Division Segmentation of the takeoff ground roll

When taking off, as an aircraft accelerates between the point of brake release (alternatively termed Start-of-Roll SOR) and the point of lift-off, speed changes dramatically over a distance of 1 500 to 2 500 m, from zero to between around 80 and 100 m/s.

The takeoff roll is thus divided into segments with variable lengths over each of which the aircraft speed changes by specific increment ΔV of no more than 10 m/s (about 20 kt). Although it actually varies during the takeoff roll, an assumption of constant acceleration is adequate for this purpose. In this case, for the takeoff phase, V₁ is initial speed, V₂ is the takeoff speed, n_TO is the number of takeoff segment and s_TO is the equivalent takeoff distance. For equivalent takeoff distance s_TO (see Appendix B), start speed V₁ and takeoff speed V₂ the number n_TO of segments for the ground roll is

and hence the change of velocity along a segment is

and the time Δt on each segment is (constant acceleration assumed)

The length s_TO,k of segment k (1 ≤ k ≤ n_TO) of the takeoff roll is then:

Similarly to the speed changes, the aircraft thrust changes over each segment by a constant increment ΔP, calculated as

where P_TO and P_init respectively designate the aircraft thrust at the point of lift-off and the aircraft thrust at the start of takeoff roll.

The use of this constant thrust increment (instead of using the quadratic form (equation (2.7.8)) aims at being consistent with the linear relationship between thrust and speed in the case of jet-engine aircraft (eq. B-1).