Introduction
The Golden Globe Race 2018 commemorates the original Sunday Times Golden Globe 1968, a non-stop, single handed round the world yacht race. It was won by Sir Robin Knox-Johnston in Suhaili. Nine contestants entered and only Knox-Johnston finished. Bernard Moitessier decided not to finish but go around the world for a second time! (Ref.1). Several fascinating movies were made about this race, one of them being “Deep Water” (Ref.2). This year’s Golden Globe celebrates the technology current around 1968. Contestants have to follow strict guidelines on boat design < 1988 and ensure all devices and instruments are of the 1968 period (Ref.3). Eighteen skippers started the race at Les Sables-d’Olonne in France on July 1st, and now eight remain, presently rounding New Zealand.
Celestial Navigation for Position Determination
In 1968 GPS was still on the drawing board. Electronic navigation systems were expensive and complicated. They consisted of using RDF radio direction finding or hyperbolic coastal navigation systems such as Decca and Loran. For most sailors, the sextant was an indispensable tool. According to Sir Robin Knox-Johnston’s book “A World of My Own” (Ref. 6) on November 18th: “At midday I set sail again to clear Solander Island, as we had drifted slowly down onto it during the morning”. Let’s work out the basics of what a meridian passage sextant sighting would have looked like for Sir Robin on this date. Figure 1 shows the location of Solander Island on the southern tip of New Zealand as seen from Google Earth.
Reading off Google Earth or an appropriate chart, we determine the coordinates of the southern tip of Solander Island:
Latitude = 46deg 35′ South
Longitude = 166deg 54′ East
We can use modern software to regenerate the Nautical Almanac page for November 18th_1968 (Ref.4) which is shown in Figure 2. We can double check these values with the Nautical Almanac for The Year 1968 (Ref.5) which is available on line. Let’s figure out the sextant angle Hs measured for a meridian passage on this date and for this location. Knowing that the sun travels 15 degrees every hour, we can determine the time difference between Solander Island and Greenwich = 11hrs 7.6minutes [[166+(54/60)]/15 = 11.126667].
Figure 2 Regenerated Nautical Almanac Nov 18th_1968
From Figure 2 we can determine the GMT when the Sun GHA is directly on Suhaili’s meridian of 166deg 54’East or GHA = 360deg – 166deg 54′ = 193deg 6′. At 0hrs GMT the GHA is approx 184deg and at 0100hrs GMT the GHA is approximately 199deg. Interpolation for 193deg 6′ gives GMT = 0hrs 37minutes 33secs [[(9+23/60)/(14+59.8/60)]*60]. The Sun DEC at this time is 19deg 12′ S.
Figure 3 Oblique Spherical Triangle
Now we are in a position to calculate the sextant angle. Figure 3 shows the oblique spherical triangle formed by the position of the observer on Suhaili, the Sun GP and the North Pole at meridian passage. The Zenith Distance Zd = 90deg – Ho. The Zenith Distance is also equal to the arc distance between the Sun GP and the observer latitude since they are directly on the meridian.
Zd = 46deg 35′ – 19deg 12′ = 27deg 23′.
Ho = 90deg – 27deg 23′ = 62deg 37′.
Let’s assume Sir Robin took lower limb sightings, his height of eye above the water was 3m and his Plath sextant had no errors. We can convert our calculated Ho–>Ha–>Hs with the following equations:
Ho = Ha – R + PA +/- SD
Ha = Hs +/- Index Error – Dip
R = Refraction = 0.0167/tan(Ha+7.32/(Ha+4.32)) deg at 10degC/1010mb = 0.5′
Dip = 1.76xsqrt(Heye_m) = 1.76xsqrt(3) = 3′
SD = 16.2′ from Nautical Almanac page Nov 18th_1968
Ha = Ho + 0.5′ – 16.2′ = 62deg 37′ + 0.5′ – 16.2′ = 62deg 21.3′
Hs = Ha + Dip = 62deg 21.3′ + 3′ = 62deg 24.3′
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References
#1 – “Sunday Times Golden Globe Race”
https://en.wikipedia.org/wiki/Sunday_Times_Golden_Globe_Race
#2 – “Deep Water”
https://www.imdb.com/title/tt0460766/
#3 – “GGR Golden Globe Race 1968 Website”
https://goldengloberace.com/
#4 – “The PyAlmanac”, Python Script to Write Nautical Almanac Using PyEphem, Python2.7, TeXLaTeX
https://github.com/rodegerdts/Pyalmanac
#5 – “The Nautical Almanac for The Year 1968”, US Naval Observatory & UK HMSO, Google Digitized Books, University of California Library
https://babel.hathitrust.org/cgi/pt?id=uc1.b4522390;view=1up;seq=1
#6 – “A World of My Own: The first ever non-stop solo round the world voyage”, Robin Knox-Johnston, ISBN: 978-0713668995
