Tom, The sort of situation you've described is what happens in Solent racing all the time. In that situation Jimi's method works well. In fact you can ignore the tide question. Both vessels will have an equal (roughly) velocity due to tide and the other boat will only appear to be gaining or losing on the background if it is going ahead or astern of you. It's not a question of whether it is moving against the background, but whether it is moving against it faster or slower than you are, so that you can see background disappearing behind his forestay (going ahead of you) or coming out from his forestay (going behind you). Difficult to explain in words but easy to assess on the water.
BUT, if there's a remote risk of a collision, watch him all the time because the relative course and velocity of two boats in this situation changes all the time with headers or lifts, and helmsmen who decide to pinch to see if they can get in front of you.
Think I'm getting your drift (sic) though having raced in the Solent myself I've never used the land to judge closing rate. The tide was just to accentuate the movement.
How on earth do you judge whether you or the other boat is moving faster against the background? Sounds like you're using the forestay and ignoring the relative movement of the land, in which case this is the same as a relative bearing and we're all reading off the same hymn sheet.
Jimi's method will only work if the distance between you and the boat in question is much less than the distance between you and the shore you're looking at.
If the lands a long way off (over a mile, maybe?) the bearing between you and a point on the land won't change significantly in the space of a couple of minutes. Therefore, all you're really doing is using the same method as you use with a handbearing compass, in that you looking to see if bearing between you and the boat in question is changing or not.
What worries me is that people are talking about using it in confined water, when it won't work, as the lands close enough that the bearing to points on the land will change significantly in a relatively short space of time.
It works well racing because it doesn't require you to memorise or write down h/b compass bearings. Imagine you tacking out from the Island shore on port, with a bunch of stbd tackers coming in. You''re not going to shoot each of them with the h/b, then do same 30 secs later to assess whether you'll beat them or not. But by observing them against Hampshire you'll be able to decide, say. that no 1 is going to cross ahead, number 2 will go behind. number 3 will go behind, and number 4 is going to be a problem. So then you decide whether to duck 4 or tack on his weather when you get there. To sort that lot out using an h/b would be difficult, but using the background method it can be done in a few seconds.
I sense convergence (!) on this issue. I only ever use the hb compass for collision avoidance when in open waters, and use shrouds or whatever in confined waters. You'd be popping about like a man possessed if you tried too use the hb compass on a busy day in the Solent.
Back to the example I gave earlier, if I chose a landmark 1 mile distant and we were travelling up the Solent at a groundspeed of 10 knots then the land bearing would change around 5 degrees in 30 secs, this being about the time it would take to make the close call judgement. If the landmark was much further off then I could see it work.
Let's look at the mathematics. A shore-line point is on the same bearing as your worrisome other boat. You are travelling at 6kts, say, and the shore is 1nM distant, say. Keep it simple and have both of them abeam (worst case). The bearing of the object will change about 0.6deg/min. So I'll give you that one. If the shore is only half a mile, it is still only 1.2deg/min. Closer than that, and the method starts to niff a bit. Personally, whether racing or cruising, I prefer to use things on the boat to line up with.
In the case of a transit, then your technique is spot on. Trying to cross a river on the ebb, to round a mark of the course on the other side, lining the mark up with shore, and holding it so, is the way to do it.
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