Balanced field takeoff
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 V, or critical engine-failure recognition speed (V), is the fastest speed at which the pilot must take the first actions to reject the takeoff (RTO). At speeds below V the aircraft  may be brought to a halt before the end of the runway. At V the pilot must continue the takeoff even if an emergency is recognized. To achieve a balanced field takeoff, V is selected so the remaining takeoff distance with one-engine-inoperative is equal to the remaining and 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: Calculation of the balanced field length traditionally involves relying on an expansion program model, where the various forces are evaluated as  a function of speed, and step-wise integrated, using an estimate for V. The process is iterated with different values for the engine failure speed until the accelerate-stop and accelerate-go distances are equal. This process suffers from the inherently slow and repetitive approach, which is also subject to round-off errors if the speed increment between the steps is not carefully selected, which could cause some issues in first principle aircraft performance models provided to airlines for day-to-day operations. Alternate approaches using a more mathematically complex but inherently more accurate and faster algebraic integration method have  however been developed. Regulatory background. 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 V. On longer runways a pilot can nominate a V within a range, but where the runway length is no longer than the balanced field length only one value for V will exist. Landing and Takeoff Performance Monitoring Systems Using the balanced field  takeoff concept, V 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.