The Kolbe-Leduc 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
Vivacity:
 /100 bar/sec.
Check for double base:
(Powder highlighted yellow)

What this program does
The main use of this program is to enable you to determine the most suitable powder for a given cartridge/projectile/calibre combination, and get a reasonable idea of how it will perform.

This program uses a development of the well known Leduc equation for projectile velocity -vs- distance travelled in the barrel, where the constants of the equation have been rendered in terms of propellant properties and loading conditions based on sound thermodynamic principles. This provides for a very simple, but surprisingly accurate internal ballistics system to predict chamber pressures and muzzle velocities.

User inputs
You need to enter the usable case capacity for your particular cartridge in grains of water. This is the case capacity behind the loaded projectile, not the capacity to overflowing. The more accurate this usable case capacity, the better. There is a YouTube video showing how you can measure this easily. However, the case capacity up to the bottom of the neck is a reasonable estimate and a limited list of approximate usable case capacities is given to get you started .

You will also need to enter: the barrel length from the bolt-face to the muzzle in inches, the case length in inches, the calibre in inches (use the groove diameter of the barrel), the powder charge weight in grains and the projectile weight in grains.

You will need the vivacity of the powder. The vivacity is the fractional rate at which the original weight of powder burns away per unit pressure, and is how powder companies usually give the 'quickness' of the powder. The table below gives the vivacities of a number of powders from a number of different powder manufacturers. The vivacities given are as the rate per second per 100 bar of pressure, and this is what should be entered into the program.

The program needs to know whether the powder is single or double base. Double base powders are highlighted in yellow in the table below. Double base powders have a lot more energy than single base powders and so a double base powder having the same vivacity as a single base powder will actually produce higher pressures and muzzle velocities than the single base powder; it will effectively be a 'quicker' powder. For this reason, a double base powder and a single base powder having the same vivacity are not equivalent. Two single base (or two double base) powders having the same vivacity will be equivalent (within the limits of this model).

Program outputs
When the program is run, a 'Summary of Results' is given, which includes the load density, the maximum chamber pressure (P-Max) the distance the bullet had travelled to P-Max and its velocity at that point. Also given is the muzzle velocity, the muzzle pressure and the muzzle energy of the bullet which is given in ft-lbs. There is also an estimate of how far up the barrel the bullet had travelled when the powder was all burnt. One of the assumptions of the program is that the powder is all burnt in the barrel. If the program finds the powder is not all burnt in the barrel, you will be informed that either the vivacity or the powder charge is too low.

The calculated P-Max pressure will have a coloured background. Chamber pressures in modern firearms should be safe if they are under 50,750 psi and pressures below this will have a green background. Pressures over 65,250 psi are generally higher than is considered the safe maximum working pressures for most cartridges, so pressures over this will have a red background. Pressures in between these limits will have an orange background. These are arbitrary limits, however. You should consult the relevant CIP or SAAMI standards for the maximum safe working pressure of your particular cartridge when working up a load.

Graphs are given of the chamber pressure -vs- time, chamber pressure -vs- distance up the barrel the bullet had travelled, and bullet velocity -vs- distance up the barrel the bullet had travelled.

How to use this program
Either: choose a powder of interest from the table below and enter its associated vivacity (and whether it is single or double based) into the form above. Adjust the powder weight so that the calculated maximum pressure is around 40,000 psi to 50,000 psi. Ideally, you want a loading density somewhere near 100% (case nearly full). If you cannot achieve these pressures with your chosen powder with 100% loading density, it is too slow. Choose a powder with a higher vivacity. If you can achieve the desired pressure but the loading density is too low (less than around 75%) then the powder is too fast. Chose a powder with a lower vivacity.

Or: for a load where the loading density is around 100%, adjust the vivacity so the the calculated maximum pressure is around 40,000 psi to 50,000 psi. Look in the table below to find a powder with a matching or near vivacity. Fine tune the load for the chosen powder.

This program helps you find the right powder for your application and suggests a possible load, but you must check the relevant reloading manuals to find the recommended safe starting loads and maximum loads. Follow safe reloading practices at all times.

Assumptions
The program assumes a constant value for the propellant density of 0.0584 lb/in3, which actually does not vary much from powder to powder. A bulk powder density of 0.0322 lb/in3 is assumed. This is a pretty good average, but a given powder could have a significantly different bulk density, and so the consequent loading density as listed at the output may vary from what you will experience. Powders come in two two basic types: single base, which are assumed to have a typical value for the Force of 3650000 in-lb/in3 and a gamma value of 1.24. Double base base powders are assumed to have a typical value for the Force of 3950000 in-lb/in3 and a gamma value of 1.225. ('Force' is the usable propellant energy density, and 'gamma' is the ratio of specific heats for the propellant gasses).

Table of Vivacities for various powders

Vivacity
Chemie-Swiss
Hodgedon
IMR
Lovex
Norma
Alliant
Vectan
Vihtavuori
100
99
98
97
96
95
N130
94
93
92
91
8208, 3031
N133
90
89
S060
TU3000
88
4166
87
86
4895
85
4064
RL7
N530
84
83
4320
82
81
N135
80
79
SP10
78
77
RS40
201
N140
76
SP9, TU5000
75
AR Comp
74
N150
73
RS50
S062
72
SP11
71
4451
202
70
D073.4, D073.5
69
68
67
RS52
S065
N540
66
TU7000, SP7
65
203B
64
4350
D073.6
RL15
63
62
N555
61
RS62
4831
RL16
N160, N550
60
RS60
59
S070
58
57
S071
URP
56
204
TU8000
55
7828
54
RS70
53
52
MRP
RL19
51
RL22
SP12
50
49
N560
48
RL26
47
N170
46
N565
45
44
43
RS76
217
SP13
N570
42
24N41
41
RL33
40
39
D100
39
37
36
20N29
35
RS80
34
33
32
31
30