Intercept en la Playa del Condado Puerto Rico

Miré hacia el Caribe desde la playa del Condado, imaginé que Ponce de León estaba parado en el mismo lugar, midiendo el ángulo del sol con su astrolabio.

Ponce de León conocía su posición exacta porque le preguntó al Taíno Cacique Agueybaná dónde se encontraban exactamente en la galaxia. Así pudo calcular su intercepción.

Tomé una medida y los parámetros fueron:

El Tiempo = 16 de marzo de 2019 11:53:15GMT

Hs = 18grd 10.5′ ( Miem. Inf.)

Alt de Ojo = 2m

Error de Sextante = +4′

Ha = Hs +/-EdeS – Incl = 18grd 10.5′ + 4′ – 2.5′ = 18grd 12′

Ho = Ha – R + SD = 18grd 12′ – 2.9′ + 16.1′ = 18grd 25.2′

Intercept = Ho – Hc = 18grd 25.2′ – 18grd 23.4′ = 1.8′ = 1.8Nm

El Almanaque Náutico Sábado 16 de Marzo de 2019.

Playa del Condado de Tierra Google
Triángulo Náutico

Castillo San Felipe del Morro

Castillo San Felipe del Morro

Recientemente visité el Castillo San Felipe en San Juan Puerto Rico. Nunca he visto una fortificación tan enorme e impenetrable como esta. Me imaginé que era un soldado español en el siglo XVI y que el pirata Drake apareció alrededor de la Punta Escabron. Tomé el rumbo de la brújula y disparé el cañón, ajustándome al rango.

San Juan
San Felipe – Punta Escabron
Brújula Global

Golden Globe Race 2018 – 50 Year Anniversary


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.

Figure 1 Google Earth View of Solander Island on Southern Tip New Zealand

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′


#1 – “Sunday Times Golden Globe Race”

#2 – “Deep Water”

#3 – “GGR Golden Globe Race 1968 Website”

#4 – “The PyAlmanac”, Python Script to Write Nautical Almanac Using PyEphem, Python2.7, TeXLaTeX

#5 – “The Nautical Almanac for The Year 1968”, US Naval Observatory & UK HMSO, Google Digitized Books, University of California Library;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

Maiden – Whitbread Round The World Race 1989

Just saw Alex Holmes’ s documentary “Maiden” at the Toronto International Film Festival. It’s about Tracy Edwards all female crew that sailed around the world in the Whtibread 1989 race. It follows Tracy’s early life and the various steps leading up to the race. An incredible study of courage, persistence and bravery in the face of incredible opposition, problems and of course mother nature. Any one interested in sailing or adventure this is for you.  A testament to the optimism of youth.

Norfolk to Lord Howe Islands Great Circle Distance

On March 31st 1931, Sir Francis Chichester left the Northern Tip of New Zealand on an East to West flight across the Tasman sea. He stopped to refuel at Norfolk Island and Lord Howe Island. Let’s determine the great circle distance and bearings that his Gypsy Moth float plane Madam Elijah ZK-AKK had to fly between these two points using the Spherical Haversine law.


The great circle distance using the Spherical Haversine law is:


GCD = 895.3Km (483.4Nmiles), Bearing of Lord Howe Island = 249.9deg. This agrees with the Google Earth plot.

Intercept at Trillium Park Lat = 43.6296degN Long = 79.4095degW


“I must go down to the seas again, to the lonely sea and the sky, And all I ask is a tall ship and a star to steer her by;” from Sea Fever by John Masefield

Currently I am calibrating my 3 sextants from several known locations in Toronto. One requires a water horizon and the other 2 have bubble horizons. Trillium Park is gorgeous, it’s like looking out over the Pacific ocean! I am also reading Ian Strathcarron’s biography of Sir Francis Chichester “Never Fear”. I love Chichester’s cure for mental & physical scurvy: Scotch Whiskey + Lemon!!