Shortround6
Major General
Two stage superchargers need (demand?) intercoolers.but generally improved performance and a two-stage supercharger doesn't seem completely unfeasible.
We have two conflicting problems. The more boost you use, the hotter the intake charge is and the more likely the intake charge is to detonate in the cylinders.
The higher octane fuel you have the more boost you can use before detonation.
Germans used lower boost limits and so needed lower octane, then they jacked up the cylinder compression which needed more octane (knock resistance).
If you want 1.42 Ata at 25,000ft you have to compress the air at 3.8 times the air pressure. If you want to higher or use more boost you need to compress the air more and the intake aid is going to be even hotter.
At 20,000ft if you want 1.42 you only have to compress the air 3.09 times.
The two stage supercharger is feasible, but you need everything that goes with it. The size intercooler you need depends on what you are trying to do. It is on a curve and you get get modest results using an equal amount of air to the intake charge, You can get about 50% more cooling by doubling the amount of cooling air but things go down hill fast. You need over 3 times the amount of cooling air to get just under twice the cooling of the modest result. You have low performance fuel and you are trying to use more than modest boost you need a big intercooler.
Good superchargers are around 70% efficient. There is a certain amount of heat just from compression even if everything was perfect. In the 70% supercharger 30% of the power going to the supercharger does nothing to compress the intake charge/air and winds up as extra heat in the air of the intake charge.