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 & 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 juncture. 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 shoulder angle approaches zero-degrees, granule travel distance to the shoulder-to-neck juncture 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 juncture 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 that geometric arguments 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….