Is there magic in a case's shoulder angle relative to its neck length?
Dimensions of the 22 PPC & 6 mm PPC
By: C. Bekker
The 22 PPC cartridge was designed by Dr. Louis Palmasano and Ferris Pindell in 1974. The intention being to design an efficient benchrest cartridge. It was based on the 220 Russian case, which has a smaller head size than the 308 with a small rifle primer, a 30degree shoulder and necked down to .224 calibre. The fact that the 22 PPC cartridge is winning benchrest matches support the theory of efficient case design, which is depicted here: 
The 6mm PPC is an outgrowth of the 22 PPC and has the same case configuration with the neck expanded to take 6 mm (.243") bullets. Body taper is minimal to ensure a firm grip in the chamber. The neck is slightly longer, .301" instead of .270", but it has the same shoulder angle of 30 degrees. The 6 mm PPC was also developed by Dr. Louis Palmisano and Ferris Pindell and is enjoying an even greater success than the 22 PPC.
This leads to the question if there is not perhaps a magic ratio between the shoulder angle and the length of the case neck. Both cartridges have the same case length of 1.515" which is considered "short". It is a known fact that shorter and fatter cases yield more velocity for the same amount of powder in relation to longer cases, but the fact that they are consistently winning competitions, seems to suggest that an ideal position or 'sweetspot' has been hit. So, let us focus on case dimensions and compare a few popular cartridges by using trigonometric calculations, and see if we can establish a meaningful trend.
There is a venturi effect, if one reduces the diameter of a pipe or nozzle and likewise when one necks down a cartridge case. The powder granules will collide and converge at some point, which can still be inside the neck or just outside depending on the shoulder angle of the case. I want to focus at this point of convergence to see what percentage of the neck is ahead of this point which apparently produce a more even pressure from then on onto the bullet. A 30degree shoulder angle seems to create less turbulence than say a 40degree angle, as the deflection of powder granules/gases off the neck wall is less and the collision in the centre of the neck is at a lesser angle. Thus it consumes less energy trying to get down the barrel. But what is wrong with a 20degree angle that produces less turbulence? The only way I can rationalise this is, that the bullet swells at the base as it is pushed into the rifling of the barrel, and the 30 degree angle or thereabouts, seems to provide a more stable push from all sides to eliminate a yaw before entering, as opposed to a less sharp angle or no angle at all, where there is a greater change to gyrate as the tip of the bullet attempts to enter the rifling which also lies at an angle. I assume therefore that the pushing effect is more even, provided the convergence happens inside the length of the neck at some specific point. So, the ratio of the shoulder angle to the neck's length, will determine the point of convergence, which may be an important parameter in obtaining a sweetspot.
With trigonometric relationships, we can solve where the point of convergence is, given the angle of the shoulder of the case. I will use the 6 mm PPC as an example. The convergence point will be on the centre line of the case neck or bore, so we can divide the diameter by 2 to derive the radius or the one side of a right triangle (A) that is formed. Since the angle of attack is 30 degrees, the other angle must be 60 degrees as the sum of the inside angles of a triangle must be equal to 180 degrees. The inverse of Tan is equal to Cot and vice versa. You can either use Cot 30* or Tan 60* as they can be proven to be equal.
A = (.243/2) = 0.1215"
B = a (cot A) = (0.1215 x 1.732) = 0.2104"
(P/L) = (0.2104/0.301) x 100/1 = 69.9%
This means that convergence takes place at 69.9% or 30.1% below the mouth of the case, leaving sufficient length to stabilise the collision or venturieffect. Short necks also cause more throat erosion than those cartridges with longer necks. Let us do a comparison now to see if there is a positive trend or at least a degree of correlation.
