NOTE: We wrote the following article very early in
the development of what became the patented
and trademarked SMc cartridge design.
As such, we later proved that many things we speculated on in
this article were imprecise.  I have included this article
on the web page for historical completeness only.
~~~~~~~~~~~~~~~~
June 2000,
M. L. (Mic)McPherson,
Ballistician;

With contributions from Mr. Robert Byrom Smalley, Jr.,
Rocket Scientist

Co-Titles:
Optimizing Case Shape and Design
(McPherson);
A Rocket Scientist’s Thoughts on Optimizing
Shouldered-Case Design

(Smalley)

Synopsis: Despite more than 150 years of the self-contained cartridge, we have seen precious little documentation covering research into case design optimization. New information — gleaned from the disparate design disciplines of solid-fuel rocket engines and, of all things, 2-Cycle engine exhausts — suggests that a relatively short, fat case with a specific shoulder design may very well be ideal.

Owing to the difficult nature of this subject, I have erred toward too much detail; therefore, the following article contains a measure of deliberate repetition. Please note, that as the primary author, I (M.L. McPherson) must take responsibility for this text, while Mr. Smalley and I have worked together in an effort to fairly represent this subject, we do not necessarily fully agree on the importance or accuracy of every aspect discussed in the following text. Furthermore, I am happy to take full responsibility for any errors, conceptual, factual, or otherwise. Finally, please, bear in mind that our goal is only to present the details of a basic argument.

Mr. Smalley (who prefers the moniker, By) retired as a principal engineer in solid rocket engine design, a field with definite relationships to cartridge design. As a hobbyist, he participated in the design of several World Record holding model airplane engines. Specializing particularly in exhaust system design, By designed and optimized an exhaust system based upon an idea originated in the late 1800s. He thereby helped design a 0.049 cubic inches, 2-Cycle engine with world-beating size- and weight-to-horsepower ratios, which propelled a scale airplane to 120 mph! Later, we will see the surprising relationship that work has to one aspect of optimizing cartridge design.

I am not shy about theorizing; sometimes that is good. My recent forays into the discussion of case design seem to have been of that ilk. Regarding my speculation on, ultimate case design, I have heard from my friend, Bob Bell (respected, long-time Handloader’s Digest Editor), many PS readers, two reamer manufacturers, one gun manufacturer and now a genuine rocket scientist, Mr. Robert Byrom Smalley, Jr.

Numerous responses from various Precision Shooting readers suggest that this subject is of general interest. In his letter, Mr. Bell noted that a half-century ago, “There was considerable debate among shooters along these same lines.” He kindly added that such debate was “… without any firm direction or any comments showing the advanced thinking that your articles suggest.” He goes on to offer evidence that, for most shooters, the entire issue amounts to much ado about almost nothing — existing designs are so good (emphasis, mine). Nevertheless, I would contend that better is better and progress toward that unobtainable goal perfection is at the heart of the pursuit of Extreme Rifle Accuracy.

During various telephone conversations, By, confirmed that I am on the right track. While an overall optimum case design may not exist, it is possible, at least in theory, to optimize case design for any particular set of components and cartridge performance level. Critical variables include: powder column length-to-diameter ratio, case shoulder angle, bullet mass compared to cross sectional area, bullet base configuration (boattail versus flat base, etc.), effective friction load (neck and barrel), seating depth, case filling ratio and ratio of case volume to bore cross-sectional area. Generally, such a design will represent a unique accommodation to three factors: first, minimization of interior surface area; second, minimization of distance from initiating primer blast to furthest powder granules; third, a suite of shoulder design considerations, which have several critical influences.

Military small arms and artillery designers have some incentive to produce the most efficient case shape. However, that research information is not readily available and, after all (excepting a few weight-critical applications, such as helicopter armament), adding a bit of steel to a gun or material to a cartridge case or powder to a propellant charge is of little relative importance. Furthermore, for most applications, cartridge design must also accommodate handling and chambering considerations.

On the other hand, in rocketry, weight considerations dominate — with current technology, it can cost $20,000 to place one pound of anything into orbit and, critically, every pound added to the engine results in a significant payload loss. In other words, in rocketry, designers have the ultimate incentive to design the most efficient (lightest) engine possible. Those pushing the envelope of cartridge design have precisely the opposite motivation; for them, cost (weight) is not an issue — only results matter.

