Eric, nice picture (before it was adulterated! <img src="http://www.catsailor.com/forums/images/graemlins/grin.gif" alt="" />)

I've been out racing at times when fog would blow in ... if you generally know what direction you were heading, you can count up to a specific number (or use a timer) and start tacking at the conclusion of that time. Say, if you know your point is directly upwind, sail close hauled on each tack for 60 seconds. It's a little trickier downwind but if you maintain trim and know your angles (and the wind is relatively consistent), you can be quite accurate.