Cartridge 
Neck
Diameter
in inches 
R = Radius
D/2
in inches 
Shoulder
Angle
Degrees 
L = length
Of Neck
in inches 
T = Tangent 
R x T
P = Point of
Convergence 
Percentage
P/L 
222 Remington 
0.224 
0.1120 
23 
0.313 
67 degrees = 2.3558 
.2638 
84.3% 
223 Remington 
0.224 
0.1120 
23 
0.203 
67 degrees = 2.3558 
.2638 
130.0% 
22 PPC 
0.224 
0.1120 
30 
0.270 
60 degrees = 1.7320 
.1940 
71.6% 
6 mm PPC 
0.243 
0.1215 
30 
0.301 
60 degrees = 1.7320 
.2104 
69.9% 
6.5 x 55 mm 
0.263 
0.1315 
25 
0.320 
65 degrees = 2.1445 
.2820 
88.1% 
6.5284 Norma 
0.263 
0.1315 
35 
0.270 
55 degrees = 1.4281 
.1878 
69.6% 
308 Winchester 
0.308 
0.1540 
20 
0.304 
70 degrees = 2.7474 
.4231 
139.2% 
3006 Spr 
0.308 
0.1540 
17* 16' 
0.383 
73.73 degrees = 3.2172 
.4954 
129.4% 
300 Win Mag 
0.308 
0.1540 
25 
0.264 
65 degrees = 2.1445 
.3303 
125.1% 
In some cases the theory seems to gel, but in other cases it does not provide an explanation, for example:
1. There is general consensus that a 223 Rem cannot compete with a 222 Rem. The above table suggests a marked difference, but accuracy differences are not that big in reality. (84.3% vs 130%)
2. The 22 PPC takes a close second to the 6 mm PPC. The above statistics are indeed very similar and one tends to think that the dimensions do in fact play a strong role. (71.6% vs 69.9%)
3. None of the bigger calibres can compare with the 6 mm PPC out to 300 yards, not even the 6.5.284 Norma and yet there convergence percentages are almost the same  69.9% vs 69.6%. Perhaps its sharper shoulder of 35 degrees versus 30 degrees and its longer powder column come into play?
4. I expected the 308 Win to follow the theory more closely as opposed to the 3006 Spr and 300 Win Mag. The 308 Win, with its shorter powder column and lower recoil, is generally superior over the other two longer and more powerful cartridges, contrary to what the above table suggests  a serious dichotomy! In fact, the 308 Win seems to be the worst of the bunch in terms of the theory  139.2% which is 39.2% beyond the neck of the case and into the throat.
Here are some aspects that may vary from one rifle setup to another:
· Capacity and shape of the case, relative to the chamber and throat dimensions, which will result in a specific operating pressure  different for each cartridge and its bullet/load combinations.
· The relative burning rate of the powder which also differ for each cartridge.
· The amount of powder used and the percentage 'case fill'  being interactive with the above.
· The diameter, weight, and the bearing length of the bullet yielding different resistance.
· Length and interior dimensions of the barrel which refers to precision tolerances, twist rate and its consistency, number and depth of grooves, smoothness of barrel, a square crown and consistent barrel harmonics (i.e. stressrelieved or not).
· Uniformity of primer ignition and intensity relative to the loading density of the powder. If a primer is too hot for a given powder load, it will ignite the powder too fast, which will cause the pressure curve's front end to be steeper. Steep enough to slam the bullet into the rifling too hard. Probably hard enough to significantly upset (deform) the bullet's back end that it won't shoot so accurate.
So, it is not quite so simple to explain, as cartridges do have different lengths, different capacities and they all yield different pressure levels, which contributes to the efficiency of the burning, whereas the shoulder angle has to do with convergence and the neck length to absorb the collision of hundreds of particles. Furthermore, the above need to be brought in line with different throat dimensions that will affect the chamber pressure as well, as it too forms part of the overall combustion volume. Each cartridge uses its own propellant to work optimally and there is no magic formula for that. As burning rates differ, we know that some propellants work better than others in a given cartridge, and in some cases Somchem do not have the equivalent propellant of overseas manufacturers. In Rifle Accuracy Facts by Harold Vaughn, he stated the effects of bullet "cant" and verified that 'how the bullet enters the rifling' has a very dramatic and predictable effect on accuracy. He also discusses throat diameter and alignment with the bore and states that nearly every factory chamber he has studied was deficient in this regard.
So, many factors seem to be at work and it seems the jury is still out on explaining exactly the accuracy phenomenon of the 6 mm PPC, rather than solely case design and dimensions. We need a universal truth across a range of cartridges, before we can say the theory works.
3006 Spr, 3006 Imp & 7.82 (.308) Lazzeroni
Lazzeroni is confident though, that a shorter and wider case is the way in the right direction, as bolt flex is less in shorter actions in more powerful cartridges. Lazzeroni's cases are even fatter than the WSM's with the result that it is not easily adapted to a lot of bolt actions. The real test would be to mimic the dimensions of the 6 mm PPC in other cartridges and see if accuracy improvements will follow. For example, to redesign the 308 Winchester with a 30 degree shoulder and a 69.9 % convergence point in the case's neck, but never can the powder column be as short. Even if it cannot be mimicked, we do know that the 6 mm PPC design has hit a sweetspot. Perhaps the main reason is purely that it has a shorter and wider powder column in relation to its height, so that more powder is instantly ignited by the primer flame for a given depth, which presumably creates a more uniform burning of powder for a smoother pressure curve, which yields a smaller shot to shot variation.
Chris Bekker (abc@telgonline.co.za)
0827720690
