Making Land
Leaving Balmoral, we had just made sail when the southbound Manly ferry made its appearance. Mindful of the ferry's absolute right of way, I watched it chug past North Head and it suddenly struck me that it was impossible to judge whether or not we would pass safely astern based on the ferry's apparent progress against the shore in the background.

Our boat is said to be "making land" on another boat between it and the shore when the other craft appears to be moving backwards relative to the shore in the background. The shore appears to be coming out from behind the other boat's bows. In the case of parallel courses, making land on another boat means that we're sailing faster. But what about courses that aren't parallel?

Unless the velocities are identical or we're on a collision course, the sightlines from boat A to boat B will always cross, making all three possibilities for motion of shore relative to boat B dependent only on the location of the shore. In the case illustrated,

  • land 2 would be seen as consumed by B
  • land 3 would be seen as fixed relative to B
  • land 4 would be seen as produced by B, the "making land" case

Without delving into navigational challenges of interposed peninsulas, the last interesting case for land is on the other side of boat A, land 1 in the diagram, the sight lines being from B to A:

  • land 1 would be seen (from B) as being consumed by A

So making land on another boat only allows us to say that we're on the open side of the sight-line triangle. The other conditions are dangerously ambiguous as they might apply to boats which are running parallel to each other at the same speed or on a collision course. In those cases, each boat would also see the other as gradually consuming land.

Of course, we can no longer say anything about the relative speed of the boats. Holding the sight lines constant and fiddling with the start and end points of the velocity vectors, it is easy to construct cases where A is faster than B, or B is faster than A.

So, will we pass ahead or behind? Well, if we were on a collision course the sight lines would be parallel. So, if we take a line parallel to the first sight line and advance it towards the point where the courses cross it appears obvious that the boat in the closed end of the sight line triangle (B in the illustration) must arrive at the point where the courses cross after boat A. But there are other possibilities: Suppose that the courses of A and B crossed inside the sight line triangle such that the first sight line was from A to B while the second was from B to A. Now, advancing the parallel to the first sight line clearly shows that B will cross ahead of A. Of course the "sight lines" in this case are unrealistic, but we can fix that by scaling the course vectors back proportionally (ie. reducing the time between sightlines) until they no longer cross.

So the only conclusion we can draw from this exercise is that if you are making land on another boat you can't possibly be on a collision course with it. You can't tell if you'll pass ahead or astern of it.