The airplane crashed immediately after liftoff during a three-engine takeoff. The flightcrew had shortened their rest break; rest periods were not required for ferry flights. The flightcrew was fatigued from lack of rest, sleep, and disruption of circadian rhythms. The flightcrew did not have adequate, realistic training in three-engine takeoff techniques or procedures. They did not adequately understand three-engine takeoff procedures, including the significance of VMCG. The flight engineer improperly determined the VMCG speed, resulting in a value 9 knots too low. During the first takeoff attempt, the captain applied power to the asymmetrical engine too soon, was unable to maintain directional control, and rejected the takeoff. The captain agreed to modify the procedure by allowing the flight engineer to advance the throttle, a deviation from the prescribed procedure. FAA oversight of the operator was inadequate because the Principal Operations Inspector (POI) and geographic inspectors were unable to effectively monitor domestic crew training and international operations. Existing FAR Part 121 flight time limits and rest requirements that pertained to the flights the flightcrew flew prior to the ferry flights did not apply to the ferry flights flown under FAR Part 91. Current one-engine inoperative takeoff procedures do not provide adequate rudder availability for correcting directional deviations during the takeoff roll compatible with the achievement of maximum asymmetric thrust at an appropriate speed greater than ground minimum control speed.