It´s also a matter of the desired performance envelope.
A turbo-supercharger requires the exhoust gase of the engine to operate. A mechanically driven supercharger eats up engine power but does not use up the energy stored in the exhoust gases.
These could be utilized for some significant amount of extra power by jet stacks.
I rephrase what I wrote with regard to the Jumo-213 / RW-2800 discussion in the B-29 vs Luftwaffe thread, as it examplifies the problem:
Considering that You get basically comparable high speed performance by a lot simplier and subtsantially lighter powerplant design without turbocharger, the supercharger option is attractive for lightweight, high speed high altitude A/C such as single engined, single seat fighters.
The turbo-supercharger offers significantly better poweroutput at high altitudes and lower speeds, so it´s the more attractive solution for slower flying, high altitude planes, such as bombers and load carriers.
Jet exhoust stacks were introduced in the early 40´s, when the P-47/P-38 design was already advanced. For a considerable time, there was an uncertainity whether or not turbocharged engines offer the best high altitude performances compared to jet augmented superchargers or slave engine driven* versions wrt to weights and power.
According to Spitfire Performance, test on the Merlin shows about 20% thrust horsepower is gained by exhaust gas thrust.
If we compare the P-47M to the Ta-152H, one with turbo supercharger and the other with supercharger and both designed for high altitude combat, we can see some of the tradeoffs of the turbo supercharger in performance.
At SL, hp, airspeed
Ta-152H 2050hp, 370 mph
P-47 2600hp, 365 mph
It is apparent that the Ta-152H is a much cleaner airframe
10k
Ta-152H, 1890 hp, 397 mph
P-47M 2800 hp, 405 mph
20k
Ta-152H, 1690 hp, 436 mph
P-47M, 2800 hp, 437
30k
Ta-152H, 1340 hp, 463 mph
P-47 2800 hp, 467
33k
Ta-152H, 1300 hp, 458 mph
P-47 2800 hp, 475 mph
35k
Ta-152H, 1200 hp, 455 mph
P-47, 2600 hp, 475 mph
Now assuming the Jumo 213E engine has an advanced and efficient supercharger, it is apparent that the turbo-superchargers are significantly better capable of maintaining horsepower than superchargers by themselves. Now if we do some manipulations with the P-47 engine we should be able to somewhat compare the turbo with the non-turbo. Assuming an imaginary P-47 with a similar supercharger set up as the Ta-152H and a max SL hp of 2600, and assuming it has the same power profile as the Ta-152H, we find that the imaginary P-47 would generate approximately 1690 hp at 30k ft., or 1110 hp less than the turbo-supercharged version. I don't believe that exhaust thrust can make that up. I would have preferred a comparison to the F4U-5, a PW2800 powered supercharged high altitude fighter, but I did not have the necessary data.
Conversely, if we take the Ta-152H and add a turbo-supercharger that performed as the P-47M turbo-supercharger did, it would be generating 2050 hp at 30k ft, or 710 more hp than the supercharged version, about 50% more power. I don't think exhaust thrust can come near making up for this difference.
So, the question is whether this performance makes up for the added weight of the turbo-supercharger, about 940 lbs minus the added complexity of the supercharger. Apparently the engineers at Focke-Wulf felt that the performance did not warrant the increase in weight and complexity, and the engineers at Republic, with the knowledge of the exhaust thrust by the time the P-47M/N came along, felt that the turbo-supercharger still provided the best answer for their performance envelop.
This is a light overview of a complex topic of which I have little knowledge, but it might show some of the issues facing a designer.
The turbo-supercharged PW R-2800-57 was one of the most impressive piston engines of WWII with 2800 hp flat rated to 33k ft and with probably 2000 hp available at 40k. There were few engines that flew operationally, if any, able to match it.
