First a consideration of the ski ramp. There are two different ways:
For single engine aircraft, V/STOL or STOVL, the aircraft runs up the slope and leaves at the top at some 80 mph with a considerable contribution of engine thrust ( the Harrier turns down its fan and core exhausts 40 degrees). If during this procedure the engine fails the pilot leaves his office using his personal elevator.
For a multi engine aircraft the situation is different. Multi engine aircraft have such notions as decision speed and balanced runway length. These do not apply to ski ramp ships. When the ship retracts the wheel chocks there is no going back. So the assumption is that the critical engine fails at the moment the moment the wheel chocks are retracted and the aircraft will accelerate to the top of the ski ramp achieving about 60% of the speed it would have without engine failure, and fly off - dropping any external stores say two seconds after leaving the ramp - flying a curved trajectory at reduced lift to reduce induced drag - and accelerate to a safe flying speed and not drop into the sea. The case for engine failure is the governing case for determining the maximum allowable take off weight.