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Yes, it's an engineering problem... design it based on requirements, implement it with a limited model and materials, test, and reiterate. I'm at phase 1 with the process.Okay, that makes sense. Is there a way to prevent such a sudden change in pressure, such as perhaps a thermoplastic restrictor in the nozzle that burns out over the same time period the motor comes up to pressure?
The burst disk (or plug) at the nozzle must hold until the critical pressure is exceeded. That's the pressure where the propellant has reached a self-sustaining combustion (the chuff-free zone). This pressure depends on the propellant formula. Next requirement is that the igniter pyrogen amount and its configuration need to provide the heat flux level and spreading to transition to full ignition. One can size the igniter to give the pressurization needed, but if the pyrogen doesn't provide sufficient heat production, the motor won't light. Also, if the heat production is good but it's constrained and directed toward the burst disk, the disk will pop too early. (This is likely what happened with Jim's second stage in October). The head-end "basket" should be smaller than the grain ID and directed evenly.
One brute-force approach is to design the disk/plug to hold statically beyond the motor's operating pressure! The hope is it will melt before the motor overpressurizes.
Another way to "wing it" is to make the igniter essentially it's own rocket motor which will provide choked flow at the nozzle before the main propellant gets to that point! It also has to provide heat flux which is spread out enough to ignite the main propellant. A burst disk is optional in this case. The risk is that the shock of this transient could damage the propellant.
For both of the oversized igniter approaches, things get scarier for long motors. It can cause a shock wave or acoustic resonance. This will increase the propellant burn rate along the shockwave, and also could damage the grains. Even with a correctly sized igniter at the head end, this can happen with weak/erosive propellant.
Summary: 1) Design the burst disk to hold between the critical pressure and the operating pressure, and hold long enough to allow for self-sustained combustion. 2) Size the igniter pyrogen to produce that pressure. 3) Choose a pyrogen with high heat flux per gram. 4) Physical design of the igniter "basket" must hold the pyrogen to complete combustion and allow unrestricted flow to a wide area of the grains near the head end. 5) Oversizing the igniter has risks, especially with long motors.