Originally posted by Gerard:
Hello Ray,
quote:
show us the difference between the various formulas you linked.
Classic Greenhill:
T' = 150 / L'
Modified Greenhill:
T = 150 * D^2 / L
Bowman:
T = 3.5 * V^0.5 * D^2 / L
Since then Don Miller has done variants of the modified Greenhill such as the Miller formula below:
Sg=(30*C5)/((C7/C4)^2*C4^3*C6/C4*(1+(C6/C4)^2))*(C8/2800)^(1/3)*((C9+460)/(59+460)*29.92/C10)
All of these are inadequate. An entry level system to use is McGyro or one of the calculators at JBM Ballistics or Border Barrels. Both are based on McGyro below.
McGyro:
10 REM MCGYRO, APRIL 1986, BY R. L. MCCOY.
20 REM ESTIMATE OF GYROSCOPIC STABILITY FACTOR (SG)
30 REM FOR A UNIFORM DENSITY PROJECTILE. USES THE
40 REM MCDRAG INPUT FORMAT, WITH TWO ADDITIONAL QUANTITIES;
50 REM PROJECTILE DENSITY (GRAMS/CC), AND RIFLING TWIST
60 REM RATE (CALIBERS/TURN). OUTPUT IS ECHO OF INPUT
70 REM FOLLOWED BY A TABLE OF LAUNCH MACH NUMBER, LAUNCH
80 REM GYROSCOPIC STABILITY FACTOR, AND RIFLING TWIST RATE
90 REM REQUIRED TO GIVE SG=1.5 (SLOWEST ACCEPTABLE TWIST RATE).
100 REM
110 REM THE STANDARD DEVIATION OF THE SG ESTIMATE IS
120 REM 5 PERCENT AT SUBSONIC AND SUPERSONIC SPEEDS, AND
130 REM 10 PERCENT AT TRANSONIC SPEEDS.
150 CLS
160 KEY OFF
170 COLOR 7, 1, 8: CLS
180 KEY ON
190 DIM M(22), N15(22), S6(22)
200 REM
210 REM define table of launch mach numbers
220 REM
230 DATA 0.5,0.6,0.7,0.8,0.9,0.95
240 DATA 1.0,1.1,1.2,1.3,1.4,1.5
250 DATA 1.6,1.7,1.8,2.0,2.2,2.5
260 DATA 3.0,3.5,4.0,5.0
270 FOR I = 1 TO 22
280 READ M(I)
290 NEXT I
300 RESTORE
310 REM input projectile dimensions
320 CLS
330 PRINT "Enter the McGyro Inputs, one quantity at a time."
340 PRINT
350 PRINT "Enter projectile reference diameter (mm):";
360 INPUT D1
370 PRINT
380 PRINT "Enter projectile total length (Calibers):";
390 INPUT L1
400 PRINT
410 PRINT "Enter nose length (Calibers):";
420 INPUT L2
430 PRINT
440 PRINT "Enter RT/R (Headshape parameter):";
450 INPUT R1
460 PRINT
470 PRINT "Enter boattail length (Calibers):";
480 INPUT L3
490 PRINT
500 PRINT "Enter base diameter (Calibers):";
510 INPUT D2
520 PRINT
530 PRINT "Enter meplat diameter (Calibers):";
540 INPUT D3
550 PRINT
560 PRINT "[NOTE: Do not enter the center of gravity"
570 PRINT "location. Program assumes the center"
580 PRINT "of gravity is at the volume centroid]"
590 PRINT
600 PRINT "Enter projectile density (grams/cc):";
610 INPUT R10
620 PRINT
