A method of generating shaft power in a system comprising an air cycle and supercritical fluid cycle, comprising the steps of: a) burning a fossil fuel in air so as to produce a combustion gas (19, 120, 176, 216, 303); b) expanding said combustion gas in at least a first turbine (26, 304) so as to produce an expanded combustion gas, said expansion of said combustion gas generating shaft power; c) compressing a supercritical fluid in a first compressor; d) flowing at least a portion of said compressed supercritical fluid (48, 5, 322) through a first cross cycle heat exchanger (10', 100, 130, 306), and flowing said combustion gas through said first cross cycle heat exchanger so as to transfer heat from said combustion gas to said compressed supercritical fluid so as to produce a heated compressed supercritical fluid; e) expanding at least a portion of said heated compressed supercritical fluid in a second turbine so as to produce an expanded supercritical fluid (41, 102, 124, 170), said expansion of said supercritical fluid generating additional shaft power; f) further expanding at least a first portion of said expanded supercritical fluid (42, 108) in a third turbine (12") so as to produce a further expanded supercritical fluid (46, 112, 204, 318), said further expansion of said supercritical fluid generating additional shaft power, wherein said third turbine drives a first shaft; g) transmitting torque from said first shaft to a second shaft without contact between said first and second shafts via an eddy current coupling; h) flowing a portion of said compressed supercritical fluid to said eddy current coupling so as to cool said coupling and heat said portion of said compressed supercritical fluid; i) flowing said portion of said heated compressed supercritical fluid from said eddy current coupling to said first cross cycle heat exchanger; and j) flowing at least a portion of said expanded supercritical fluid through a second cross cycle heat exchanger, and flowing said air through said second cross cycle heat exchanger prior to burning said fossil fuel in said air so as to transfer heat from said expanded supercritical fluid to said air. a) burning a fossil fuel in air so as to produce a combustion gas (19, 120, 176, 216, 303); b) expanding said combustion gas in at least a first turbine (26, 304) so as to produce an expanded combustion gas, said expansion of said combustion gas generating shaft power; c) compressing a supercritical fluid in a first compressor; d) flowing at least a portion of said compressed supercritical fluid (48, 5, 322) through a first cross cycle heat exchanger (10', 100, 130, 306), and flowing said combustion gas through said first cross cycle heat exchanger so as to transfer heat from said combustion gas to said compressed supercritical fluid so as to produce a heated compressed supercritical fluid; e) expanding at least a portion of said heated compressed supercritical fluid in a second turbine so as to produce an expanded supercritical fluid (41, 102, 124, 170), said expansion of said supercritical fluid generating additional shaft power; f) further expanding at least a first portion of said expanded supercritical fluid (42, 108) in a third turbine (12") so as to produce a further expanded supercritical fluid (46, 112, 204, 318), said further expansion of said supercritical fluid generating additional shaft power, wherein said third turbine drives a first shaft; g) transmitting torque from said first shaft to a second shaft without contact between said first and second shafts via an eddy current coupling; h) flowing a portion of said compressed supercritical fluid to said eddy current coupling so as to cool said coupling and heat said portion of said compressed supercritical fluid; i) flowing said portion of said heated compressed supercritical fluid from said eddy current coupling to said first cross cycle heat exchanger; and j) flowing at least a portion of said expanded supercritical fluid through a second cross cycle heat exchanger, and flowing said air through said second cross cycle heat exchanger prior to burning said fossil fuel in said air so as to transfer heat from said expanded supercritical fluid to said air.