ProSTools  IBMortar  ЋММ  PROGRAM IBMortar – SHORT DESCRIPTION Purpose 1. Calculation of burning of grains in barrel. 2. Calculation of velocity, acceleration and traveling path of projectile in barrel of mortar. 3. Calculation of pressure and temperature of gases in barrel . Description Program numerically solves (integrates) two degree of freedom equations of motion of a projectile for mortar barrel and one equation of burning powder grain for given characteristics of projectile, barrel and grain, and initial conditions. Program is written in MatLab, organized in modular way, so that it can be easily extended. Assumptions and Limitations Main assumptions and limitations of the program are: – The grain is burning in parallel surfaces without erosion. – Powder is burning under the mean pressure in the barrel. – Burning velocity is proportional to the pressure. – The gas flow through clearance is proportional to the pressure impulse and relative burned web. Input Data Input data are supplied through one input file or through interactive graphical interface which gives high working flexibility. Structure of input data are fixed, but format number is free. Input data are organized into following groups: – System information, – Projectile characteristics, – Launcher characteristics – Grain characteristics, – Simulation data. 1 ProSTools  IBMortar  ЋММ  Output: Output results are printed in output file and diagrams Origin: Own development based on published literature and own experience. Machine: Personal computer with operating system: Windows XP, Windows Vista. Program language: MATALAB version 6.5 and greater. Contents of package: source code, short theoretical manual, user manual and two examples: mortar 82mm and mortar 120mm. 2 ProSTools  IBMortar  ЋММ  3 ProSTools  IBMortar  ЋММ  4 ProSTools  IBMortar  ЋММ  V-t Diagram 250 200 150 ] s / m [ V 100 50 0 0 5 10 15 20 t [ms] V-x Diagram 200 150 ] s / m 100 [ V 50 0 0 0.2 0.4 0.6 0.8 1 x [m] 5 ProSTools  IBMortar  ЋММ  t-x Diagram 18 16 14 12 ] 10 s m [ 8 t 6 4 2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 x [m] p-x Diagram 500 400 300 ] r a b [ p 200 100 0 0 0.2 0.4 0.6 0.8 1 x [m] 6 ProSTools  IBMortar  ЋММ  T-x Diagram 3500 3000 2500 2000 ] K [ T 1500 1000 500 0 0 0.2 0.4 0.6 0.8 1 x [m] Acc-x Diagram 6000 5000 4000 ] g 3000 [ a 2000 1000 0 0 0.2 0.4 0.6 0.8 1 x [m] 7 ProSTools  IBMortar  ЋММ  Input file IB_Mortar_82mm.m % Projectile characteristics dref = 0.082; % m reference diameter Sref = 0.005281; % m^2 reference area Sp = 0.0052282; % m^2 effective projectile cross section mass0 = 3.4; % kg projectile mass % % % Launcher characteristics Sbar = 0.0053074; % m^2 area of the barrel cros section Llaunch = 1.02; % m barrel lentgh L0 = 0.136; % m lentgh of burning chamber Lquide = 0.6; % m projectile guidance length cfric = 0.10; % - friction coefficient theta0 = 45.0*deg2rad; % deg initial inclination Aceta = 0.001; % - leackage coefficient % % % Grain characteristics omega0 = 0.0072; % kg mass of the primer charge domega = 0.0061; % kg incrimental charge mass ncharge = 6; % number of incremental charges W0 = 0.72E-3; % m^3 initial combustion volume Rp = 373.4; % kJ/kg/K gas constant T1p = 3000; % K burning temperature; alphap = 0.85E-3; % m^3/kg covolume u1 = 1.1E-9; % m/s/Pa burning velocity at norm. cond. gamap = 1.15; % - ratio of specific heat coeff. f0 = 679E3 % kJ/kg force of the primer charge deltap = 1640; % kg /m^3 powder density L0 = 0.136; % m initial lentgh of burning chamber e1 = 0.0605E-3; % m powder grain semiweb kappa = 1.25; % - kappa lambda = -0.2; % - lambda mu = 0.0; % - mu 8 ProSTools  IBMortar  ЋММ  Output file IB_Mortar_82mm.txt - Basic quantities Charge = 1 Time path Vel press Temp e/e1 Wfree acc ------- ------- ------- ------- ------- ------- ------ ------ [ms] [dm] [m/s] [bar] [K] [-] [dm^3] [g] ------- ------- ------- ------- ------- ------ ------ ------ 0.00 0.000 0.0 68.3 3000.0 0.000 0.716 1063 0.50 0.013 5.3 72.1 2973.4 0.063 0.723 1123 1.00 0.053 10.9 74.2 2944.3 0.130 0.744 1155 1.50 0.122 16.6 74.2 2914.0 0.198 0.781 1155 2.00 0.219 22.2 72.4 2883.2 0.264 0.832 1128 2.49 0.343 27.6 69.3 2852.6 0.329 0.897 1078 2.99 0.494 32.7 65.2 2822.7 0.390 0.977 1015 3.49 0.670 37.5 60.7 2794.1 0.447 1.070 944 3.99 0.869 42.0 56.0 2766.8 0.500 1.175 872 4.49 1.089 46.1 51.5 2741.2 0.549 1.291 801 4.99 1.329 49.9 47.2 2717.1 0.594 1.418 735 5.49 1.587 53.3 43.3 2694.7 0.635 1.554 673 5.99 1.861 56.5 39.7 2673.7 0.673 1.699 618 6.49 2.151 59.4 36.5 2654.1 0.707 1.851 567 6.99 2.455 62.0 33.6 2635.8 0.739 2.012 522 7.49 2.771 64.5 31.0 2618.6 0.768 2.179 482 7.99 3.099 66.8 28.7 2602.6 0.795 2.352 446 8.49 3.438 68.9 26.6 2587.6 0.820 2.531 413 8.99 3.787 70.8 24.7 2573.5 0.844 2.715 384 9.49 4.146 72.6 23.1 2560.2 0.865 2.904 358 9.99 4.514 74.3 21.6 2547.6 0.886 3.098 335 10.49 4.889 75.9 20.2 2535.8 0.905 3.297 314 10.99 5.273 77.4 19.0 2524.6 0.923 3.499 295 11.49 5.663 78.8 17.9 2514.0 0.939 3.705 277 11.99 6.061 80.2 16.9 2503.9 0.955 3.915 262 12.49 6.465 81.4 15.9 2494.3 0.970 4.128 247 12.99 6.875 82.6 15.1 2485.1 0.984 4.344 234 13.49 7.290 83.7 14.3 2476.4 0.997 4.564 222 13.99 7.711 84.8 13.6 2464.2 1.000 4.786 211 14.49 8.138 85.8 12.9 2451.3 1.000 5.011 200 14.99 8.569 86.7 12.3 2439.0 1.000 5.239 191 15.49 9.005 87.6 11.7 2427.1 1.000 5.469 182 15.99 9.445 88.5 11.2 2415.6 1.000 5.701 174 16.49 9.890 89.3 10.7 2404.6 1.000 5.935 166 16.84 10.204 89.9 10.4 2397.1 1.000 6.101 161 ======================================================================== 9