When I was young, I worked at an ammunition factory. My boss was testing a new cartridge, a scaled-down version of the soviet 7.62x39, named the 6.5x35. At the time there was plenty of powder suitable for the .30 M1 Carbine, so various attempts were made to load it into the very small case of the mini-AK.

Unfortunately, the case capacity was not the only thing to take into account, and the pressure gun tests showed excessive breech pressure and low muzzle velocity.

I knew nothing about powders, but it was not too difficult to realize that the propellant and/or the bullet were not the right ones. The new cartridge was soon dropped, due to a huge order for the 7.62x51 NATO blank cartridge, but I started to read avidly about powders, loading, testing and so on, with the strong will to really understand the matter. In the following you can find a quick report of my studies.

Propellants are tested in an airtight vessel named a "closed bomb." A small amount of powder, put intside it, is ignited by an electric heater, and measuring equipment fitted to the bomb records both the pressure attained and elapsed time.

With reference to the perfect gas law, the test gives figures as the specific pressure (i.e. the pressure the unit of load can develop in the unit of capacity, lbs./sq.in. or Bar or MPa), and the co-volume (i.e. the smallest volume the mass unit of burnt gases can be reduced to under an infinite pressure, cu.ins./gr. or cc/g).

The specific pressure can also be referred to as specific energy (i.e. the energy released by the complete combustion of the unit of load, ft.lbs./gr. or J/g), and it is usually known as force. Force and co-volume are well defined by the theory of explosives, together with the heat of explosion (in this case, better named as "heat of combustion" or "energy potential").

The heat of combustion (measured by a device named "chalorimeter", ft.lbs./gr. or J/g) is somewhat like the specific energy, but it refers mainly to the mechanical work that the burnt gases can do during their expansion, while the specific energy refers mainly to the pressure that the burnt gases can reach in a close vessel.

Due to the low loading density (namely 0.2-0.3 grams per cubic centimeter, so that the vessel will not burst under the gas pressure), the ratio between the recorded pressure and the final one nearly equals the burnt load fraction.

Plotting pressure vs. time gives an ever raising curve; its slope is initially mild, then gets steeper, and finally goes down to zero.

From the first derivative of pressure respect to the time, divided by the pressure itself, and divided still by the final pressure, the so-called "dynamic vivacity" (dimensionally the inverse of pressure times time) can be calculated and plotted, giving in addition a mean value, with reference to the burnt load fraction.

Force and dynamic vivacity are often slightly different from lot to lot of the same powder, so they are usually expressed in percent of those achieved for a reference lot.

Pressure and time attained at the end of combustion depend upon the loading density. The higher the loading density, the higher the pressure, and the shorter the time of combustion.

Nevertheless, the area under the curve until the end of combustion (dimensionally pressure times time), for a given powder of given composition, shape and dimensions, does not vary at all (at least theoretically), regardless of the loading density. But what is the physical meaning of this figure?

Now let us think to the mass of burning gases acting along the bore of a gun, thrusting against the base of a bullet. The only difference in respect to the closed bomb is that in the barrel a wall is free to move forward. At least theoretically. Some major differences in reality are the powder ignition by a primer, and the higher loading density according to the amount of powder in the case.

Subsequently the pressure curve during a cartridge test, as recorded in a pressure gun fitted with the same recording equipment as the closed bomb, is no longer ever rising. It first reaches a peak, then it suddenly decreases as the bullet continues down the barrel, falling to zero when the bullet leaves the muzzle.

The test provides figures including the ignition delay (i.e. the lag time between the blow of the firing pin and the start of combustion), the time of rise (i.e. the time elapsed until the pressure peak occurs), the time of fall (i.e. the time elapsed until the bullet goes out), the time in barrel (i.e. the sum of the three ones) and, last but not least, the peak pressure.

Such figures, together with the muzzle velocity (separately recorded with a chronograph), are mainly used to check the uniformity of cartridge lots as they come from production lines, and also during cartridge development.

Is there any link between tests running in closed bombs and pressure guns?

One main assumption of the interior ballistics theory just stated is that the area under the curve of pressure plotted vs. time, until the end of combustion, for a given powder of given composition, shape and dimensions, is a constant. Another main assumption is that this is as true in a closed bomb as in a gun bore.

These two assumptions are very handy in order to find the link between the two kinds of test, the one for powders, the other for cartridges. If we were able to find the time when the combustion ends, running a cartridge test in a pressure gun, we could establish a true comparison with a powder test runned in a closed bomb (obviously testing the same powder loaded in the cartridge).

