In the following diagrams, the backing wind is shown by the green arrows. It is square at the starting line, but has backed by (an extreme) 45 degrees at the windward mark. The course sailed is divided into equal-length straight-line segments, with the local wind shown by a little tag line at the top of each segment. The segment is oriented at 45 degrees to the local wind; we assume for simplicity your boat tacks at 45 degrees to the wind.
In the first diagram, the windward mark is directly to windward of a spot on the starting line, from where Blue starts on starboard and Purple starts on port. Two segments later, Blue tacks onto the lifted, curved port layline for the buoy. Purple on the other hand first takes the lifted port tack as far as it goes, and then tacks onto the starboard layline. Unfortunately, Blue is long gone, having taken 25% less distance/time!
In the second diagram, the windward mark is placed so that it can just be laid on port without tacking. We have Purple starting at the extreme port end of the start line, therefore, and laying the mark. Blue starts on starboard from the other extreme starboard end of the starting line, and then tacks onto port when she gets to the port layline. We know, from the first diagram, that any course other than getting to the lifted port layline as soon as possible is a loser, but Blue still loses out by one and a bit segments (the "bit" is to take account of the time lost by Blue in having to tack, which Purple didn't do).
The final diagram shows a start line that is offset to starboard. If the wind didn't back, then (other things being equal) any position on the starting line would "normally" be as good as any other. Both boats start at the extreme port end of the start line, as "close" to the mark as they can get; with a bent wind, the previous diagrams show that starting anywhere else would be bad news. Blue starts on starboard, and tacks onto the lifted port layline after 2.5 segments. Purple starts on the lifted port tack, and only tacks onto starboard when she reaches the starboard layline. As before, however, Blue is long gone, having taken 28% less time/distance.
What can we conclude?
The metric involved in a "bent" wind field can't be represented two-dimensionally, like the city block metric of an unvarying wind. The possibilities from each segment of a course are different depending upon the particular segment, a bit like Quantum Electro-Dynamics and a photon field...
For our next challenge, let's see what happens when the start line is biased by the Race Committee in an attempt to compensate for a backing wind. As before, we imagine that the wind backs 45 degrees at the windward mark, and so the RC sets a line that is square to the "average" wind between the starting area and the mark. This is illustrated in the following diagram.
In the few minutes before the start we are the Orange boat, milling about near the start line, trying to decide which end to start at, and whether to start on port or starboard. As we sail up towards the starboard end of the line, we notice that the wind backs slightly, and we also notice that the starboard end seems to be definitely to windward of the port end. Then, as we sail down towards the port end of the line, we notice that the wind seems to veer slightly, and we also notice that the port end seems really far to leeward of the starboard end. Great, we say; we'll start at the starboard end of the starting line, and start on starboard with everyone else. Our buddy, the Blue boat, fouled up his pre-start and is stuck right down at the port end. He is starting on starboard tack as well because he can't face taking the sterns of the horde about to descend upon him.
Using our knowledge about city block metrics, we estimate that we'll take about 7 "segments" to get to the mark, and our buddy will have to take 8; we feel the starboard end is biased about 10 degrees in its favour. The following diagram shows the city block grid aligned at the starboard end of the line with the local wind, to suit us as the Orange boat.
The good news is that, by hanging onto starboard tack until we reach the port layline and accepting being headed a little, we are lifted to the mark by the backing wind, and it only took us about 6.5 "segments" to get there. The bad news is that, to our astonishment, our buddy is right there with us, bows to bows. He didn't take the expected 8 "segments" at all. He was on the port layline before we were, and got a much longer lift. The Race Committee got it about right.
Let's look at it from our Blue buddy's point of view. Using the city block metric, he was feeling a little depressed about messing up his start. From the port end of the line, he could see that the port end was apparently severely disadvantaged, suffering a 22 degree bias against it. He also thought that the Orange boat would be able to lay the mark without tacking, and take about 6 "segments" doing it, while he thought he'd have to take about 8 "segments". The following diagram shows the situation from his point of view, with the city block grid aligned with the local wind for the Blue boat down at the port end of the line.
