When Should I Change Course?

In my last post I expressed my frustration with the limited success I have had in plotting my great grandfather-in-law’s dead reckoning course from St John’s Newfoundland to Burin. It was time to change tactics. I figured that since I would be retracing his route, I might as well start planning my own strategy with an eye to the instrumentation and methods available in 1886. 

One of the first lessons that all sailors learn is that a sailboat of any era cannot sail directly into the wind. Even in a modern sailboat we can only sail to within approximately 45 degrees of the wind. (The two courses: one with the wind on the port (left) side and the other with the wind on the starboard (right) side are referred to as lay lines.) In captain Robert’s schooner he may have had to sail even further off the wind, perhaps as much as 60 degrees. Given this necessity, we make progress to windward in a zig zag course first on one lay line then the other. Each zig is called a tack. From plain geometry we know that if we make only one zig and one zag or many of each we will traverse the same total distance. Assuming for simplicity that we want to make the destination with only one change of tack, we are left with the decision how far to travel along the first lay line before we change to the other.

On Virago, we usually answer this question by setting a waypoint at the destination on our chart plotter. This provides a constant display of the bearing to the mark. We start on the lay line closest to the bearing and watch the display of the bearing to the mark until it lies on the lay line of the other tack. Then we tack. All well and good in this 21st century, but how would Captain Roberts have known when to tack? I found my answer in an entry in that same 1829 London Encyclopedia I used in my last post—this time its article “On Plying to Windward”.

The entry is shown on the left and an explanatory drawing of the problem above. To understand it I had to grapple with two issues.

First, I had to understand the calculations. While rummaging around in some old memory cells I recalled the concept of logarithms. To make math more practical before calculators the author used log sines and number logarithms to turn multiplication and division into addition and subtraction. In practice, sailors often used a Gunter Rule (a precursor of the slide rule.) The logarithmic calculations were accomplished by using ordinary dividers much like pacing off distances on a latitude scale. I don’t know if Captain Roberts had a Gunter Rule, but he well could have.

Second, I had to understand how a sailor might use this in practice. To make life simple, suppose I wish to sail from St John’s to Burin Newfoundland with only one tack. Motoring, I would go from St John’s to Cape Spear, to Cape Race, and to Burin’s sea buoy. This would usually be an impossible sail since the prevailing wind is from the Southwest (225º True). Assuming that Virago can tack through 90º, our two lay lines would be 180º and 270º. I would thus set out on the starboard lay line 180º, but when would I tack if I didn’t know when Cape Race was on my port lay line of 225º at Tack Pt 1?

Here’s where the law of sines does its magic. Assume a triangle with angles a,b,and c and opposite sides of A,B, and C. The law tells us that sine a / A equals sine b / B and sine c / C. In our example:

sine 90º/71 = sine 17º / port tack = sine 73º / starboard tack.

This is another way of saying what our 19th century author said. Being a creature of the 21st century, I chose to create a spreadsheet as my digital ‘Gunter Rule’ analog. Given this calculation no matter how done, I can see that I should sail for 68 miles on the starboard leg before tacking. Then I would sail for 21 miles before falling off at Cape Race for the reach to Burin.

In practice, a sailor might choose to sail out to sea (where there is little to hit) at night and head for land during daylight when it is visible. Looking back at Captain Robert’s log, it looks like that was his strategy. He approached land at 1400 hours on July 13th then headed roughly East (away from land). Later he headed West again spotting Cape Race light at 0200 hours on July 14th and headed more Northward for Burin. Given the geometry, I might choose a similar strategy by sailing seaward from Cape Spear for one half the distance (34 miles), turn towards land for 10 miles, return to seaward for the other 34 miles, and then back to the West for the final 10 miles.

In sum, I feel that I have satisfied my desire to understand Captain Robert’s dead reckoning well enough to expand my sailing repertoire. I am working with my navigator for the trip James English to experiment with dead reckoning as a practical procedure rather than just an ‘in case of electronic failure’ backup plane. We will report our results and observations this summer.