The critical engine of a multi-engine, fixed-wing aircraft is the one whose failure would result in the most adverse effects on the aircraft's handling and performance.
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When one of the engines on a typical multi-engine aircraft becomes inoperative, a thrust imbalance exists between the operative and inoperative sides of the aircraft. This thrust imbalance causes several negative effects in addition to the loss of one engine's thrust. For reasons listed below, the left engine of a conventional twin-engine propeller-driven aircraft is typically considered critical.
When one engine becomes inoperative, a torque will be developed which depends on the lateral distance from the center of gravity (C.G.) to the thrust vector of the operating engine multiplied by the thrust of the operating engine. The torque effect attempts to yaw the aircraft's nose towards the inoperative engine, a yaw tendency which must be counteracted by the pilot's use of the flight controls. Due to P-factor, the right-hand engine typically develops its resultant thrust vector at a greater lateral distance from the aircraft's C.G. than the left-hand engine. The failure of the left-hand engine will result in a larger yaw effect via the operating right-hand engine, rather than vice-versa. Since the operating right-hand engine produces a stronger yaw moment, the pilot will need to use larger control deflections in order to maintain aircraft control. Thus, the failure of the left-hand engine is less desirable than failure of the right-hand engine, and the left-hand engine is critical.
It is important to note, however, that this example depends upon both propellers turning clockwise as viewed from the rear. On aircraft with counterclockwise-turning engines (such as the de Havilland Dove), the right engine would be critical.
Most aircraft which have counter-rotating propellers do not have a critical engine defined by above mechanism, however some such the Lockheed P-38 Lightning had both engines critical because the propeller rotation was purposely reversed for better gunnery.
Aircraft with center-line thrust propeller configurations (e.g. the Cessna 337) may still have a critical engine, if failure of one engine (either the front or rear) has more of a negative effect on aircraft control or climb performance than failure of the other engine.
On certain aircraft, hydraulic, pneumatic or electrical systems may be powered by one engine. Since these are not aerodynamic effects, they do not cause an engine to be considered the "critical engine". However, it is important to understand the consequences of such system failures in the context of engine-failure scenarios.
Airplane Flying Handbook. U.S. Government Printing Office, Washington D.C.: U.S. Federal Aviation Administration. 2004. pp. 12–27 to 12–28. FAA-8083-3A. http://www.faa.gov/library/manuals/aircraft/airplane_handbook/.
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