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Hey tomo pauk,
re: "Depends who you're asking. On 2-stage V-1710s, relocating the carb from the entry of 1st stage to the entry of 2nd stage earned ~2500 ft worth of rated altitude for military power (1125 HP)."
I may be wrong but I think we are saying the same thing here, just using the carburetor in front of 2nd stage instead in front of the 1st stage on the Merlin 60 series or the only stage (on the Merlin XX anyway). The 2-stage Merlin cut-away that fliger747 linked above shows the carburetor position relative to the compressor stages. I do not know exactly how the 2-stage V-1710 is layer out, but I think the 1st and 2nd stage were separate assemblies? They may not have had a practical choice of where to put the carburetor if they wanted to get the same cooling effect from the fuel.
re: "Goes without saying that I'd love to see the tests or math predictions for S/C efficiency."
I did not download it when I ran across it back in the early 2000s, but there is a UK memorandum/wartime report/(or some other name thing) with Hooker's findings, including the mathematical descriptions. I am not a theoretical mathematician (I am a semi-retired mechanical/automotive/systems/manufacturing engineer & machinist/fabricator) but I got the general idea of it. If you are up for the math it is quite interesting. Otherwise, the Rolls Royce Heritage Trust published a small booklet on Hooker's work on the supercharger in combination with the Merlin XX which gives a good explanation of what was done and why, but without the more complicated mathematical descriptions of the problem. I am sorry but I do not remember the title.
re: "Have you calculated in the losses due the carb being present?"
No. But, assuming the carburetor design had the airflow volume capability necessary, there should not be a significant impact on efficiency except when transitioning through power settings (I think?). The rammed air 'column' (my name for it) should already have been constricted to the area of the throat of the carburetor or less, and the area of the throat would be enough that only the airflow control valve should cause any increased back pressure. Pretty much the same as for a throttle body on a car but modified for higher velocity/pressure air at the entry orifice. Makes sense?Maybe?
Any fuel injection system, even direct injection, needs a metering section for measuring the mass flow and adjusting such flow to effect throttling. Indeed the metering functions would perhaps have somewhat less "drag" than the restriction required to create low enough pressure in the venturi to such the fuel out in sufficient quantity for a big engine.
Perhaps a bit more informative illustration?
DB 601, looks to be a sidewinder type setup.
Depends who you're asking. On 2-stage V-1710s, relocating the carb from the entry of 1st stage to the entry of 2nd stage earned ~2500 ft worth of rated altitude for military power (1125 HP).
The illustration is for a a two stage Merlin.
I was trying to show that Hooker had improved the basic RR single stage supercharger. Which , BTW, was the best supercharger in production in 1939 before Hooker modified it. And the first modification/s that he did were to the inlet cover/elbow. He continued on to do a lot more with the two stage supercharger.
DB superchargers went through a lot of changes over the years, however "Hookerizing" (modifying the inlet) wasn't going to get then much because they already had a pretty good inlet.
there may have been a few other problems with the DB supercharger though.
https://www.flightglobal.com/FlightPDFArchive/1942/1942 - 0144.PDF
It would appear that as a first order approximation that the radial engine designers had some advantages given the greater frontal area they had available for designing efficient ducting. Certainly the Dual Sidewinder superchargers installed on late model Corsairs benefited from "space" available. The DB supercharger probably lost some of it's effectiveness from the external intake, at least as far as external form drag goes without regard to any intake loss.