We measure the distribution function of rotational velocities \phi ( \mbox { $V _ { c } $ } ) of late-type galaxies from the HIPASS galaxy catalogue .
Previous measurements of the late-type velocity function are indirect , derived by converting the galaxy luminosity function using the relation between galaxy luminosity and rotation velocity ( the Tully-Fisher relation ) .
The advantage of HIPASS is that space densities and velocity widths are both derived from the same survey data .
We find good agreement with earlier inferred measurements of \phi ( \mbox { $V _ { c } $ } ) , but we are able to define the space density of objects with V _ { c } Â as low as 30 km s ^ { -1 } .
The measured velocity function is ‘ flat ’ ( power-law slope \alpha \approx - 1.0 ) below \mbox { $V _ { c } $ } \approx 100 \mbox { $ km s ^ { -1 } $ } .
We compare our results with predictions based on \Lambda CDM simulations and find good agreement for rotational velocities in excess of 100 km s ^ { -1 } , but at lower velocities current models over-predict the space density of objects .
At \mbox { $V _ { c } $ } = 30 \mbox { $ km s ^ { -1 } $ } this discrepancy is approximately a factor 20 .