While considerably more energetic, solid rocket fuel is, for practical purposes, significantly similar to conventional smokeless powder. Furthermore, criteria for designing the most efficient solid rocket engine turn out to be germane to the issue of designing the most efficient and ballistically consistent cartridge case. Before making any general conclusions, and without entering into boring detail, I would like to review this subject and visit a few facts from various discussions between By and me.

Background, Clarification and a Bit of Review

The primer blast does several things to the powder charge. First, it drives the base of the charge forward and it can also create an axial hole to some depth. Second, it directly ignites some granules, either by condensation heating (as nascent combustion gases condense onto surfaces) or through contact heating (as incandescent particulates penetrate surfaces). Third, through compressive shock, it can significantly heat granules that do not ignite. Fourth, it can partially fluidize unignited granules, causing some degree of granule-to-granule fusing — this significantly changes the nature of individual granules and the propellant mass.

Adiabatic Heating

While compressive (shock) heating probably does not lead to direct granule ignition, in some cartridges, it is of significant importance because, by raising granule temperature, it can dramatically reduce ignition delay — when those granules are subsequently further heated by the producing energetic propellant cloud.

Also, during the combustion phase, adiabatic heating of air within the charge mass can significantly heat adjacent surfaces. This heating occurs as initially unignited granules deform plastically. First the smaller openings are sealed, which eliminates porosity. Then gas in the remaining voids is further compressed. As confining pressure increases, void volume shrinks and temperature increases.

Under some circumstances, these pockets might be large enough and become hot enough to heat adjacent granule surfaces sufficiently to cause ignition. This potentiality is particularly noteworthy in those combinations where the case is not filled with powder. There, granule heating through primer-blast-related compressive forces can be significant. This is almost certainly a factor in reduced-charge detonations with slow powders. Indirect and lesser effects of this phenomenon could also explain why the most accurate loads seldom use significantly less than a case-full charge.

Kindling Versus Ignition

Here I must clarify a significant detail. Some readers may not recognize the important distinction between kindling point and ignition point. For this discussion, we can consider kindling point as that temperature where smokeless powder ignites in response to very slow heating — the temperature gradient in the near-surface layers is very modest. Conversely, ignition point is that temperature where smokeless powder ignites in response to very rapid heating — the temperature gradient in the near-surface layers is significant. This distinction is critical, particularly when discussing late-stage ignition — where granules escaped ignition either from the primer blast or through the action of developing propellant gases until after the bullet began to accelerate.

Kindling point is also known as Thermal Decomposition Point. This is defined as that temperature where more heat is generated by decomposing propellant surface layers than is conducted into the propellant (exothermal reaction). Subsequently, in order to maintain granule surface temperature, it becomes necessary to remove heat.

Ignition Point depends upon heating rate because the faster that heating occurs, the hotter the surface layer can get before the temperature gradient in the surface layers exceeds the rate of thermal conductivity between those layers. Consider heating to any specific surface temperature: when heating occurs slowly, the heated zone gets relatively thick, so that underlying cooler layers cannot rapidly wick away additional heat; when heating occurs rapidly, the heated zone stays relatively thin, so that underlying, cooler, layers can rapidly wick away additional heat.

Kindling (thermal decomposition) point for various typical smokeless propellants is listed as a surprisingly mild 160-170 degrees C (320-338 degrees F). This reflects the temperature of slowly heated surrounding air when a sample spontaneously ignites (exothermal reaction ensues), during very slow laboratory heating. Such ignition is completely unlike what happens in a cartridge. There, condensation of primer gases onto granule surfaces results in extremely rapid heating. In this instance, if we could measure granule surface temperature at the instant of ignition, we would find that it was far higher than the laboratory-derived thermal decomposition point. A demonstration that ignition point depends upon heating rate.

