compressing air is what heats it up. using an intercooler reduces that heat. whether you use a supercharger or a turbocharger, you're still compressing the air and heating it up.
superchargers require a belt attached to the crank, which will require some horsepower to run it. the numbers are really low these days with the advances in supercharger architecture, but you'll still be drawing 1-3% horsepower to run the thing.
turbochargers use exhaust gas to run the turbine, so you're not taxing the system to run it. some of the heat from the exhaust gas, depending on where the turbo is located in the system, will get transferred to the intake charge just because of the proximity of the turbo to the origination of the exhaust, but the major amount of heat is caused by compression. some systems, like on the 4th gen that had the turbo in the rear where the muffler normally goes, reduces the temperature just because of how far the exhaust gas has to travel to get to the turbo, then how far the compressed air has to travel to get to the intake manifold. an intercooler on a system like that will reduce the temperature considerably, therefore allowing for greater amounts of power.
i don't understand the thought process behind having both types of systems on one vehicle. is he trying to reduce the tax on the system required to run the supercharger by supplementing it with turbo boost? is he trying to overcome the inherent turbo lag with boost from the supercharger? or is he just trying to be different? lag from the turbo is not quite as significant as it once was, so jump starting the system with the supercharger really doesn't make sense.
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