Shortround6
Major General
I think it was better than that, the two stage superchargers would also be blasting their air into a low pressure ambient, which also improves thrust. Higher pressure should lead to both higher mass flow and higher exhaust gas velicity. The thrust is given by F =dm/dt x v. Jet thrust is also of greater value at higher speeds where mach effects reduce airscrew efficiency
Yes, the thrust ( and power) goes up with the reduction in outside air pressure. But the charge weight is decreasing once the plane is above critical altitude. As in the examples I gave above, the Merlin XX engine dropped from a charge weight of 144lbs at 9lbs boost (or close to it) at 20,000ft and an jet speed of 1695fps to 129.1 lbs at 25,000ft at just over 6lbs boost but with a jet speed of 1840fps. the difference in jet HP was 113 to 107. or look at the difference between 15,000ft and 30,000ft a difference of just 2.5hp in jut HP even though the charge weight went from 140.5lb/min to 107.2lb/min. the jet exhaust speed went from 1395fpm to 1901. the same book does give the details for 35,000ft. The charge flow is down to 84.5lb/min and the exhaust jet speed is actually dropping a bit to 1890fps ( or instrument error?) but in any case the jet hp is down to 65. Power to the propeller is 568hp.
power to the propeller for 15,000ft, 20,000ft (48.24in boost), 20,000ft (50.67in boost), 25,000ft, and 30,000ft are, respectively--- 1048, 1073, 1126, 960, and 778hp.
Please note that the combined power at 25,000ft is 1067.2hp which is quite a bit shy of what a turbo-supercharged engine would have capable of delivering. A Turboed MK XX would have been capable of 1280hp if not more at 25,000ft to the propeller. Wither the extra 20% in power is worth the extra 400-500lbs and the extra bulk and drag of the installation is the question.
The two stage mechanical drive engines will not only get more Jet thrust from the higher charge weights but because they are operating at higher cylinder pressures and exhaust pressures, but then they also need bigger, heavier superchargers/intercoolers and ducts and drag that go with them. They are also using more fuel to drive the supercharger. The Merlin XX was using anywhere from a minimum of 132hp at 35,000ft to drive the supercharger to a maximum of 236hp at 20,000ft (and the 50.67boost) for it's single stage supercharger in high gear. A two stage Merlin would probably need in excess of 400hp to run it's supercharger set up.