This analysis applies to those granules not ignited by the primer. While the various forces involved in the ignition phase and during nascent propellant combustion typically generate granule surface temperatures far exceeding the thermal decomposition point (up to 2650 degrees C — 4800 degrees F), such granule surface heating occurs extremely rapidly; therefore, ignition temperature is a function of ignition point, not kindling point. Furthermore, once powder gases generate sufficient force to begin to move the bullet, any unignited granule typically has far less than 2 milliseconds (2/1000 seconds) to achieve combustion before the bullet reaches the muzzle. The bottom line, it is quite common for such granules to entirely escape ignition.  Anyone who does not believe this happens should talk to those folks who have watched an indoor shooting range burn to the ground because of incautious cleanliness practices that allowed too much unburned propellant to build up — Hodgdon almost lost its range this way and Nosler lost much of its entire testing facility, dozens of commercial indoor ranges have succumbed to this.

Cartridge Efficiency and Consistency

The goal of any cartridge is to convert potential chemical energy of powder granules into kinetic bullet energy. Therein, granules that do not ignite before the bullet begins to move suffer four progressive deficits. First, produced gases have less time to work on the bullet — which is moving faster and getting closer to the muzzle. Second, as bullet velocity increases, propellant push weakens — both molecular velocity and gas flow velocity through a bore are limited. Third, compared to underlying layers, energy production from deterred surface layers is lower. Fourth, as bullet movement exceeds a few inches, confining pressure decreases dramatically, so combustion occurs at a much slower rate.

Consider an example: 308 Winchester, 150-grain bullet, 50-grain charge. If a 10-grain plug of unignited powder follows the bullet into the bore, then initially, the effective bullet is 160 grains and the effective charge is 40 grains. Unless granules in this plug can ignite soon enough and burn fast enough to pressurize the developing void behind the accelerating bullet, that plug not only does not add to performance but its acceleration absorbs energy that could otherwise accelerate the bullet.

For these reasons, as the bullet progresses through the bore, energy conversion efficiency for newly ignited granules plummets. This reduction is dramatically non-linear. Compared to granules that ignite before the bullet begins to move: typically, the combustion of granules igniting after the bullet has traveled one-fourth the distance to the muzzle contributes much, much less than one-half as much projectile energy per grain of propellant gas produced; granules escaping ignition until after the bullet moves halfway to the muzzle are unlikely to ignite and, even when ignition occurs, contribute essentially nothing.

As an example, consider a typical 308 Winchester load using VarGet and the 168-grain MK bullet. In that combination, once bullet movement begins, it takes only about 0.582 milliseconds for the bullet to move 5 inches (one-fourth total travel distance for that bullet in a 21.591-inch barrel, beginning with an overall cartridge length of 2.8-inches), see graph.

Thereafter, any newly unignited granule has only about 0.540 milliseconds to contribute to bullet energy (1.122 ms – 0.0582 ms = 0.540 ms), see graph.

Equally, the purpose of any accuracy-critical cartridge is to produce the most consistent possible ballistics. Everything in the following text is predicated upon understanding that ballistic uniformity is enhanced by early (consistent) granule ignition and, conversely, ballistic uniformity is degraded by late (typically inconsistent) granule ignition (and low loading density). Briefly, increasing the delay between the primer blast and individual granule ignition increases the resulting ballistic effect of minor variations in that delay — the ideal is achieved when all granules ignite before the bullet begins to move. Refer to my earlier articles, The 6mm Shortly and Bringing the Short Fat Case to 1000-Yard Competition (Precision Shooting Publications).

Correspondences and Distinctions between
Cartridges and Solid-Fuel Rocket Engines

Now, some facts, and a bit of conjecture about comparisons between solid-fuel rocket engines and cartridge cases. First, propellant granules differ dramatically. Typical rocket engines use no more than a few granules (called grains), which are typically designed to burn one at a time, with constant energy production, and thereby to maintain constant chamber pressure as produced gases jet through the exhaust orifice, with the only significant impediment being the nozzle throat; typical cartridges use many hundreds to many thousands of granules which, as demonstrated above, produce best performance when all have ignited before the bullet begins to move and which are designed to push against a relatively heavy exhaust (bore) impediment (the bullet) and where practical barrel length is limited.

These factors lead to dramatic differences in burn times and pressures — rocket engine burns typically last many seconds and generate pressures of several hundred to several thousand psi — small arms cartridge burns typically last less than 0.002 seconds and generate breech face pressures that can exceed 75,000 psi. However, I see a more important distinction.

In a rocket engine, trapped air pockets can be devastating. There, such pockets often result in secondary ignitions that multiply total combustion area and thereby catastrophically skyrocket chamber pressure — remember all those spectacularly explosive failures in the early US space program?

