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Intake Temperature vs Waste Gate Boost Pressure

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Just to explain the scenario to my question: I have a turbo setup on an engine where boost is solely controlled by the waste gate spring, with no additional boost control.

I am trying to understand why max boost pressure increases in very cold temps and decreases in very hot temperatures when the boost is primarily controlled by air intake pressure. Not to say it's increasing or decreasing by dramatic amount; more like a 2-3 psig variance. But I would like to understand the basic physics of why that is happening, if possible.

The reason this confuses me is because it seems waste gate valve is effectively opening at a higher pressure threshold in cold weather, and opening at a lower pressure threshold in warmer weather. I'm guessing the exhaust pressure has a part to play here as to why/how this is happening but I'm not sure.

When it's cold you have more mass flow at a similar boost level and more exhaust energy/mass flow too.

As Michael said.

Also, because you're using the spring only, there's a small pressure gradient between the gate's initial opening and when it's fully open.

Thanks for responding. I'm probably over thinking it, or completely missing something, but let's consider that additional air mass flow from colder intake air is effectively used to compress the waste gate spring via intake system and increase exhaust energy. Wouldn't that additional air mass flowing through the intake and exhaust then provide more energy to compress the waste gate spring, fully opening the waste gate at an lower boost level rather than a higher boost level?

Assuming in the first instance the intake side pressure is exactly the same, the exhaust gas temperature will be almost the same (proportionally speaking) regardless of modest intake side changes, so you now have 5% more volume flow to get rid of, the feedback loop is higher EMP, more energy into turbo, slight increase in intake side pressure, more force on diaphragm, but, you still end up at a slight different equilibrium point in terms of gate position and engine mass flow. It's no different to throwing a higher flowing fuel pump into a system, the equilibrium point will shift slightly even though the FPR is a compensating device. The behaviour of these devices isn't quite as simple at the mathematical models we apply to them.

Thank you, this helped a lot to conceptualize it in a different way.