Mine occurred on my first trip up the Chesapeake Bay, on a thick, hot, hazy day, with inexperienced "crew" aboard who were helping me with a delivery. The haze/smog was so thick visibility was only a bit better than in fog. This was pre-gps, with no loran aboard, so our fixes all day long had been d.r. from buoys and the rare glimpse of land through the haze.
Towards the end of the day's sail, as we neared the approaches to Annapolis, the bow of a large ship came vaguely through the haze, dead ahead. I made a course correction to avoid it, but the ship seemed to make a similar course correction, so I made a more deliberate and unmistakable 90 degree turn to port. Unfortunately, the ship seemed to follow suit, and its bows remained pointed right at us. I concluded the ship must be following a channel, so I decided to make a marked turn to starboard. Again, the ship seemed to follow suit. Was this guy deliberately trying to run us down?!
At that anxious moment, a wisp of wind thinned the haze a bit and gave us a better view of the "ship". Have you ever seen a Screwpile Lighthouse? Until that day, I hadn't either. Thomas Point Lighthouse was trying to run us down!!
At least I got a good fix on our position, which was more than a mile west of my d.r.