In the cartridge, trapped-air pockets are unavoidable but are also relatively tiny, except, perhaps, in a partially filled case. At issue is a factor related to latent heat of compression, which manifests as a compression-related temperature increase within interstitial voids — as volume shrinks, gas molecules move faster (temperature increases). Compression of pockets, large or small, to any given pressure generates the same pocket temperature. In rocket engines and cartridges alike, pocket temperature often exceeds the kindling point temperature. However, total heat depends upon pocket volume.

Critically, it takes both heat and temperature to achieve ignition in adjacent granule surfaces. As heat is transferred from the hot gas to the cool granule, the gas cools. If the pocket is too small, it simply will not contain enough energy to heat adjacent surfaces sufficiently to cause ignition, despite the extremely high temperatures that can occur within the compressed gas voids. By and I contend that such heating occurs so rapidly that although an exothermic reaction could be initiated in the surface layer, the underlying cool layers will quench the reaction before sufficient additional heating can occur to result in a sustained reaction — as was discussed above. (Precision Shooting’s resident Rocket Scientist, Randolph Constantine, also points out that much or all of the heat in such voids could be dissipated in the endothermic — heat absorbing — decomposition of the adsorbed anti-oxidants in the surface layers.)

Thus, in a normal cartridge load, the myriad, relatively tiny, gas pockets seem unlikely to cause secondary ignitions. However, it is quite certain that this effect will expedite subsequent granule ignition. When those pre-heated surfaces are finally exposed to the combusting propellant cloud, hotter areas will ignite faster, which is a critical factor. My point here: Owing to issues of scale, not all rocket-to-cartridge comparisons are equally applicable but the basic concepts do cross over.

A second point By stressed was that dramatic powder granule compression, which occurs when a cartridge fires, results in granule fluidization. Individual particles fuse and reconfigure. Within microseconds the myriad granules become a single mass of viscous fluid. As granule surfaces begin to fuse (at least temporarily), interstitial gas pockets become isolated and essentially spherical. For this reason, further ignition results only at exposed surfaces or where granule-to-granule shearing occurs. Inter-granule shearing can open up new paths for propellant gases — we will return to this point.

Owing to adsorbed surface chemicals (which affect both physical and chemical granule characteristics) and size and separation of gas pockets, subsequent burning rate still reflects initial granule characteristics. Critically, individual granules retain the progressive burning gradients imposed by the deterrents. Further, these granules are not necessarily inseparable.

Pressure of a few thousand psi (far below peak chamber pressure) dramatically deforms unignited granules, which are generally located in continuous masses. (My testing demonstrated that a relatively mild pressure of 3000-psi compresses typical tubular and ball powders about 10%, which implies significant deformation.) For this reason, those granules escaping initial (primer blast) ignition show little difference in performance, whether stick- or ball-type.

Regardless of any such details, my pertinent points from the original articles stand (to which, please refer), ideal case designs: 1) minimize interior surface area, and 2) maximize granule-mixing rate at the shoulder-to-neck transition. By, who believes it is of significant importance, reiterated a third point 3) minimizing distance between the primer flash and the remotest granules. By also points out that we have to add a new dimension to this theorem 4) maximizing primer-blast related heating of those granules in the bore-diameter column, directly behind the bullet — which contains powder that can follow the bullet into the bore as an unignited plug. (Again, refer to the aforementioned articles for background.) See sketches 1a and 1b.

In the following text, we assume that chambering characteristics provide for the base of the bullet shank to precisely align with the neck-to-shoulder  junction of the case.

  • Minimizing Interior Case Surface Area

This aspect is critical because it minimizes conversion of primer blast heat into case heat, and for several other reasons. If this were the only consideration, the answer would be quite simple — design a spherical combustion chamber. This is certainly feasible but it will require a new case, drawn with new tooling. Meanwhile, because that basic shape cannot be achieved with a conventional cartridge, we will consider conventional (cylindrical) designs. Here, in the ideal design, powder column diameter equals length.

However, unless someone wants to dramatically shorten a 50 BMG or neck a similarly shortened 416 Rigby to 17-caliber (have fun!), we are in no danger of designing a full-power case that is shorter than it is wide. Therefore, we can say that we should use the fattest case feasible.

