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What about mounting a smaller engine behind the seats that moves a supercharger, then this compressed air is ducted to the front engine?

It increases power, reduces turbo/supercharger lag and improved weight distribution because of the rear engine weight.

The supercharger engine throttle cable would need to be connected to the gas pedal so both engines rev up when pedal is depressed.

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"There are times when a broken tool is better than a sound one, or a twisted personality more useful than a whole one.
For instance, a whole beer bottle isn't half the weapon that half a beer bottle is ..." Randall Garrett

Similar concept, check out the "Manic Beattie" hillclimb car. There's several videos on YouTube.
Sounds like God's Own Vacuum Cleaner...

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JD, father of Quinn, Son of a... Build Log
Quinn the Slotus:Ford 302 Powered, Mallock-Inspired, Tube Frame, Hillclimb Special
"Gonzo and friends: Last night must have been quite a night. Camelot moments, mechanical marvels, Rustoleum launches, flying squirrels, fru-fru tea cuppers, V8 envy, Ensure catch cans -- and it wasn't even a full moon." -- SeattleTom

You have no memory of the old jet fuel powered independent superchargers?
Wild things, fired up and run just long enough to finish the 1/4 mile.
I think they got banned after a few blew up, or maybe because they did not put a load on the engine so were not "Fair"?

So the concept has been done.

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