Take-off distance for airplanes

There are two principal ways in which the total take-off distance (taxying plus hovering plus the first part of the climb) can be reduced to a minimum. These are: 1) taxying and hovering until the maximum speed has been attained close to the ground and then changing to a steep rapid climb; 2) lifting the airplane from the ground as soon as possible and then climbing at a relatively large angle of attack. These cases, as well as all the other conceivable combinations, can be expressed with a single basic formula, which is derived from the energy equation for rectilinear flight.