(It is noteworthy that progressively fatter cases require progressively fatter actions and that such designs impose increasing levels of axial stress and primer-blast-derived shock — and vibration — into the barrel, characteristics that are probably detrimental but which we will not address further here.)

  • Maximizing Granule Mixing Rate at the Shoulder-to-Neck Junction

Consider granules trapped behind the case shoulder and not directly ignited by the primer. Chamber pressure rapidly compresses this mass and thereby eliminates permeability.

Thereafter, hot propellant gases cannot penetrate and, therefore, granule ignition occurs only at exposed surfaces. Separation of surface granules exposes new material, which can then ignite. Shearing forces and convection enhance this process.

As the bullet accelerates, the unignited mass is sheared where a bore-diameter plug begins to follow the bullet into the bore. See Sketches 1a and 1c. By contends that this shearing action is sufficient to allow ignition to progress along the sheared zone, at least where both surfaces are composed of exposed powder. However, it has been demonstrated that ignition does not occur along the perimeter of this plug where it is moving through the case mouth or the bore (evidently those relatively cold surfaces prevent sufficient powder heating). Therefore, we can predict that most of the time there will be some portion of this plug that is not ignited along the perimeter and will, therefore, burn only from the base forward.

Convection force on the viscous fluid mass that is trapped behind the shoulder is significant only at the shoulder-to-neck  junction. There, the mass is exposed to the propellant cloud jet that is rushing through the neck as the bullet accelerates. Resulting strain depends upon pressure loss in the wake of the accelerating bullet.

With regard to minimizing granule transport time from the case perimeter (where the remotest unignited granules are located) to the neck opening (where ignition will occur), geometric arguments suggest that an ideal conventional shoulder angle exists — all other things being equal, I believe this angle should be 45-degrees. With a milder shoulder (e.g., 30-degrees), granules proceed faster but must travel so much further that travel time is increased; with a steeper shoulder (e.g., 60-degrees), granules have a shorter path but must proceed so much slower that travel time is increased.

Endpoint analysis supports these conclusions — as the shoulder angle approaches zero-degrees, granule travel distance to the shoulder-to-neck  junction increases without bound; equally, as shoulder angle approaches 90-degrees, granule flow rate approaches zero. Evidently, the magic angle is 45 degrees, where flow rate and travel distance yield the fastest straight-line path.

On the other hand, a steeper shoulder increases divergence of clump velocity and propellant jet velocity at the shoulder-to-neck transition; this increases convection and thereby speeds granule separation and subsequent ignition. Shallower shoulders produce progressively less convection, as granule clump velocity approaches propellant jet velocity.

Also noteworthy is that at relatively shallow shoulder angles, shoulder-to-neck  junction convection essentially disappears.  At some point, the entire fluid mass simply swages to bore diameter, following the bullet as an elongated lump. Logically, the rearward portion of this lump would be ignited along the axis but a significant portion toward the front could well enter the bore unignited.

I believe sound geometric arguments will suggest that optimization of both convection and feed rate occurs with a shoulder angle of 60-degrees, which just happens to be near the angle of repose for smokeless powder. This angle provides significant convection while still allowing flow to proceed with reasonable dispatch.

Which of these characteristics (perimeter-to-neck transport rate versus convection strength) dominates, very likely depends upon several factors, two of which seem particularly important: geometry of powder volume escaping initial ignition, and bullet acceleration rate. Nevertheless, regardless of specific details, from this single perspective, ideal shoulder angle is evidently comparatively steep, almost certainly >45-degrees.

  • Minimizing Distance between Effective Primer Blast Ignition Zone and the Remotest Propellant Granules

Here By and I agreed that we do not have sufficient information to settle a significant point of contention. Does the primer produce a jet that tends to ignite the powder column from the axis toward the perimeter, which By believes might be an important mode; or, does the blast tend to force the charge base forward while rapidly spreading to full case diameter, and thereafter ignite the powder column from the base forward, which I believe is the dominate mode. We agree that reality is probably somewhere in the middle.

Perhaps surprisingly, regardless of actual ignition mode, minimizing the distance between the primer blast and the remotest granule in a cylindrical column requires the same shape — column diameter is twice column length. See sketches 2a and 2b.

