An equation is derived for the streamwise velocity of the tip vortex of a horizontal-axis wind turbine as the pitch of the vortex tends to zero. The equation is applicable at high tip speed ratios provided the vortex core remains of constant size and there is no flow along the vortex axis. Under these conditions, the vortex velocity is the average of the velocity in the wake and the external wind speed. This result appears to conflict with the computational need to have the vortex velocity approach the wind speed in the high thrust region. It is suggested that the conflict could be resolved by considering the axial flow within the tip vortex.