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Making a 4:1 blower or something even better would take a serious shift in culture at Allison toward a far more entrepreneurial attitude, probably driven by a new Chief Engineer or CEO
Part of that attitude was the fact that in the Spring of 1939 when the Army placed the big order for P-40s the Army owed Allison 900,000 dollars for work already done at the armies request. GM had already given 500,000 dollars to Allison for the V-12 engine project.
Army also wanted the pusher engines for the YP-37
For the Derwent turbojet Sir Frank Whittle made a blower with a 4:1 pressure ratio at 78% efficiency, or 73% after Sir Stanley deleted the inlet guide vanes due to their structural weakness. The chance of Allison finding and hiring a Whittle was practically zero, but the Germans at DB managed 4:1 at about 70% before the end of the war, so if Allison pulled out all the stops in 1940, hired some serious talent, and built a blower research lab with a good test rig, maybe they could've had a V-1710 with a single-stage, two-speed 4:1 supercharger in production for the Mustang in 1943.
Assuming a 1" drop through the carburetor, 4:1 gets us 44.5" manifold pressure at 23,000 feet, so maybe about 1100 hp. ADI would boost that a bit, and it would raise allowable WEP boost lower down, which charge temperature would severely limit otherwise. In contrast, the V-1650-7 made 1390 hp at 21,000 ft from 60.5" manifold pressure. At that height our what-if V-1710 would blow 48.8" and make about 1200 hp. A bit weak but at least good enough for a stop-gap escort fighter while Packard sorted out their production problems, plus a bit lighter and with less cooling drag than the P-51B.
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Both P&WA and Curtiss-Wright had a revenue stream outside of government contracts and financial reasons to develop technology outside of government requests; Allison had neither.
Before things slip off topic - we're probably looking at altitude power comparable to the Merlin 46/47 or the fully rated DB 605A? The impeller is the key, diameter of 11 in, give or take, although 12 in is even more convincing.
Such a what-if V-1710 will obviously need more than one speed for it's supercharger, so it's either a 2-speed gearbox, or the hydraulic drive (as known from historical 2-stage V-1710s for the auxiliary S/C stage, or on the DB engines). The water/alcohol injection, as it was historically so for 2-stage engines. So all in all, it should've provided power at all altitudes similar to the DB 605A/AM?
I'm not sure if 1100 hp at 22,000 ft for the Merlin 46 was with or without ram effect, but probably with as the maximum speed for the Spitfire V with a fuel injected 46 occurred at 22,500 ft. In that case a V-1710 with 4:1 blower would critical a few thousand feet higher than the 46. The Allison had the advantage of 7-8% higher power at the same boost. For the same reason, with a similar blower the DB 605 would make 1100 hp at higher altitude than the V-1710.
It would take a much beefier hydraulic drive than the one on the auxiliary stage, with the usual costs/benefits of that type of drive; heating the oil being one of the costs. A two-speed would cause less trouble but have the usual drop in performance around gear-shift altitude.
Space constraints may have forced them to curve the diffuser around, with the vanes bending around the curve too, i.e. turn the exit flow from centrifugal to axial. The NACA tested such designs after the war for gas turbines, and they worked.
It may be possible to raise the pressure ratio of the original 9.5 inch blower and make it variable at the same time, without changing the accessory case at all. Extend the shaft and attach two axial stages, with a swirl throttle to provide the initial swirl for the first stage, and variable stator vanes using the same mechanism. Even the last set of stators should be variable, because the swirl allows reduction of the centrifugal blower's pressure ratio. The diameter of the axial stages must be larger than the centrifugal inlet to get a high enough tip speed, which means necking down the flow after the axial blower. That may cause flow separation. Extending the shaft may cause bearing problems, and the 8.8 gears must be able to take the extra load. Of course the chances of anyone circa 1940 not only dreaming up such a device but also getting it built were practically zero. It's fun to imagine though.
Part of that attitude was the fact that in the Spring of 1939 when the Army placed the big order for P-40s the Army owed Allison 900,000 dollars for work already done at the armies request. GM had already given 500,000 dollars to Allison for the V-12 engine project. The engine 'shop' was attached to a rather profitable bearing manufacturing plant that could supply any more money (or was paying the profits to GM).
The Army never paid up. Allison had to forget about the debt in order to get permission to export the V-12 engine to France and Great Britain in 1939.
Army also wanted the pusher engines for the YP-37, the remote gear box engines for the P-39 and the turbo engines for the P-38s. At one point Allison did ask the army which projects they wanted Allison to work on as the y didn't have the staff to work on all of the armies ideas.
It is hard to be entrepreneurial for very long when the customer won't pay his bills. A bankrupt company doesn't build much of anything.
Army contracting during the was such that they only paid for a completed successful test (and timely payment even then was a rarity). In other words if an engine (or part) failed part way through a test session the contractor (Allison or Continental) had to tear down the engine, make new part/s, rebuild the engine and restart or resume the test all at their own cost. Army was not going to pay any additional money for repairs or delays.
The Allison had the advantage of 7-8% higher power at the same boost.
Really?
Actually boost is one part of the equation. The rated altitude of that boost is also important.
My point is that more power at the same boost makes it easier to get any given power output at a particular high altitude level, because a lower pressure ratio is required. The blower is easier to design and may be less complex. So if I was given the task of making 1000 hp at 30,000 ft, and could choose a Merlin or a V-1710, the latter is an obvious choice. It's a bit lighter too.
I would like to know which particular variants of each engine you are comparing, and at what altitude? And in which installation?