round Figure 3: Design Drawing for the 12” Caliber Sabot 9/16 Paper: ASAT-13-AE-25 Figure 4: The Applied Ordnance Technology AOT or XLR Gun7,8; AOT Claims It Is Capable of Developing 200 Caliber Barrels Figure 5: Schematic of the CONPRESS Model and the Pressure versus Travel Chart 10/16