Conventional Guns

	Notice:
	Please bear with us. Your ride's still a work in progress.

Introduction

Conventional Guns denotes weapon that propels a mass using the exothermic decomposition of a chemical propellant in a controlled manner, with propellant being constrained inside a barrel (as opposed to co-moving with the projectile, as is the case with rockets). Having evolved from porcelain filled bamboo tubes that expel shrapnel using the explosion of gunpowder, attested to in the 12th Century in China, and subsequently introduced to Europe by the 14th Century, its prominence in literature that touches on military matters has been remarkable. Therefore it is not surprising that conventional guns continues to feature in many science fiction with a focus on warfare, although these depiction has seldomly been fair. Quite often, conventional gun technology have been treated as one of lower technological sophistication, that cannot hope to compete with other weapon systems (such as railguns, coilguns, and especially with missiles), and authors have often resorted to "too clever by half" twists that supposedly circumvent limitation of conventional gun, only to miss important caveats and leave out more plausible advances that may come either as natural consequences of the prevailing technological advancement of a setting, or as potential advances with some effort.

In any case, whatever the reason for this deplorable state of affairs may be, in line with Galactic Library's goal of providing literature where other sources fail, this article will seek to explore the design space of conventional guns with the help of interior ballistic theory, with a special focus on its impact for science-fiction worlds, and outline some real-world advanced techniques that promises to further improve upon this basis. Naturally, this will have particular impact on settings that are more near-future.

Theory of Interior Ballistics

Perhaps one reason for the general lack of interest, even in sci-fi interest groups, that conventional guns garner, can be attributed to the sheer complexity of the associated theory that describes the acceleration of projectile under combustion of a propellant, known as the theory of interior ballistics. The nature of the process precludes simple and elegant equation like the analogous "Rocket Equation" for rocketry that encapsulates the essence of rocket kinematics. Instead, accurate models are always solved numerically. Thus this article will only go over the details of interior ballistics in so much as it lends to an intuitive understanding of the kinematics of gun systems, or as pertinent to establishing performance figures, and refer the reader to more systematic treatment of the same in reference section for the process of arriving at the detailed calculations later on. Notation in this article generally follows the Eastern tradition as established by M.E.Serebryakov, although the following argument has been much improved by consulting the work of J.Corner as well.

The Propellant

Propellant that are suitable for conventional gun must exhibit a stable burning (in this context, burning means exothermic decomposition in the absence of (appreciable) atmospheric oxygen) behavior. This is best illustrated by briefly going over the history of Nitrocellulose, the primary ingredient in almost all propellant up until rather recently.

When first synthesized circa 1845, Nitrocellulose was found to detonate violently, where upon ignition, a mechanical shockwave is rapidly setup, that propagates in all directions, compressing the material in front to the point of ignition as well. The shock front propagates at a few km/s, limited only by the (compressed) speed of sound in the combustion products, rapidly consuming all propellant. Thus, for 40 years, it was employed as an explosive, despite its advantage over black powder (thrice as much energy density, very little solid product and decreased sensitivity) being clearly evident. It was not until the mid 1880s that Nitrocellulose was tamed by dissolving it in a suitable organic solvent, such as alcohol or ether, that causes microscopic swelling of the micro structure of the fiber. In this state, the propellant behaves like a putty that can be extruded or cast to the desired shape. This leaves microscopic holes, or pores after the solvent is driven off through heat. Now, the behavior of burning changes completely: When ignited, the propellant is heated, at the surface, by the radiated heat of the exothermic combustion products. This causes burning to (largely) happen along a parallel plane to that of the initial shape, with the rate limited by the bulk thermal conductivity of the propellant, to around a few cm/s, at gun pressures, an order of magnitude reduction of 5. This development allowed Nitrocellulose to rapidly replace black-powder as the preeminent component in gun propellants in the next decade, relegating the latter to be used as an igniter and ignition booster for the most part.

A brief discussion of further development of propellant science since that period to that of modern time is given for the sake of completeness, to spare the reader of tracking down fragmentary information across multiple, cryptic DTIC reports and digging through Internet Archive.