Let us assume to have found this time, in a barrel long enough so that the powder can be burnt completely. In this case the area under the curve equals the Momentum imparted to the bullet during the complete combustion, divided by the bullet base Area. In other words, it (approximatively) equals Sectional Density times Combustion End Velocity.

We can name this figure as "Specific Impulse": "Impulse" because its original dimensions are those of a Momentum; "Specific" because it is a Momentum per unit of Area.

Actually this figure, taking into account the friction along the bore, the thermal exchange across the wall, and the flow of burning gases, is greater than the number given above, and subsequently the velocity at the end of combustion is smaller.

So the physical meaning of the figure given by powder testing in closed bombs is the following:

1. A given powder, of given composition, shape and dimensions, can provide only a well defined Specific Impulse.
2. Until the end of its combustion, it can impart to a bullet of given Sectional Density a Velocity not greater than the ratio between the Specific Impulse and the Sectional Density (due to frictional and thermal losses, and gases flow).
3. This is true regardless the actual Loading Density of the case.

This last statement sounds incredible, but its only limit is given by the First Law of Thermodynamics. In other words, the load cannot go under a certain limit, given by the fact that thermal efficiency never can be more than one.

Providing what stated above, the greater the load, the closer to the breech the end of combustion; the smaller the load, the closer to the muzzle the end of combustion. As sectional density is given in pounds per square inch, and velocity is given in feet per second, specific impulse is given in lbs./sq.in*fps.

Powders are not all the same, as every reloader knows. So let me say the following:

1. The ones showing the greater Specific Impulse can impart higher Velocities to bullets having greater Sectional Density.
2. The ones showing an intermediate Specific Impulse can impart High Velocities to Low Sectional Density bullets, or Medium Velocities to Medium Sectional Density bullets, or Low Velocities to High Sectional Density bullets.
3. The ones showing the smaller Specific Impulse can impart lower Velocities to bullets having lower Sectional Density.

Specific Impulse is inversely proportional to Combustion Rate; the smaller the Specific Impulse, the higher the Combustion Rate; the greater the Specific Impulse, the lower the Combustion Rate.

Another difference between powders is created by their different energy content. That is to say, hot powders vs. cool powders. Hot powders are generally quick burning, while cool powders are generally slow burning.

But what happens with powders having high energy potential and high specific impulse? Maybe the same with powders having low energy potential and low specific impulse? What do you think about high energy potential and low specific impulse? And what about low energy potential and high specific impulse?

You see, the matter becomes more complicated, but do not be afraid. The key is the Relative Quickness, defined as 100 times the ratio between the Energy Potential (ft.lbs./gr.) and the Specific Impulse (lbs./sq.in*fps):

This figure shows that pistol powders rate about 100-60 RQ, shotgun powders rate about 80-40 RQ, carbine and rifle powders rate 50-10 RQ, according to bore and case capacity (that is to say, the expansion ratio).

Finally, multiply RQ by 7 (as there are 7000 grains in 1 pound), and you will get the Du Pont index, so that you can compare every powder with propellants made by that firm. (Former Du Pont powders are now IMR powders and owned by Hodgdon, since being spun off by Du Pont).

Usually there is no link between tests run in a closed bomb and in a pressure gun, unless it is possible to know when the combustion is completed. After some years of studies I have found the way to get this link. I can process a file recorded from a pressure gun test, identify the combustion end point and calculate specific impulse, specific energy and energy potential of the powder loaded into the cartridge tested.

The energy potential can be calculated because there is a body (the bullet) in motion, and some work is made on it. Obviously, the same is not possible in closed bomb tests, where nothing can move.

Should the combustion end beyond the muzzle, such figures can only be estimated on the basis of recorded trend.

The software can predict whether combustion ends within the muzzle. In addition, the burnt mass fraction and the form function of the powder can be plotted, the one vs. the relative specific impulse, the other vs. the burnt mass fraction.

The relative specific impulse is somewhat similar to the burnt width fraction, but it is more convenient as it can be referred to the whole mass of the load, instead of the mean minor dimension of kernels.

The form function is similar to the dynamic vivacity, but it is dimensionless. Nevertheless, the dynamic vivacity can be derived dividing the form function by the specific impulse.

I hope that my studies are of interest to some Guns and Shooting Online readers. (Even better if they intererst some cartridge factory to which I could sell my software!)