Figure 2 Net forces on Archaeopteryx throughout its modelled take-off run. The increasingly larger vectors (V to V''') depict the incremental velocity of Archaeopteryx. a, At standstill Archaeopteryx weighs W and the hindlimbs provide an equal and opposite force S to counteract it. b, At the beginning of the take-off run, Archaeopteryx's hindlimbs produce a forward propulsion P, and when it starts to flap its wings these produce a thrust T. Owing to the generation of residual lift L, the hindlimbs need to supply a smaller upward force S' to counter the smaller net weight W'. This is called the 'vertical force migration'. c, During the take-off run, thrust T' gradually overtakes the propulsion P' (W" and S" decrease as a result of the vertical force migration).
The migration of the forward force from propulsion to thrust is called the 'horizontal force migration'. d, An instant before lift off, the horizontal force migration is completed and propulsion P' has disappeared. The only net force acting on the bird is thrust T". The vertical force migration is also completed, and the residual lift now equals weight. e, At lift-off, residual lift transitions into useful lift L. L, now a vertical net force, exerts work on the bird, lifting it up; this force translates into an ascencional velocity Thrust T''' continues to exert work on the bird. 'Residual lift' refers to a lift force that does not act as a net force and that, as long as it is smaller than the bird's weight is unable to exert any vertical work on the bird. Since it is not a net force, residual lift is not depicted in a-d.