ACE magnetic field and velocity data, taken in L1 halo orbit, are used to predict the arrival time at the Wind spacecraft of sharp southward turnings of the interplanetary magnetic field. If such events are assumed to be tangential discontinuities, their orientations can be deduced from the cross product of the field immediately upstream and downstream of them. It is shown that such an assumption results in better predictions of arrival times than using minimum variance or simply assuming a sunward normal. Of the 70% of events observed at ACE that could be identified at Wind, 93% of arrival times were predicted within 10 min using the cross product, compared to 56% using minimum variance and 67% assuming a sunward normal. The most important factor controlling the likelihood of observing events at Wind was the angle of the discontinuity normal from the flow direction, although weak dependencies on solar wind speed, flow-perpendicular separation, and normal-perpendicular separation were also found. These results suggest that the cross product is an accurate estimator of discontinuity orientations and that using L1 monitor data, it would be possible to predict arrival times of around 86% of southward turnings at Earth with an accuracy of 10 min. ¿ 2001 American Geophysical Union