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The feed system pressures in the ASI were chosen to be a "good bit" higher than the chamber pressure to mitigate backflow of gas in the main combustion chamber into the ASI lines. This is almost a non issue because the solenoids are almost guaranteed to close after the ASI burn time, but it's a good practice to have. Our oxidizer reg pressure is currently at 400 psi, and our fuel reg pressure is currently at 550 psi. Our main chamber pressure is 350 psi.
Once the igniter solenoids close, there will be a trapped volume of ASI gas between the ASI chamber and the main chamber, which should "insulate" the ASI well enough. The main chamber pressure will push on this insulated pocket, which will push on the PT in the ASI and give a pressure reading.
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