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A balanced field takeoff is a condition where the accelerate-stop distance required (ASDR) is equal to the takeoff distance required (TODR) for the aircraft weight, engine thrust, aircraft configuration and runway condition. For a given aircraft weight, engine thrust, aircraft configuration and runway condition the shortest runway length that complies with safety regulations is the balanced field length. 
The rejected takeoff initial actions speed V1, or critical engine-failure recognition speed (Vcef), is the fastest speed at which the pilot must take the first actions to reject the takeoff. At speeds below V1 the aircraft may be brought to a halt before the end of the runway. At V1 the pilot must continue the takeoff even if an emergency is recognized.
To achieve a balanced field takeoff, engine power is selected to provide enough acceleration so that at the lowest possible speed to continue the takeoff the remaining necessary takeoff distance with one engine not working is equal to the remaining & necessary accelerate-stop distance.
The balanced field length is the shortest field length at which a balanced field takeoff can be performed.
Factors affecting the balanced field length include:
Aviation regulations, especially FAR 25 and CS-25 (for large passenger aircraft) require the takeoff distance and the accelerate-stop distance to be less than or equal to the available runway length, both with and without an engine failure assumed. The speed below which takeoff must be aborted upon engine failure is called V1. On longer runways a pilot can nominate a V1 within a range, but where the runway length is no longer than the balanced field length only one value for V1 will exist.
Landing and Takeoff Performance Monitoring Systems    are devices aimed at providing to the pilot information on the validity of the performance computation, and averting runway overruns that occur in situations not adequately addressed by the takeoff V-speeds concept.
Using the balanced field takeoff concept, V1 is the maximum speed in the takeoff at which the pilot must take the first action (e.g. reduce thrust, apply brakes, deploy speed brakes) to stop the airplane within the accelerate-stop distance and the minimum speed at which the takeoff can be continued and achieve the required height above the takeoff surface within the takeoff distance.