630 PRINT "Enter rifling twist rate (Calibers/turn):";
640 INPUT N
650 PRINT
660 PRINT "Enter projectile identification:";
670 INPUT K$
680 PRINT
690 CLS
700 PRINT "McGyro, April 1986, R. L. McCoy."
710 PRINT
720 REM echo input data
730 PRINT "Projectile Identification: "; K$
740 PRINT
750 PRINT "DREF", "LT", "LN", "RT/R"
760 PRINT "(MM)", "(CAL)", "(CAL)"
770 PRINT D1, L1, L2, R1
780 PRINT
790 PRINT "LBT", "DB", "DM", "RHOB", "TWIST"
800 PRINT "(CAL)", "(CAL)", "(CAL)"; "(GM/CC)", "(CAL/TURN)"
810 PRINT L3, D2, D3, R10, N
820 PRINT
830 PRINT " LAUNCH", "LAUNCH", " N"
840 PRINT "MACH NO."; SG; ","; (SG = 1.5); ""
850 PRINT
860 S1 = SQR(1 - D3)
870 S2 = 1 - D2 ^ 2
880 FOR I = 1 TO 22
890 IF M(I) <= .95 THEN 930
900 IF M(I) >= 1.1 THEN 950
910 G1 = 71.73001 - 42.433 * M(I)
920 GOTO 960
930 G1 = 20.082 + 3.726 * (M(I) / SQR(1 - M(I) ^ 2))
940 GOTO 960
950 G1 = 35.079 - 24.066 * (SQR(M(I) ^ 2 - 1) / M(I))
960 A1 = G1 * S2
970 IF M(I) < 1 THEN 990
980 IF M(I) >= 1 THEN 1030
990 B1 = SQR(1 - M(I) ^ 2)
1000 B = .82112 + .36971 * B1
1010 A = 34.779 + (24.091 + (8.977 - 12.804 * R1 + 8.38 * R1 ^ 2) * L2) * S1 * B1 - A1
1020 GOTO 1060
1030 B1 = SQR(M(I) ^ 2 - 1) / M(I)
1040 B = 1.0528 + .23379 * B1 - .004884 * (M(I) - 1)
1050 A = 58.873 + (8.115 + (14.15 - 15.348 * R1 + 7.216 * R1 ^ 2) * L2) * S1 * B1 ^ 2 - A1
1060 N15(I) = (A * SQR(R10)) / (L1 ^ B)
1070 S6(I) = 1.5 * ((N15(I)) / N) ^ 2
1080 NEXT I
1090 REM Print McGyro Output
1100 U$ = " #.## ##.## ###.##"
1110 FOR I = 1 TO 22
1120 PRINT USING U$; M(I); S6(I); N15(I)
1130 NEXT I
1140 PRINT
1150 PRINT
1160 PRINT "Copy this? (Enter Y for Yes, N for No):";
1170 INPUT K2$
1180 IF K2$ = "N" THEN 1410
1190 LPRINT
1200 LPRINT
1210 LPRINT "McGryo, April 1986, R. L. McCoy."
1220 LPRINT
1230 LPRINT "PROJECTILE IDENTIFICATION: "; K$
1240 LPRINT
1250 LPRINT "DREF", "LT", "LN", "RT/R"
1260 LPRINT "(MM)", "(CAL)", "(CAL)"
1270 LPRINT D1, L1, L2, R1
1280 LPRINT
1290 LPRINT "LBT", "DB", "DM", "RHOB", "TWIST"
1300 LPRINT "(CAL)", "(CAL)", "(CAL)", "(GM/CC)", "(CAL/TURN)"
1310 LPRINT L3, D2, D3, R10, N
1320 LPRINT
1330 LPRINT "MACH NO.", " SG", "(SG=1.5)"
1350 LPRINT
1360 FOR I = 1 TO 22
1370 LPRINT USING U$; M(I); S6(I); N15(I)
1380 NEXT I
1390 LPRINT
1400 LPRINT
1410 REM CHECK FOR ANOTHER CASE
1420 PRINT
1430 PRINT
1440 PRINT "Run another case"
1450 PRINT "Enter Y for Yes, N for No:";
1460 INPUT K1$
1470 IF K1$ = "Y" THEN 310
1480 END
New toy. That is funny. See
this post dating back six years.