Context : Radiation-driven mass loss plays a key role in the life-cycles of massive stars .
However , basic predictions of such mass loss still suffer from significant quantitative uncertainties .

Aims : We develop new radiation-driven , steady-state wind models for massive stars with hot surfaces , suitable for quantitative predictions of global parameters like mass-loss and wind-momentum rates .

Methods : The simulations presented here are based on a self-consistent , iterative grid-solution to the spherically symmetric , steady-state equation of motion , using full NLTE radiative transfer solutions in the co-moving frame to derive the radiative acceleration .
We do not rely on any distribution functions or parametrization for computation of the line force responsible for the wind driving .
The models start deep in the subsonic and optically thick atmosphere and extend up to a large radius at which the terminal wind speed has been reached .

Results : In this first paper , we present models representing two prototypical O-stars in the Galaxy , one with a higher stellar mass M _ { \ast } / M _ { \odot } = 59 and luminosity \log _ { 10 } L _ { \ast } / L _ { \odot } = 5.87 ( spectroscopically an early O supergiant ) and one with a lower M _ { \ast } / M _ { \odot } = 27 and \log _ { 10 } L _ { \ast } / L _ { \odot } = 5.1 ( a late O dwarf ) .
For these simulations , basic predictions for global mass-loss rates , velocity laws , and wind momentum are given , and the influence from additional parameters like wind clumping and microturbulent speeds discussed .
A key result is that although our mass-loss rates agree rather well with alternative models using co-moving frame radiative transfer , they are significantly lower than those predicted by the mass-loss recipes normally included in models of massive-star evolution .

Conclusions : Our results support previous suggestions that Galactic O-star mass-loss rates may be overestimated in present-day stellar evolution models , and that new rates thus might be needed .
Indeed , future papers in this series will incorporate our new models into such simulations of stellar evolution , extending the very first simulations presented here toward larger grids covering a range of metallicities , B supergiants across the bistability jump , and possibly also Wolf-Rayet stars .