Kicking it old school: Navigating without electronics

A ship like the R/V Sikuliaq is pretty much covered in sensors. Data is constantly streaming in with information about the ship’s location, speed, and path. Other instruments record data on the conditions around the boat: water currents, wind, temperature, ocean depth, seafloor geomorphology, and distance to any nearby ships. Despite the availability of electronically recorded data, though, the ship’s mates are [somehow] easily able to determine the position and speed of the ship using only a few simple tools… and occasionally some very confusing math. I was lucky enough to get a crash course.

 Getting a lesson on navigation with night-friendly lighting on the bridge.

Determining your location without a GPS (Global Positioning System, or GNSS for Global Navigation Satellite System) is no easy feat. Doing so while at sea is even harder. The basic idea is to calculate your distance or direction relative to something you already know the location of, whether it’s your previous location, land, the sun, or stars. By doing that you can plot a Line of Position (LOP), meaning a line or arc along which you must be located – even if you don’t know what point you’re at on that line. Intersecting three LOPs gives you an exact position.

A simple way to plot an LOP is to take your last known location and advance it: moving it forward on a map by the amount you have moved since then (speed) and the direction you were travelling in (heading). If you’re near land then another good way to get an LOP is to calculate your bearing to headlands or peaks. Using a set of triangles, you then plot your LOP from the headland/peak. While you don’t know your distance to the feature, you know you are somewhere along that line.  If you had known your distance, from a radar measurement, you would use a compass to plot a circle of equal distance around yourself.

An example chart with track lines shown in black. The top shows a coastline with two headlands and a peak – all of which can be used to calculate distances and bearings. From a starting position (yellow) you can take a bearing to Headland B and advance it every hour based on your speed and direction (pink). Same goes for radar ranging (green) and a bearing to a nearby peak (light blue). The celestial navigation section is shown in bottom left, with sun fixes shown in light blue and bathymetry in dark blue.

When you’re not near land is when it really gets good. Now you will have to find your LOP using the position of the sun and a couple of very dense books. The device used to observe sun position is called a sextant, and it has been in use since prior to the 18th century when it replaced the octant as a primary navigational tool for mariners.

R/V Sikuliaq third mate, Marian Tudoran, using a sextant to precisely measure the angle of the sun above the horizon.

‘Shooting the sun’ means measuring the angle between the sun and horizon, with a corresponding measurement of time. A person can use a Nautical Almanac and the Sight Reduction Tables for Marine Navigation to determine where the sun should be in the ‘celestial sphere’ at all times.  Basically, the celestial sphere is just a frame of reference for stars, planets, and galaxies – but it’s tied to the terrestrial (earth) reference frame at the earth’s center to allow you to convert between the two.

You use this coordinate system to specify where the sun appears to be in your view of the sky, after correcting for your position relative to sea level, the elliptical nature of the sun’s path, and instrument error. This is called the observed altitude. Based on where you think you are, which need not be particularly close, you calculate where the sun should be when viewed from that assumed position. This is called the computed altitude. The difference between these angles is the ‘altitude intercept’, which allows you to draw a line of position based on your assumed location. In the chart above we used two celestial lines of position and our bathymetry, or the ocean depth beneath the ship. The device used for such measurements is called a fathometer.

If that written description didn’t thrill you, don’t worry because the math looks worse. Above is a scratch celestial navigation calculation done by Sikuliaq’s third mate. Below is the calculation when an Apply-to-Sail student tries to figure it out.

Taking these measurements every hour and advancing previous measurements based on the ships speed and direction allows you to intersect three LOPs to find your exact location using only your sextant measurements and calculations. Around twilight you can also take measurements of other bodies such as stars.

Although in practice all navigation is done using GPS these days, the ship’s mates still perform these calculations to double check that the GPS is working properly and to keep sharp in case of power failure or emergency. While it is highly unlikely, part of their certification involves having the skills to determine a ship’s location without electronic aids. So next time you’re stuck on a boat with no power, all you will need is your handy sextant, compasses, string, chart paper, precision timepiece, nautical almanac, and reduced sight tables. Duh.

-Tiegan Hobbs

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