diff --git a/docs/winch.md b/docs/winch.md index fcb98fd..06f70b8 100644 --- a/docs/winch.md +++ b/docs/winch.md @@ -1,15 +1,17 @@ ## Winch model First, we calculate the acceleration of the tether at the ground station. It can be calculated as -$$a_{t,o} = \frac{1}{I_w} \frac{r}{n} (\tau_g + \tau_d - \tau_f)$$ +$$a_{t,o} = \frac{1}{I_w} \frac{r}{n} (\tau_g + \tau_d - \tau_f)$$ where $I_w$ is the winch inertia as seen from the generator, $r$ the drum radius $n$ the gearbox ratio, $\tau_g$ the generator torque, $\tau_d$ the torque exerted by the drum on the generator and $\tau_f$ the friction torque. The torque exerted by the drum depends on the tether force $F$ as follows: + $$ \tau_d = \frac{r}{n}~F$$ The friction is modelled as the combination of a viscous friction component with the friction coefficient $c_f$ and the static friction $\tau_s$ + $$ \tau_f = c_f v_{t,o} + \tau_s~\mathrm{sign}(v_{t,o})$$ ### Torque controlled winch