Determination of V1
V1 is defined as the maximum speed in the takeoff at which the pilot must take the first action (e.g., apply brakes, reduce thrust, deploy speed brakes) to stop the aircraft within the accelerate-stop distance. V1 also means the minimum speed in the takeoff, following a failure of the critical engine at VEF, at which the pilot can continue the takeoff and achieve the required height above the takeoff surface within the takeoff distance.
In its simplest form, V1 is selected such that accelerate-stop distance is equal to accelerate go distance. For a given runway length, this results in the maximum allowable takeoff weight. For a given weight, this allows for the least runway length required for takeoff. This condition is commonly known as "Balanced Field Length". If runway length is not limiting, V1 can be adjusted to any speed between Vmcg, which is fixed for a given engine takeoff thrust value, and VR which is limited by additive factors over stall speed and Vmca and thus varies with takeoff weight.
The difference between V1 and Vef is the time allowance for the recognition of the failure, and the subsequent time for the pilot to react and initiate aborted takeoff procedure. V1 will not be below Vef and Vef will not be below Vmcg, the speed at which directional control can be maintained on the ground. This makes sense as directional control must be able to be maintained if a takeoff is able to be continued after V1.
V1 speed selection can be dependent on a wide variety of factors, but two principle ones are that V1 must be greater than or equal to Vmcg and less than or equal to VR speed. The reasons are simple. If V1 is below Vmcg, with an engine failure and a go decision, the aircraft would be uncontrollable directionally using aerodynamic controls alone. If V1 is above Vr, following an engine failure a pilot could elect to abort after the rotation has started.
During the recognition period, an aircraft will travel a set distance. Acceleration is affected by temperature, elevation, weight, humidity, runway slope and surface conditions. Therefore we cannot translate the distance before V1, only time can be determined.
Selecting a suitable V1 for a given set of conditions is a matter of comparing ASDR (Accelerate Stop Distance Required) with TODR (Takeoff Distance Required). The point where ASDR and TODR intersect is known as the BFL (Balanced Field Length). Using a V1 less than that for the BFL indicates that the TODR (failure) is the more limiting factor. At speeds greater than that of the BFL, the ASDR becomes the more limiting factor in the selection of V1. Next, the BFL is compared with the TODR (normal). Usually, the TODR (normal) will be of a shorter distance than the BFL which then becomes the more limiting factor. Usually the manufacturer will select a V1 that coincides with BFL as this becomes the shortest distance required. This process is repeated for a range of weights and temperatures and published in the aircraft flight manual.

Reduced Take Off Thrust Procedure
Reduced takeoff thrust method compares the takeoff performance for the actual brake release weight, with the maximum weight the aircraft is capable of lifting under given atmospheric conditions. The assumed temperature method trades excess performance with the assumption of higher temperatures, resulting in in a lower thrust setting for takeoff and the utilization of runway distance that would have otherwise been unused.
Chart weight (maximum weight capable of being lifted under prevailing atmospheric conditions) is noted by the crew. This weight provides an indication of the excess performance capabilities. Next, the maximum temperature at which the actual weight of the aircraft can be lifted os determined. V1, Vr and V2 for this temperature are noted as these are the speeds that will be used for takeoff. The N1 values used are those for the assumed temperature. A small buffer for safety is added in the form of reducing the assumed temperature, resulting in a slightly higher N1 thrust setting. There are operating limitations for the application of reduced thrust takeoff, such as the requirement for no tailwind, no standing water, and no windshear being present. There must be operative anti-skid and ground spoilers, and normal takeoff flap setting must be used.

Daniel Tear

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