Sailing Flow Chart

At Cowes week this year one of my friends reassured a Fastnet Race competitor that sailing was essentially very easy, in fact you just point the boat where you want to go and pull the sails in until they stop flapping. This made me wonder if there was a very simple but functional algorithm for sailing that could be expressed as a small flowchart. It's slightly more complicated than my friend's description because it also covers the case where you can't pull the sails in enough to make them stop flapping whilst pointing the way you want to go:

SailingFlowChart

I think this pretty much covers it, at least as far as white sails go. You end up either close hauled and constantly steering to the point where the sails flap, or reaching and constantly trimming to the point where the sails flap. I know that in practice it can be more complicated that this, but not much, this flowchart certainly captures the two essential modes of sailing. I also like the fact that there is no end point, no state which you can relax in, you're doomed to constantly trim, or steer, to the edge of flapping: I think that's pretty accurate!

Start-line Bias

Two weeks ago I did a yacht race in Shoreham and there was some interesting discussion before the start about which end of the line was favoured. Normally, when the windward mark is directly upwind from the start line, picking the favoured end is very simple. In this case it was a bit trickier; the start line was not square, which is not unusual, but also the 'windward' mark was so far off to the starboard that the port layline for the windward mark actually bisected the start line. In this situation, starting from the starboard end of the line would mean that you would have to tack, whilst starting from the port end of the line would mean that you could reach to the mark in one. In the case of this race in Shoreham, the port (windward) end of the line was actually closer to the windward mark than the starboard end (as pinged by our GPS), so not only did it offer a faster point of sail, but less distance to sail as well: no-brainer, start at the port end! The more interesting question is what would have been the best part of the line if the windward end had been further from the mark than the leeward end?

Figure 1: the startline as it actually was, C-B, and the more interesting case, A-B.

Figure one shows the windward mark, W, the start line as it was in Shoreham, C-B, and the more interesting case of a squarer startline, A-B. When the windward end is further from the top mark than the leeward end there is a trade-off between the extra distance you have to sail and the extra speed you get on a lower point of sail. So how do you resolve this trade-off and find the optimal starting point?

The answer lies (as do the answers to so many sailing questions) in the polar diagram for the boat. The polar tells us how fast the boat will sail at every wind angle, so we must be able to use it to find the point on the start line which will get us to the windward mark in the least time, we just need the right bit of geometry.

The right bit of geometry is shown in figure two; step one is to draw/trace/superimpose the polar diagram centred on the windward mark, but we draw it upside-down relative to the wind direction, scale doesn't matter. Next we transpose the startline (maybe with a parallel rule) towards the windward mark until it just touches the polar. Finally, we draw a line through windward mark and the point where the polar and the transposed startline touch, extending it until it intersects the actual startline. The point of intersection between this line and the startline is the optimal place to start, easy!

Figure 2: geometric construction to find optimal starting point, X. The upside-down polar is shown centred on the windward mark in blue. The port layline is shown in red. Transposed start-lines are shown in green.

Figure 2: geometric construction to find optimal starting point, X. The upside-down polar is shown in blue, centred on the windward mark. The port layline is shown in red. Transposed start-lines are shown in green.

In the case of a one-design fleet sailing on the course shown in figure two, a boat starting from X will take about 4.5% less time to reach than a boat starting on the layline (from L). So if these boats do 6kn (knots) when hard on the wind (i.e., along L-W) and the distance L-W is one mile, then the boat starting from L will reach the windward mark after 10 minutes. By which time the boat that started from X will be 27 seconds ahead, which is a lead of 83m!

Looking at it another way, the J92 I was sailing on in Shoreham is 9.2m long, so it does one length every 3s when travelling at 6kn, which means that even if the windward mark was only 250m from L, the boat starting from X would still be able to round the windward mark clear ahead of the boat that started from L without having to give mark room!

The table below lists the distance sailed, speed, and time to reach W for each of four boats that start at A, X, L, and B:


starting point distance (nM) speed (kn) time
A 1.15 7.16 9:40
X 1.10 6.91 9:33
L 1.00 6.00 10:00
B 0.95 5.33 10:41

So clearly working out where on the line to start is well worth it in situations such as this, if we had assumed that the line can only be biased towards one end or another then we would have been over two lengths behind where we could have been had we started at X.

Figure three shows us practising our reach to the windward mark, that's me in red and white easing the jib sheet:

Figure 3: Upstart on a practise reach from the line to the windward mark.

Figure 3: Upstart on a practise reach from the line to the windward mark.

America's Cup: The F1 of Sailing

When Ben Ainslie said that the America's Cup was "the Formula One of sailing" he was more right than he may have realised. Recent rumours that Oracle Team USA's boat had an automatic foil control system fitted to it half way through the regatta are raising speculation about a possible legal challenge by Team New Zealand on technical grounds. Rule circumvention by clever engineers has been at the heart of F1 for decades, and now it's making a front page appearance in sailing. Without passing judgement on the legality of Oracle's system, here I have a look at the differences between the mature F1 technical regulations and the AC72 class rule which is, of course, a first edition.

For clarity, the suspicion is that the Oracle system modulates the angles of the foils using hydraulic power produced by sailors grinding winches, but is controlled by a computer fed with information from various sensors on the boat. It may turn out that it is actually a passive mechanical system.

If the America's Cup is the Formula One of sailing, then perhaps the AC can take something from the rules of F1 regarding automatic control of things like foils. The F1 technical regulations have been preventing automatic control in several areas for a while, so they're far more developed in this area than the Racing Rules of Sailing, or even the AC72 class rule. For example, the F1 rule that prevents computer controlled ABS (Anti-skid Braking System) is 11.1.4:

Any change to, or modulation of, the brake system whilst the car is moving must be made by the driver's direct physical input, may not be pre-set and must be under his complete control at all times.

The key phrase here is 'under his complete control at all times', which means that you can't have something that plays around with the brakes without going via the driver's head. You can have things which present information to the driver, but you can't control the brakes independently of the driver. Note that the rule doesn't go into detail about what specific devices are allowed and what mechanisms can or cannot be involved, it just says that the driver is the only control device allowed.

The AC72 class rule has a more round-about way of trying to achieve the same thing, firstly, it says that stored energy (batteries etc.) is not allowed, except for several things, including:

[19.2] (e) for electrical operation of
(i) hydraulic valves. These operations shall only provide the input for the
position of the valve;

So from that it seems that having electrically operated valves is fine, BUT, read the rest of 19.2 and you find the bit where they tried to prevent computer control of things:

The operation for (i) [valves] and (ii) [clutches] above, shall not receive external input from any source other than manual input. Any data acquisition system, associated sensors or electronics shall be physically separate and completely isolated from any electrical operation referred to in (i) and (ii) with the exception of the voltage supply.

The problem with rules as specific as this is that it's relatively easy to get around them: the rule specifically bans computer control of valves that are operated by stored energy. It doesn't ban computer control of valves which are driven directly from a dynamo on a winch, for example. In fact it doesn't ban computer control of anything that's not operated using stored energy, as those things don't even fall into rule 19.

If the AC wants to be the F1 of sailing, then the technical regs need to be written like the F1 technical regs - ban general concepts, like automatic control, rather than the specific instances that the rule writers happen to have thought of. If you collect the kind of engineers that Larry can afford, then you can run rings around regulations like the AC72 class rule.