What seems a more realistic representation of reality follows: As the primer blast penetrates into the powder column, proceeding from the base toward the shoulder, the leading edge rapidly extends to full case diameter, while developing a roughly hemispherical face. Refer to photograph of unconfined primer flash and sketch 3.

Regardless of specific details of actual ignition — which seem almost certain to vary, depending upon powder type, charge density, primer type, total case volume, flash hole configuration, and several other factors — it seems evident that in this regard, a short, fat case provides a significant advantage.

  • Maximizing Initial Heating in Powder Column Directly Behind Bullet

To understand the importance of this point, we must first realize that any granules in the column directly behind the bullet that do not ignite before the bullet begins to move will thereafter simply follow the bullet into the bore as part of a single clump. Thereafter, ignition of the forward portion of this clump is likely to occur only at the base. This means a good percentage of these granules will escape ignition for a relatively long time (and until the bullet has proceeded far into the bore). Equally, we must recognize that anything resulting in increased granule preheating will reduce subsequent ignition delay.

The importance of this factor likely depends upon what percentage of the total charge is included in this zone. Here, the shorter, fatter case excels because, for an equal case volume and caliber, this column will be shorter and contain a smaller percentage of the total charge. Compare sketches 1a and 1c.

The pertinent point is that a primer-generated shock wave travels through the powder column, ahead of the flame propagation front. As noted above, this energetic wave compresses air in interstitial spaces while compressing and deforming granules. Details of this shock wave propagation are of little importance to this analysis. The critical point is what happens as that shock wave reaches the case shoulder, where some portion is reflected. With regard to early ignition of granules in the column behind and adjacent to the bullet base (which are those that can enter the barrel as an unignited mass), location and size of the zone where these reflected waves subsequently focus is critical.

Analysis of pressure wave propagation in cylindrical columns, which relates to a similar analysis By did when he designed a World Record setting 2-Cycle engine exhaust, is not trivial. I will gladly abstain from trying to present anything resembling a rigorous discussion; rather, I will simply report what By calculated.

First, at a shoulder angle near 60-degrees, reflected shock wave energy from the case shoulder is directed back, toward the primer. See sketch 4. Therefore, essentially zero reinforcement of primary shock wave induced heating occurs where it is needed. Equally, at a shoulder angle of about 30-degrees, reflected shock wave energy from the case shoulder is directed toward the central powder column, near the bullet base, where it focuses and generates significant reinforcement of primary shock wave heating, thereby bringing about faster subsequent ignition of this ballistic-consistency-critical mass. See sketch 5.

Shoulder designs with angles shallower than 30-degrees seem to be of little benefit in this regard. Moreover, such designs focus more energy on the bullet base and therefore increase the likelihood that the primer blast will dislodge the bullet, which is detrimental. Angles steeper than 30-degrees seem to be progressively less beneficial, owing chiefly to lack of proper focusing but also owing to an increase in the magnitude of axial shock delivered to the barrel through the chamber shoulder, which is also detrimental.

Shock Wave Velocity in a Powder Column

The primer blast generates a sonic shock wave. This wave moves through the powder column in a complicated manner — depending upon column diameter, column air density, powder granule solid density and elasticity and almost certainly the manner in which granules interact with each other, interstitial air and the case walls. (Shock wave velocity has been precisely measured in specific applications; however, that information is hard to obtain.)

We can, however, make certain reasonable assumptions and predict a velocity of about 1800 fps. This suggests that in the 308 Winchester, shock wave arrival at the case shoulder occurs about 0.069 milliseconds after production from the flash hole. The reflected shock wave focuses at the center of the powder column behind the bullet by about 0.072 milliseconds — long before generated propellant gas pressure is sufficient to begin to move the bullet.

As this primer-blast shock wave travels through the powder column, both air and powder granules are compressed. As this pressure wave passes, granules are fluidized and the entire affected volume can obtain a consistency similar to bread dough. Typically, as this wave passes, developing propellant gas pressure, which travels through the compressed column faster than the initial shock wave travels through the undisturbed column, immediately reinforces the pressure, thereby maintaining granule fluidization.

In response to compression and fluidization, granules obtain a new shape and a greater packing density. Thereafter, very rapidly, those granules can ignite and propellant pressure will become sufficient to move the bullet. As noted, whether a granule ignites before or after the bullet begins to move is the critical point.

