The pneumatic turbine-powered drilling engine (PTDE) is a unique tool for directional drilling when using air or gas as the drilling fluid. The engine consists of a pneumatic turbine motor coupled to the bit by a four-stage planetary gear transmission and a thrust-bearing assembly, and is supported within a steel housing. The tool was built and bench tested in New Mexico, and field tested at the Geysers Geothermal Field in Santa Rosa (Calif.). In order to predict and analyze the field performance of the tool, two analytical models were derived and validated. A torque model was developed to predict the bit torque as a function of bit rpm at a given air-flow rate and a known air speed entering the turbine rotor. A pressure-loss model was used to calculate the air speed entering the rotor as a function of the bottomhole air pressure, the bottomhole temperature, the air-flow rate, the size of the bit jets, and the tool internal geometry. The two models were validated in a full-scale bench test of the two prototype tools. The validated models were then used to develop turbine air speed and WOB response charts. These charts are for field use in selecting the engine set-up. They are used to select bit jets, and to predict required weight on bit, bit rotary speed, bit torque and bit horsepower.