on the BADA 3.10 User Manual [@Bada2012]. BADA is based on the total-energy model where the rate of work is equal to the rate of potential and kinetic energy. Here, the rate of climb is obtained by controlling the speed and the throttle. From [@Bada2012] p.14:eq.3.2-7 and by transforming the quantities into functions of altitude $h$, speed $V$ and mode $q$, the rate of climb is defined by: $$\label{eq:roc}
  \dot h(V,q) =  \frac{T(h) - \Delta T}{T(h)} \left[ \frac{(Thr(h) - D(V,h)) \cdot V}{m \cdot g} \right] \cdot f(V,h,q)$$ where the function $T(h)$ is defined in BADA 3.10 User Manual [@Bada2012] p. 10, $Thr(h)$ at p.22, $D(V,h)$ at p.20 and $f(V,h,q)$ at p.15-16. As a first approximation, the mass $m$, the gravitational acceleration $g$ and the temperature differential $\Delta T$ are constant during the climb phase. According to [@Hull2007], this is a reasonable assumption since the climb phase lasts around 20 minutes. The terms $h$, $V$ and $q$ are variables that evolve with the system and one must specify the evolution of the two remaining independent variables. However, the acceleration in function of the aircraft dynamic is not specified in BADA. From [@Hull2007], it is given by: $$\label{eq:acceleration}
  \dot V(h, \dot h) 