the maximum deflection of the flexible shaft in a straight housing fig9 shows the complex deflected shape of the flexible shaft in a bent housing versus percent of length of the drive shaft end line c shows deflection of the shaft in a first plane i e the plane of the bend in the housing line d shows deflection of the shaft in the plane normal to the first plane and line e shows deflection of the shaft in the plane bisecting the angle between the first and second planes a drilling motor of the present invention having an outer diameter of 9 5 8 inches was designed and built based on consideration of the above discussed constraints and design variables the motor includes a 79 25 inches long 9 5 8 inches diameter 1 u00b0 bent housing wherein the center of the bend i e the point of the intersection of the two principal longitudinal axes of the housing is disposed 57 54 inches from the downhole end of the housing a 135 inch long 2 5 inch diameter 4140 alloy steel shaft was used as the flexible shaft a 2 1 4 inch p3 male polygon was machined on each end of the flexible shaft and mating connections were provided on the rotor tail shaft and drive shaft cap starting from the downhole end of the rotor a 3 554 inch.