Monthly Archives: January 2016

Celestial Navigation Part Two: Longitude (how far east or west)

To determine position on the open seas, one need to measure the Latitude (north and south) and Longitude (degrees east and west). But longitude is a more difficult task.

Quick review:

  • Latitude: how far north or south, referenced to the equator (halfway between the north and south poles).
  • Longitude: how far east or west from some agreed upon position (now-a-days pinned to the Royal Observatory in Greenwich, England).
Latitude and Longitude from Wikipedia

Latitude and Longitude from Wikipedia

From Wikipedia (

While it is possible to determine the longitude by observing the stars (or even the moons of Jupiter), these measurement require a degree of accuracy impossible on the rolling deck of a ship at sea.

A solution to this problem is the use of accurate timepieces.

  • …Two observers note the time when the sun reaches its highest point in the sky
  • …The difference in time is directly related to the angle between the two observers on the surface of the earth
  • …24 hours = 360 degrees
  • …Each hour of difference = 15 degrees
  • …The angle between the position of the two observers can be use to determine distance
  • …Each degree = (circumference of the earth)/(360 degrees) = 69.2 miles where the circumference = 24900 miles.
  • …Using Nautical miles, each degree = (21639 nautical miles)/(360 degrees) = 60 nautical miles
  • …So that each minute of angle (60 minutes to a degree) = 1 nautical mile
  • …So for each hour of difference between the two observers, they are 60 nautical miles apart (or 69.2 land miles).
  • Easy. Right? Well, it’s only easy if the two observers are using clocks that have been synchronized and keep accurate time.

Today, any pair of inexpensive wristwatches would suffice. However, not until the eighteenth century, could such accurate clocks be constructed.


John Harrison’s first chronometer

Prior to the 18th Century, navigators could determine latitude (distance north or south) but could only guess their east-west position by dead reckoning (estimating the speed of their ship, estimate of the direction of travel, and estimating their time duration). Hence the name “dead” reckoning.

In my time-travel, alternative history novels, common wristwatches become a highly valued navigational aid. (In your story, make sure they run on internal springs and not batteries!).

The tale of John Harrison’s construction of an accurate chronometer in the 18th Century is well told in “Longitude” by Dava Sobel.

Celestial Navigation Part One: Latitude

To determine position on the open seas, one need to measure the Latitude (north and south) and Longitude (degrees east and west).

Screen Shot 2016-01-02 at 7.48.47 PM

From Wikipedia (

To determine distances position north and south, one needs three things: a tool to measure the angle between the horizon and the max altitude of the sun, the date, and charts with the latitude as a function of the sun’s maximum altitude.

The measurement tool can be as simple as an outstretched hand or as complicated as a sextant. From Wikipedia ( Accurate angle measurement evolved over the years. One simple method is to hold the hand above the horizon with your arm stretched out. The width of the little finger is an angle just over 1.5 degrees elevation at extended arms length and can be used to estimate the elevation of the sun from the horizon plane and therefore estimate the time till sunset.

The need for more accurate measurements led to the development of a number of increasingly accurate instruments, including the kamal, astrolabe, octant and sextant. The sextant and octant are most accurate because they measure angles from the horizon, eliminating errors caused by the placement of an instrument’s pointers, and because their dual mirror system cancels relative motions of the instrument, showing a steady view of the object and horizon.

Screen Shot 2016-01-02 at 7.42.58 PMFrom

The date can just be an accepted calendar.

The charts (using the same calendar) must be generated by hand using pre-determined latitude positions. For example, using Reykjavik (Iceland) which is located at 64 degrees North, one can generate the following data (by taking measurements throughout the year):

Latitude (degrees)dateMax Sun Altitude
64January 1st3.2
64February 1st9.92
64March 1st18.8
64April 1st30.9
64May 1st41.3
64June 1st48.2
64July 1st49.1
64August 1st43.8
64September 1st34.0
64October 1st22.6
64November 1st11.4
64December 1st4.3

To complete the chart, one needs more dates (which I have avoided here for simplicity) and the angles at different Latitudes (here I just added three, again for simplicity) to obtain:

DateMax Sun Altitude at
Latitude = 44 degrees
Max Sun Altitude at
Latitude = 54 degrees
Max Sun Altitude at
Latitude = 64 degrees
January 1st23.9 13.1 3.2
February 1st28.918.98.9
March 1st38.828.818.8
April 1st50.940.930.9
May 1st61.351.341.3
June 1st68.258.248.2
July 1st69.059.149.1
August 1st63.853.843.8
September 1st54.044.034.0
October 1st42.513.13.2
November 1st31.321.411.4
December 1st24.114.14.3

Obviously, more intermediate dates and latitudes are necessary. These would fill a very large atlas (think of the number of data points for 365 days and 180 degrees!).

The above date collected from this Navy site:

So, if you are sailing in a Viking ship (as my characters do in my second book which will be published in late 2016), you need to monitor the altitude of the sun above the horizon. Take several readings during the noon hours, chose the largest value and check that value in your atlas. If the maximum value is 49 degrees and the date is August 15th, the latitude is approximately 58.8 degrees from the above table. If you are sailing to Reykjavik, you better turn North a bit as the latitude of Reykjavik is 64 degrees.

How far east and west are you? I’ll cover longitude in my next post.