He quickly found out that the situation was nowhere near as bad as he'd thought (and his confidence in the Race Committee lifted as well), but he had to be quick to tack over to port, apparently much too early, and take a few sterns on the way up the lift.
The last diagram shows the catastrophe awaiting us or our buddy had we decided to start on port tack from our respective start line positions.
What can we conclude?
Finally, let's have a look at three different kinds of "wind bend field" that could occur. We will keep our wind backing, and place the windward mark directly "above" the port end of the line. In each case, we'll have the wind at the windward mark backed at about 45 degrees, while the start line is roughly 22.5 degrees to the "average" local wind. In each case, if you failed to check out the wind at the windward mark, you'd think that the starboard end of the line was quite heavily favoured. In fact, as the diagrams make clear, the best start is usually from the port end of the line with a short starboard tack, and then tacking to port to take the long, beautiful lift all the way to the mark. That way, you head to the favoured port side of the course, the inside of the wind bend, before taking the lift. The diagrams also make clear that starting from the apparently favoured starboard end of the line and keeping on starboard tack to the inside of the wind bend is a pretty foolproof tactic as well.
Within these parameters, however, there are still three main ways for the wind to bend, and they can give different signals.
In the first scenario, the wind bends "horizontally" across the course. Starting from 0° at the bottom of the course, it backs to 45° at the top. In this scenario, all the port tacks are strongly curved and obviously lifted; so while you were on port tack, it would be clear that the wind was backing. On starboard tack, however, the tacks are weakly curved; so while you kept on starboard, it would not be nearly so obvious how much the wind was backing. Your first clue would come from any boats on starboard below you; they'd be pointing up towards you and you'd be wondering what the hell was wrong with your trim. You could be forced to tack over to port as windward boat; you could grit your teeth and pinch; or you could recognise what was happening and go for the inside of the wind bend, footing and taking sterns on the way. Your next clue would come from watching the boats who tacked over to port; they'd be clearly lifted. You'd make sure you stayed on starboard tack until you reached the port layline, when you'd tack for the lift.
In the second scenario, the wind bends "diagonally" across the course. Starting from 0° at the bottom right of the course, it backs to 45° at the top left, while at the other two corners it has backed about 22.5°. In this scenario, all the tacks, both port and starboard, are strongly curved, but only once you are within the bent wind field. You'd have a real problem if you "cleverly" started on port tack at the starboard end of the line, because you'd never know about the wind bend until you tacked over to starboard and got a very rude shock indeed. Otherwise, any starboard tack would quickly show you that you were being headed, and no one to leeward would be pointing up at you. If you took an exploratory port tack, you'd feel the lift. Gritting your teeth yet again, you'd flop back onto starboard to take the rest of the header, only coming onto port tack on the lifted layline.
In the third scenario, the wind bends "vertically" across the course. Starting from a 45° bend at the left of the course, it veers to 0° at the right. If you were paying attention, you'd notice that the bias on the starting line seemed to favour port when you were at the port end, while it seemed to favour starboard while you were at the starboard end. But what you'd really notice was that the port side of the course was clearly favoured, allowing you to pretty much lay the mark from anywhere on that side. All starboard tacks are obviously curved and strongly headed, while port tacks are relatively weakly curved. It should be clear, if you were on starboard, that you'd need to carry on to get to the left side of the course before laying the mark on port. If you were on port and on the wrong, right-hand side of the course, you'd need to be watching the other boats to realise that things were going badly wrong. If you were on port and on the left of the course, it'd be clear that you could ride the lift on offer all the way to the mark.
So what conclusions can we draw here? First, check out the sides of the course. You know to check the ends of the starting line; you know to check the wind direction at the windward mark; and now you know to check the sides.
On the assumption we are dealing with a continuously bent wind, and not a transient wind shift:
©2011 Lester Gilbert