In the decades immediately following, Nitroglycerin was added to the mix and the propellant is dissolved in the common solvent Acetone, greatly increasing both the energy density and flame temperature (and errossiveness) of propellant. This being known as the double-base propellant, the original formulation became retroactively known as single-base propellant. In the wake of WW1, the German innovation of using a Nitroglycerin - Ethyl Centralite mixture as both a component of the final propellant and a solvent to cause swelling, eliminating the time and expense necessary to extract the solvent. This "solvent-less" gun powder was rapidly adopted, and especially useful in rocket motors where it would have been extremely difficult to extract solvent due to the thickness of the cast involved. Immediately prior to WW2, another German innovation, that of a modified double base propellant where Nitroglycerin was replaced in part or in full with Diethylene Glycol Dinitrate (DEGDN), both relieved the war-industry of the burden of Nitroglycerin production (which depended upon foodstuff) while also improving the thermal-chemistry of propellant gasses, with overall lower molecular weight, facilitating either increased force or reduced temperature. The downside is reduced thermal stability, much noticeable in hotter climates. Triple base propellant, involving the addition of Nitroguanidine, as the primary energetic component, increasing the performance further, although the higher cost (and limited supply) of Nitroguanidine delayed its adoption until after WW2.

As of late, modified double-base propellant and triple-base propellant appears to be the choice when performance is required for gun system, and expanse can be spared in pursuit of the same, while single-base propellant remains dominant for small-arms purposes. Reflecting their usage, the former two usually comes in grains of defined shape and perforation, sized to suit their gun, while the latter tends to be made in simpler geometry like strand or ball.

Although attempt has been made since then to replace triple base propellant with Mixed Nitrate Ester propellant of greater availability, and indeed various mixture had been type classified, composed of Nitrocellulose mixed with varying proportions of BTTN, TMETN, TEGDN and DEGDN. this appears to not have been widely adopted, perhaps due to a lack of necessity. Finally, it bears mentioning the composite propellant, consisting of a heterogeneous mixture of oxidizer and fuel particles. This appears to not have been adopted for internal ballistic use as much as it is prevalent in rocketry (various Aluminum Percolate Composite Propellant, or APCP comes to mind), due to its lower performance than pure CHON systems.

In recent years, two of the more promising lines of research that bears special mention includes the work on Nitramine propellant, and that of highly energetic poly-Nitrogen Compounds (otherwise colloquially known as Nitromemes in relevant interest circles). The premise behind Nitramine propellant is simple enough: that of taming RDX (Hexogen, Cyclonite) and HMX (Octogen), well known and highly energetic chemical explosives, for use as propellants. It was found that by grinding RDX particles down to 5 micrometers or so, and suspending these particles in plasticizes, these energetic materials could be made to combust stably enough for use as propellant (specifically, this brings the burn rate pressure exponent below 1). RDX based propellant development effort has already bore fruit, with formulations being type classified by the 1980s to 1990s, while HMX based propellant is still under investigated. Work on denser, and even more chemically favorable polycyclic nitramines like CL-20 (also known as HNIW) based propellant is well underway as well.

Another, more speculative line of research concerns poly-Nitrogen compounds. While Nitrogen allotropes, whose names grows in exoticism with the number of atoms being forced together, from Trinitrogen (N3) and Tetranitrogen (N4), to the likes of Hexazine (N6), Octaazacubane (N8), and Bipentazole (N10), are generally considered too unstable for use as propellant (indeed many aforementioned species are considered meta-stable with lifetime measured in seconds). If these can be made to be somehow stable in storage, and dissociate at a reasonable rate after ignition, the much higher density of energy stored within coupled with reasonable molecular weight (the primary product will be N2 (gas) at ~28, as compared to 23-25 of current propellant) would expectantly produce gun system of tremendous performance. However, there is no research at present hinting at how this might be achieved. As a concession to practicality, less energetic compounds can be had with the addition of C,O,H,F to high enthalpy Nitrogen, creating chemically stable structures. It is possible that with the use of inert binders and by applying similar techniques to that of stabilizing Nitramine propellant discussed above, these could be made to burn at reasonable rate, although this too remains in the realms of speculation.

Five propellant properties are relevant to interior ballistics:

• Propellant Force $f$, also known as specific impetus, measured in unit of energy per unit of mass. This is the analogous property, in ballistics theory, to the concept of specific impulse in rocketry. Unfortunately, it has a more tortuous definition of either "the difference between the enthalpy and energy of gas product at adiabatic isochoric flame temperature $T_{v}$ for one unit mass of propellant burned", or equivalently, "the work done by an unit mass of propellant ideal gas expanding in an adiabatic and reversible way from the adiabatic isochoric flame temperature $T_{v}$ down to 0K". By definition, propellant force is:

  $f={\frac {R_{0}T_{v}}{M}}$

  Where $R_{0}$ being the gas constant in appropriate unit, $\gamma$ for the adiabatic index (ratio of specific heat) and $M$ the average molecular mass of gas product. In practice this value is usually derived via closed-bomb test according to ballistic theory, which differs slightly from that predicted by thermal-chemical balance calculations. By assuming ideal gas relationship (i.e.$T_{v}=T_{p}\gamma$), this allows relating the (ballistic) propellant force to the (rocketry) specific impulse via:

  $I_{sp}\cdot g_{0}={\sqrt {{\frac {2f}{\gamma -1}}[1-({\frac {P_{e}}{P_{c}}})^{\frac {\gamma -1}{\gamma }}]}}$

  Where $P_{e}$ and $P_{c}$ being the exit and chamber pressure condition, respectively. In the limit of expansion to vacuum, this approaches:

  $\lim _{P_{e}\to 0}I_{sp,vac}\cdot g_{0}={\sqrt {\frac {2f}{\gamma -1}}}$

  Modern propellants generally have force ranging from 9,500 J/g to 11,500 J/g.
• Bulk Density $\rho _{p}$, or the density of propellant formulation. For most propellant in use this value is around 1.6 g/cc, although propellant with higher density (CL-20 @ 2.0g/cc) is not unknown.
• Covolume $\alpha$, measured in the inverse of density unit, covolume is found in the Nobel-Abel equation of state commonly assumed for interior ballistics work:

  $P(V-\alpha W)={\frac {W}{M}}R_{0}T$

  Where $P$, $V$, $W$ and $T$ are the gas pressure, volume, mass and temperature respectively. The covolume factor here corrects for the deviation of real gas from ideal gas behavior, due to incompressibility effect of real-gas under extreme compression. This correction is practically speaking only necessary for ballistic work, as the effect at rocket pressure (some few tens of MPa) is usually negligible. In practice this is usually fitted to a closed-vessel test fire data, making it really an average over the range of condition experienced by gas in chamber. Since, in fact covolume is dependent on chamber loading condition and pressure developed, it is fortunate, then, that its effect is most prominent during the starting phase of ballistic cycle where gun pressure are the highest, and deviates only a few percent from the value calculated from the more sophisticated (but developed much later) Virial equation of state, taking the first 3 Virial coefficients, at the highest density for products. The error this cause at smaller loading density is small.
  For almost all propellant currently used the covolume lies between 0.9-1.1 cc/g.
• Burn Rate Coefficient $u_{1}$ and Burn Rate Exponent $n$. The dependency of burn rate upon reaction zone temperature and pressure is a complex topic. By examining partially burnt propellant through specially vented chambers, it was established in the 19th century that propellant burning proceeds parallel to the surface of a propellant grain, or in other words, at any time the surface of burnt propellant roughly parallels the surface it had before burning. This observation is known as the Piobert's Law (see above for an explanation), gives rise to the definition of "propellant (linear) burn rate" as the rate at which this parallel surface recedes.
  It is now known that propellant burn rate exhibit several distinct "zones" with each range exhibiting different temperature or pressure dependency, especially in the low pressure ranges (~few tens of MPa). Historically, due to the limitation of instrumentation these idiosyncrasies were not known to a reasonable degree of accuracy, ballisticians have resorted to fitting burn rate to pressure in the range where accurate representation is most important, i.e. at high pressure and close to the operating pressure of guns. By far the widest used representation, is:

  $u=u_{1}P^{b}$

  This is sometimes known as the de Saint Roberts formulation, where $u$ denotes the linear burn rate under pressure $P$. Depending on the exact range of fitted data, the exponent can vary from 0.7-0.9 for modern propellants, and while there are no hard rule to this, it is generally desired to have a exponent of less than unity to prevent excessive pressure spiking, and ~0.7 for rocketry work.
  These two properties are perhaps the least explained of all as propellant performance is concerned. While empirical rules have been developed to describe the burn rate of arbitrary mixtures of some well known propellants , and it is possible, through very detailed calculation, to predict the burn rate of a propellant, this is in practice seldomly done unless very specific features of combustion is being studied. Uncertainties in these areas are also the primary concerns for prospective and hypothetical propellants, since these generally require enough quantities to be synthesized in enough quantity to be tested in a closed vessel, and even then sometimes data are only available for very low pressures due to the scarcity of high-pressure closed vessel apparatus capable of performing such experiments.

The Simplest Gun

The simplest gun system in terms of ballistics theory is one where all the propellant has burned to depletion before the projectile has appreciably moved. This type of gun promise the highest possible ballistic efficiency (the amount of energy transferred to the projectile out of the total energy content of the propellant load) out of a given barrel length and given weight of propellant and projectile.