Tag: C/C++ Hybrid Programming

Blog Entry (c) Thursday, November 21, 2024, by James Pate Williams, Jr. Comparison of Homegrown Fifth Order Runge-Kutta Method Versus a Limited Number of Predictor-Corrector Algorithm

The first table is based on Conte-de Boor Fourth Runge-Kutta formulas that I converted to Fifth Order Runge-Kutta. Initial values: V = 2600 feet per second angle of elevation 30 degrees diameter 16 inches coefficient of form 0.61 density ratio 1.00 are from LCDR Ernest Edward Herrmann’s Exterior ballistics, 1935 My results are given first then LCDR Herrmann’s results:

x deg min sec time v vx vy y
0 30 0 0 0.00 2600 2252 1300 0
563 29 50 45 0.25 2578 2236 1283 325
1122 29 41 24 0.50 2556 2221 1266 646
1677 29 31 57 0.75 2535 2206 1250 962
2229 29 22 25 1.00 2515 2191 1233 1275
2776 29 12 47 1.25 2494 2177 1217 1583
3321 29 3 4 1.50 2474 2163 1201 1887
3861 28 53 15 1.75 2455 2149 1186 2188
x deg min sec time v vx vy y
0 30 0 0 0.00 2600 2252 1300 0
561 29 50 7 0.25 2582 2259 1285 323
1120 29 41 4 0.50 2564 2227 1270 642
1675 29 32 2 0.75 2546 2216 1255 958
2228 29 22 5 1.00 2529 2204 1241 1270

It is amazing how accurate Herrmann’s results were based on only a couple iterations using the Mayevski seven zone velocity retardation formulas.