The Mayer-Hart Internal Ballistics Model

REQUIRED DATA
Usable case capacity:
 grains of water
Case length:
 inches
Bullet weight:
 grains
Calibre:
 inches
Barrel length:
 inches
Powder weight:
 grains
Powder Force:
 in-lbs per lb
Vivacity:
 /100 bar/sec.
Powder Density:
 lbs per cubic inch
Bulk Density:
 lbs per cubic inch
Gamma:
 

Powder Type
Vihtavuori
Force
in-lbs/lb
Vivacity
/100 bar/sec.
Nitro. Density
lb/in3
Bulk density
lb/in3
Gamma
Cp/Cv
N110
3650000
148
0.0584
0.0288
1.24
N120
3650000
130
0.0584
0.0310
1.24
N130
3650000
92
0.0584
0.0314
1.24
N133
3650000
89
0.0584
0.0317
1.24
N135
3650000
77
0.0584
0.0314
1.24
N140
3650000
74.5
0.0584
0.0328
1.24
N150
3650000
71
0.0584
0.0328
1.24
N160
3650000
60
0.0584
0.0332
1.24
N165
3650000
51
0.0584
0.0332
1.24
N170
3650000
44
0.0584
0.0346
1.24
24N41
3650000
39
0.0584
0.0350
1.24
20N29
3650000
33.5
0.0584
0.0346
1.24
N530
3950000
79
0.0584
0.0335
1.225
N540
3950000
67.2
0.0584
0.0339
1.225
N550
3950000
58
0.0584
0.0346
1.225
N555
3950000
54,5
0.0584
0.0346
1.225
N560
3950000
48
0.0584
0.0346
1.225
N565
3950000
42.5
0.0584
0.0346
1.225
N570
3950000
40
0.0584
0.0346
1.225

What this program does
This program uses the analytic solution to the ballistic equations, as published by Mayer and Hart* in 1945 and used for many years in various guises by the Ballistic Research Laboratory in the United States. It is not a numerical simulation. Because it is an analytic solution, a number of simplifications and approximations have to be made to achieve a closed solution. Even so, it is interesting and instructive to see in what ways an analytic model such as this compares well to the real world, and in what ways it does not.

Analytical solutions like this are also useful to validate a numerical method, in that given the boundary conditions of the system, the solutions are exact. Any numerical computer model, given the same boundary conditions at the input, should give the same answers at the output.

Using the program
The parameters for the range of powders by Vihtavuori are given above. This will enable you to get some practical idea of how the system works in practice. It should be noted that "usable case capacity" here is the volume (in grains weight of water) in the case behind the loaded projectile. The output includes a summary of various parameters such as the peak breech pressure and the muzzle velocity. Curves of mean pressure and velocity as a function of distance travelled are also given. It is not possible to derive an analytical function of pressure as a function of time, but this can be extracted from the curves for pressure and velocity.

Accuracy
The system should give muzzle velocities that are accurate to 2 - 3%. It is actually quite difficult to do much better than this even with "exact" numerical models, due to the uncertainties in determining burning rates, ratios of specific heats, and other constants - most of which are not actually constant as the powder burns and the pressure varies.

Description of the Mayer Hart system
For those with a deep interest in the technicalities of internal ballistics, and with a strong mathematical background, a derivation of the Mayer Hart ballistic equations used in this program is given.

* J.E. Mayer, B.I. Hart,"Simplified Equations of Internal Ballistics", Journal of the Franklin Institute, 240, pp 401-411, (1945)