I was playing around with the math for getting a pressure-fed rocket to orbit and came across something that I haven't seen addressed anywhere.
In a pressure-fed rocket, the chamber pressure of the engine is related to the pressure of the propellant tanks. It is equal to the pressure in the propellant tanks minus the pressure drops in the feed system and across the injector.
The ISP of a rocket engine increases with chamber pressure. A higher ISP means more delta-V with a given mass fraction. However, getting a higher chamber pressure requires more tank pressure, which requires stronger tanks, which requires more wall thickness, which will increase tank mass. As far as I understand, this is a ROUGHLY linear relationship (e.g. double the tank pressure, double the wall thickness, double the mass).
The weird part is that (after playing around in RPA) ISP doesn't seem to decrease linearly with chamber pressure. That means that decreasing tank pressure (and thus chamber pressure) decreases ISP but actually INCREASES delta-V because the mass fraction improves at a faster rate than ISP falls off.
My first question: Is it correct that ISP does not fall off linearly with chamber pressure?
My second question: Are there other inherent factors that stop delta-V from increasing with decreasing ISP?
My third question: What factors (if any) prevent a rocket from taking advantage of this and running at extremely low chamber pressures (like 5bar)?
Follow-up question: I assume combustion instability is the limiting factor, correct? Can that be mitigated by using more, smaller nozzles?