A Better Idea, Maybe

I was quite pleased when we applied the above noted considerations to the 6mm Thermos Bottle, with its essentially maximized body-to-shoulder radius. This design interacts in each of the above four areas as follows:

  1. It is trivial to prove that for a conventional cylindrical case body and for any given volume and diameter, this shoulder design provides minimum possible interior case area.
  2. It is reasonably simple to demonstrate that, so long as neck diameter is not significantly larger than or smaller than one-half of case body diameter, this design approximately maximizes both granule flow rate and convection at the shoulder-to-neck junction.
  3. If initial primer blast penetration into the powder column is similar to what I have hypothesized (see sketch 3), this design also minimizes distance between effective flash front and remotest powder granules.
  4. This design does a splendid job of focusing primer shock wave energy where that is needed (see sketch 6), as explained in the following discussion.

A final consideration in favor of the Thermos Bottle shoulder design relates to the shock impingement of the primer blast upon the case shoulder. Here, as opposed to what happens with a conventional shoulder, a shock wave striking near the perimeter is deflected very slightly and then reflects again and again until it reaches either the powder column directly behind the bullet or the boattail bullet base (where it strikes at a high angle so that it is reflected back into what will become the trapped powder mass behind the case shoulder, which is also beneficial).

Similarly, looking at the next shoulder increment (the radial zone just closer to the neck), that parcel is initially reflected at a slightly greater angle and therefore ends up, on average, focusing into the powder slightly behind the zone where the first parcel impinged; significantly, this parcel will contain somewhat less energy, compared to the previous parcel. This process continues so that this energy is well distributed into the column of powder behind the bullet — just where it is needed and with surprisingly good distribution. See Sketch 6. Importantly, while this is happening, shock energy transfer into the barrel is spread out in time, which is also beneficial because it should result in milder vibrational excitation.

Additional Thoughts from By

Extremely special case body and shoulder designs could have merit. Among the myriad possibilities are: parabolic configurations (with no distinction between body and shoulder) and elliptical and hemispherical shoulder designs. While interesting, parabolic and elliptical designs could tend to focus the reflected primer blast too tightly, so the hemispheric (or possibly a parabolic) design seems most interesting to me (see sketch 6).

Powder column width-to-diameter ratio is an important consideration when using a conventional shoulder. By believes the proper mix of the above-discussed characteristics leads to a design where interior diameter is about twice bullet diameter and shoulder angle is near 30 degrees for small capacity applications (shorter cases) and near 40 degrees for large capacity applications (longer cases) — he agrees that the hemispherical design may well be a superior choice. We are both impressed that, through trial and error, Ackley seems to have gotten the shoulder angle quite right for hunting cartridges and the target fraternity seems also to have managed quite well — such subsequent proof of empirical results is not unusual. Formerly, it was difficult to find cartridge cases with sufficient body diameter to meet By’s proposed twice bullet diameter criteria. At least for the smaller sporting calibers, this is no longer true. Therefore, new short fat designs should become more and more popular for this and other reasons.

Two other points By felt very strongly about are: 1) bullet mass will influence ideal shoulder angle — a least with a conventional shoulder design — and 2) bullet base configuration might also influence ideal shoulder angle. I might add that effective bullet mass, as influenced by bullet specific characteristics (core and jacket materials, etc.), neck tension, crimp, friction proofing and bullet-to-rifling jump, which will all influence how fast the bullet initially accelerates, is also an important consideration

Preliminary Conclusions

If the above analysis has merit, it seems evident that there is no such thing as a universally ideal conventional shoulder angle. As noted previously, each powder column length-to-width ratio, each effective bullet mass and each case volume favors a unique angle; this angle depends upon which of the above discussed effects dominates in that particular system. On the other hand, if the Thermos Bottle design works in the manner this analysis suggests, then that basic design might work extremely well across a wide range.

Before closing, I must note that I have been told that, early on in PPC experimentation, a design with a large body-to-shoulder radius was tested; that particular combination proved to generate excessive case stretching, owing (I presume) to lack of adequate headspace control. If that is a general characteristic of such a design, I can only hope that cases with a wider shoulder will mitigate the effect sufficiently to be useful. Time will tell that tale.