V speeds of an aircraft

The takeoff speed required varies with air density, aircraft gross weight, and aircraft configuration (flap and/or slat position, as applicable). Air density
is affected by factors such as field elevation and air temperature. This relationship between temperature, altitude, and air density can be expressed
as a density altitude, or the altitude in the International Standard Atmosphere
at which the air density would be equal to the actual air density.

Operations with transport category aircraft employ the concept of the takeoff
V-Speeds, V1, VR and V2. These speeds are determined not only by the above
factors affecting takeoff performance, but also by the length and slope of the runway and any peculiar conditions, such as obstacles off the end of the runway. Below V1, in case of critical failures, the takeoff should be aborted; above V1
the pilot continues the takeoff and returns for landing. After the co-pilot calls
V1, he/she will call Vr or "rotate," marking speed at which to rotate the aircraft. The VR for transport category aircraft is calculated such as to allow the aircraft to reach the regulatory screen height at V2 with one engine failed. Then, V2 (the safe takeoff speed) is called. This speed must be maintained after an engine failure to meet performance targets for rate of climb and angle of climb.

In a single-engine or light twin-engine aircraft, the pilot calculates the length of runway required to take off and clear any obstacles, to ensure sufficient runway to use for takeoff. A safety margin can be added to provide the option to stop on the runway in case of a rejected takeoff. In most such aircraft, any engine failure results in a rejected takeoff as a matter of course, since even overrunning the end of the runway is preferable to lifting off with insufficient power to maintain flight.

If an obstacle needs to be cleared, the pilot climbs at the speed for maximum climb angle (Vx), which results in the greatest altitude gain per unit of horizontal distance travelled. If no obstacle needs to be cleared, or after an obstacle is cleared, the pilot can accelerate to the best rate of climb speed (Vy), where the aircraft will gain the most altitude in the least amount of time. Generally speaking, Vx is a lower speed than Vy, and requires a higher pitch attitude to achieve.