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.