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.

Forensic Navigation -- Recreating a Route from an 1886 Schooner's Log

Why would someone with over 10,000 miles of coastal cruising as well as a USCG 50 Ton Masters license pursue a US Sailing Coastal Passage Making certification? My best explanation is that my experience resembles a wheel of Swiss cheese - impressive looking, but full of holes. Take navigation for instance. Even after 18 years of experience cruising keel boats and passing the rigorous Coast Guard exam, I had a new experience in my Club Nautique Coastal Navigation class. As an exercise we plotted a course based only on a vessel log book. As with most textbook examples, it worked perfectly. I have to admit that my own log book is much too sparse to admit such perfection. Could I take what I had learned and apply it to a real life log which recorded heading and speed at regular intervals and whenever the vessel changed course?

Cover of Schooner Runnymede's Log Book

As it happens, I do have such a log. My great grandfather-in-law Nathaniel Roberts was a sea captain sailing out of St John's, Newfoundland in the 1880s. The family still has his chart case containing charts, instruments, ephemeris, sailing directions, and the Book of Common Prayer. I was excited to view his charts with the hope that he had plotted his courses there. Alas, the good captain left his precious charts pristine. In addition to this legacy, a facsimile of his log from the schooner Runnymede has been printed by the Mystic Seaport Museum. That log has become my DIY kit for recreating and eventually following a voyage he made from St John's to Burin in 1886.

What type of vessel was she? There is a register of the British Merchant Navy for 1886 showing two schooners named Runnymede out of St John's. On was of 53 tons and one was of 57 tons. Neither was owned by Nathaniel Roberts. Looking at modern schooners and seeing that the highest speed he recorded in her log was 8 knots, I estimate her to have been about 80 ft overall with a 50 foot waterline. I will try to find more definitive info when I visit St John's this summer. 

Here is the first page of the log describing the first day as he sailed out from St John's harbor. Consulting an almanac for that date obtained from the Google library, we can see that he left with the tide. This was wise as St John's harbor is long and narrow with step hills on either side. I don't know if British practice followed the American rules that gave sailors the Sabbath off except for when leaving or arriving at port, but perhaps not coincidentally July 11, 1886 was a Sunday.

There were of course other aspects of 18th century usage that raised questions:
1: What did the column headings mean? 'H' meant hour, 'K' meant speed in knots, 'HK' meant additional half knot, 'Courses' probably meant course to steer given to the helmsman, although usage could vary, 'Winds' meant directions from which the wind blew and its strength (not strictly adhering to the Beaufort scale), 'Leeway' meant number of points course made good differed from the steered course, and 'Remarks' were just free form text.

Pages for July 11 and 12 1886

2: What are the times? Consulting period publications I found out that 19th century mariners usually kept time from noon to noon as opposed to midnight to midnight. This made sense at sea since the noon sight required precise determination of high noon. For this reason I interpret his locations 'by observation' to be his position at noon. It took some research to discover that the phrase 'on account' referred to what we nowadays call dead reconing.
3: Are the bearings magnetic or true? Today, purists insist that we plot our courses and fill our log books with true bearings. In practice, small vessels usually use magnetic bearings. I plotted this course both ways and found no bearings that were impossible either way. With no hard evidence to go on, I chose to interpret his bearings as magnetic.

32 Points of the Compass

4: How do we translate his 32 point compass readings into degrees? Since there are 360 degrees in a circle, each 32nd must be 11.25 degrees. The easiest way to translate this is with a table like this one.
5: How do we convert his magnetic bearings to true so we can plot his courses? The Newfoundland Almanac for 1886 gives the variation as 32 degrees and 30 seconds (p. 5). Given the degrees magnetic, all navigators know that since "Timid Virgins Make Dull Companions--Add West" means we should subtract the West variation to correct his magnetic bearings to true.
6: How did he do his 'accounting' or what we call dead reckoning? I can't be sure, but my go in assumption is that he recorded his speed for every two hour period and whenever he changed course.
7: How did he establish his true position? In the 1829 edition of The London Encyclopedia, the Navigation entry says that navigators are adept at determining the distance to landmarks and thus consider the bearing and distance to a landmark an accurate fix.
8: Did he use celestial navigation? We have one entry where he listed one latitude 'on account' (by dead reckoning) and another latitude 'by observation' (noon sighting.) Their distance apart of six miles is considered acceptable.
9: Besides navigation information, what do the Remarks tell us? I interpret the liberal sprinkling of boiler plate like "crew employed as duty required" and "pumps attended to" as an indication that his log was subject to review by the ship's owners.

I decided that my first step was to transcribe the log as best I could to make it more easily accessible

Transcription of Pages for July 11 and 12 1886

    My second step was to develop a technique for plotting the fixes found in the Remarks that could be electronically illustrated. Let's take the very first one:"5 pm Cape Spear bore North by West distant 3 miles." From our table we see that North by West equals 348 degrees and 45 seconds. To correct this to true we subtract 32 degrees 30 seconds yeilding 316 degrees and 15 seconds. Typically we need to take the reciprical of the bearing to the landmark and plot our bearing line from the landmark to the vessel. The reciprocal is calculated by subtracting 180 degrees giving us a bearing of 136 degrees and 15 seconds. Along this line we measure the distance and voila we have our fix.

First Sighting in iNavX

Route of July 1886 in iNavX

My tool of choice for this exercise was iNavX on my iPad. By using the range tool I can draw a vector from Cape Spear outward for 3 nautical miles at a bearing of 136 degrees. Then I can add a waypoint at that position and label it July 11 1700. By a similar procedure I can enter all the waypoints for this particular trip.

My third step was to create a route in iNavX linking all of the waypoints.The tool calculates all the individual bearings and distances of the legs of the trip. In addition it shows the total distance of 207 nautical. It took the Runnymede just about a week to make the 207 mile trip we see in this overview. iNavX also allows exporting the route to a KML file readable by Google Earth.

Chart of Route in July 1886in iNavX

My fourth step was to follow the bi-hourly entries line by line to recreate an 'account' or as we call it, a dead reckoning. To date, this effort has been a frustration. To take an obvious example, notice the time gap between the last entry for July 11 and the first entry for July 12.  There appear to be no entries for a twenty four hour period. In addition, there are times when he recorded lite winds and yet showed three knot speeds. I am incredulous that his 18th century schooner was capable of making three knots in lite winds. I have tried to recreate the dead reckoning of each leg of this trip as well as the return voyage he made in August of the same year. So far, no luck. I hope his log keeping was not as sparse as my own.

So, what is the net of all this effort?
1: First it is a fascinating exercise in navigation putting to use some of my training.
2: Second, it has pulled me into my wife's family history and piqued our interest in taking Virago from Mane to St John's. To that end, I am planning a cruise from Portland, Maine to St John's Newfoundland and back to Bar Harbor, Maine this summer. On the leg from Burin to St John's I will make an effort to recreate at least some of Captain Roberts' sightings.
3: Third, it has made me more conscious of how valuable a well kept log might be in the future. I intend to be more diligent in my log keeping on any upcoming trip.

Google Earth View of Upcoming Trip in a KML File.