We study the origin of the bi-stability jump of the terminal velocity of the winds of supergiants near spectral type B1. Here, the ratio v_infty/v_esc drops steeply from about 2.6 at types earlier than B1 to a value of v_infty/v_esc=1.3 at types later than B2. To this purpose, we have calculated wind models and mass-loss rates for early-type supergiants in a T_eff grid covering the range between T_eff = 12500 and 40000 K. These models show the existence of a bi-stability jump in mass loss around T_eff = 25000 K for normal supergiants, with dot{M} increasing by about a factor five from T_eff ~ 27500 to 22500 K for constant luminosity. The wind efficiency number eta= dot{M} v_infty/(L_*/c) also increases drastically by a factor of 2-3 near that temperature.

To understand the origin of the bi-stability jump, we have investigated the line acceleration for models around the jump in detail. We argue that the mass-loss rate of radiation driven winds is determined by the radiation pressure in the subsonic part of the wind, just above the photosphere. Our models demonstrate that dot{M} increases at the bi-stability jump due to an increase in the line acceleration of Fe III below the sonic point. This shows that the mass-loss rate of B-type supergiants is very sensitive to the abundance and the ionization balance of iron.

Furthermore, we show that the elements C, N and O are important line drivers in the supersonic part of the wind. The subsonic part of the wind is dominated by the line acceleration due to Fe. Therefore, CNO-processing is expected not to have a large impact on dot{M}, but it might have impact on the terminal velocities.

Finally, we discuss the possible role of the bi-stability jump on the mass loss during variations of Luminous Blue Variable stars.