Sensitivity of the jet head position and speed to kinetic power and wind ram pressure for Cygnus X-1. The jet kinetic power is divided by 10 from CygX1 (red) to CygX1_mP (blue). In the weak case, the jet is slower, but the position fits the theoretical evaluation for a longer time. The speed diagram shows no oscillations. The wind speed is increased by 50% for run CygX1_wind (green), which results in a higher starting speed, a shorter reacceleration phase, and a weaker bump in the second deceleration phase. The average speed in the turbulent phase is weaker. The speed and position plots differ faster from the theoretical 1D values in the strong wind case.