Disclosed herein are screw shaft turbine compressors having (i) a compressor section, (ii) a turbine section, (iii) a combustion section coupling to the compressor section and the turbine section, and (iv) a grooved shaft. The grooved shaft can include one or more grooves for providing fuel from the compressor section to the combustion section and for allowing exhaust to leave the combustion section and exit the turbine section. A method for generating different speed to torque ratios on the shaft and a system for generating torque on the shaft are further disclosed.