John Pederson Homemade Celestial Navigation General Overview: For the past several years, as a researchbased hobby, I’ve set out to learn and practice the “lost art” of celestial navigation. In the past, navigators would measure the angular heights of the sun and stars, using the information to plot their position on the globe (in degrees of latitude and longitude). With instruments I made from household materials, I’ve sought to pinpoint my location in the same way, drawing on techniques from various cultures around the world. The Polynesian seafarers, whom I researched as a history project, used their knowledge of star positions to navigate and colonize a third of the Earth’s surface without any instruments. Arab traders used simple ones to tell their latitude in the featureless Arabian Desert. European and American navigators, up until World War II, used highly accurate sextants to locate themselves to within a mile. I’ve researched all of their techniques to help me do the same. As a further challenge, American explorers used such instruments to determine the local time; this compensated for their inaccurate timepieces. I researched and performed this task as well; the technique uses the same navigation concepts. Constructing the Instruments: Building instruments at home of the same caliber as those of professional craftsmen is impossible, so I used various tricks to overcome the limitations of household items. Below is one of the first instruments I created, a quadrant. It can measure the vertical angle of an object above the horizon by using a plumb bob. When one tilts the quadrant a certain number of degrees upward, its plumb bob points to the equivalent number of degrees on the scale. In usage, I sight through the tube on top, let the string swing downward and settle, pinch the string to its place on the scale, and read the angle. I fitted the sighting tube, a straw, with a pinhole sight, allowing focus on both faraway and nearby objects simultaneously. (It’s similar to the pinhole camera used to produce the famous James Bond gun barrel sequence, where the target and the gun barrel’s rifling are both in focus.) Below is picture of the instrument, plus one showing me sighting the top of a tree.
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Transcript
John Pederson
Homemade Celestial Navigation
General Overview:
For the past several years, as a research-‐based hobby, I’ve set out to learn and practice the “lost art” of celestial navigation. In the past, navigators would measure the angular heights of the sun and stars, using the information to plot their position on the globe (in degrees of latitude and longitude). With instruments I made from household materials, I’ve sought to pinpoint my location in the same way, drawing on techniques from various cultures around the world.
The Polynesian seafarers, whom I researched as a history project, used their knowledge of star positions to navigate and colonize a third of the Earth’s surface without any instruments. Arab traders used simple ones to tell their latitude in the featureless Arabian Desert. European and American navigators, up until World War II, used highly accurate sextants to locate themselves to within a mile. I’ve researched all of their techniques to help me do the same.
As a further challenge, American explorers used such instruments to determine the local time; this compensated for their inaccurate timepieces. I researched and performed this task as well; the technique uses the same navigation concepts.
Constructing the Instruments:
Building instruments at home of the same caliber as those of professional craftsmen is impossible, so I used various tricks to overcome the limitations of household items.
Below is one of the first instruments I created, a quadrant. It can measure the vertical angle of an object above the horizon by using a plumb bob. When one tilts the quadrant a certain number of degrees upward, its plumb bob points to the equivalent number of degrees on the scale. In usage, I sight through the tube on top, let the string swing downward and settle, pinch the string to its place on the scale, and read the angle.
I fitted the sighting tube, a straw, with a pinhole sight, allowing focus on both faraway and nearby objects simultaneously. (It’s similar to the pinhole camera used to produce the famous James Bond gun barrel sequence, where the target and the gun barrel’s rifling are both in focus.) Below is picture of the instrument, plus one showing me sighting the top of a tree.
The second instrument I made is a sextant, an instrument that relies on the positioning of two mirrors to optically determine angles between objects. One looks into the device, swings the arm (or in my case, rotates the CD mirror) until the two objects’ images appear superimposed, and reads the angle on the scale.
Because the instrument requires a high degree of dimensional precision, I used Legos to provide precise right angles. The perpendicular pivot point is also difficult to replicate, so I used a CD case. (Everything that reflects light on the sextant must be perpendicular to the base, for not doing so causes the images one sees to be misaligned; this affects the angle measured.)
The tiny arc (only about 6 cm in radius) is impossible to read past integer degrees, so I drew and printed a vernier scale to theoretically achieve minute accuracy. (1 degree = 60 minutes of arc.) In practice, I could only read the scale to around 15 arc minutes, for extreme precision is needed to match the arc of the vernier exactly with the arc of the sextant arm.
The mirror edges are rough, for they are cut-‐up makeup mirrors. I removed half of the silvering from the mirror on the CD case – this allows me to see both sighted objects at the same time, one in each half of the mirror.
The above image shows the sextant in operation; I’m measuring the angle between my desk lamp and my globe. The central mirror on the CD itself (its edge is just visible on the right) rotates with the CD, allowing the angle it makes with the mirror on the CD case (very center of picture) to be easily adjusted. The light coming from the lamp (just outside the picture, to the right) is reflecting off the central mirror on the CD, reflecting again off the mirror on the CD case, and reaching the camera as an image of the lamp (visible in the CD case mirror). In this picture, the lamp appears to be visually lined up with the edge of the globe. By reading the angle that the central mirror was rotated, I can determine the angle between the two objects.
The third instrument I made is an artificial horizon. In the suburbs of Houston, I cannot see the horizon – there are way too many trees and buildings in the way. A sextant, without a plumb line, needs an external reference to measure angles. North American and Antarctic explorers solved this problem: by using a pan of mercury covered with a windscreen, they would sight the angle between a star and its reflected image in the tray. This measurement was double the angle between the star and the invisible horizon.
For obvious reasons, I didn’t want to handle mercury, so I used plain water in my horizon. The windscreen needs to have perpendicular glass panes (to avoid refraction error), so I used Legos again to get sufficient ninety-‐degree accuracy.
Also, the water’s surface needs to be completely shielded from wind, so pardon the unattractive masking tape – it’s making an airtight seal. Below is a photo of the reflected image it produces.
You can see both a flashlight and its reflected image in this picture of the artificial horizon (the triple dots in the clear plastic dish). If the flashlight were as far away as the stars, the bisector of the angle between the images would be the true horizon.
Calculator Programming:
The theory behind celestial navigation involves a lot of spherical geometry and trigonometric ratios, for one is calculating angles and distances on triangles that span the globe. In the past, navigators used precomputed tables to “reduce” their sights; nowadays, a scientific calculator can do the calculations directly. I learned calculator programming from a friend of mine, so I wrote the requisite formulas into
a program that prompts you for values, performs the calculations, and returns the information I need to plot my position on a chart.
The method of sight reduction I use to turn measured celestial angles into chart positions is called the “azimuth intercept method”. The method uses the sighted angle and the time of observation to produce a “line of position”, or a line across the Earth’s surface that passes through where I am. To find my position on this line, I need at least two lines of position to intersect.
I created a second program to plot the lines on the calculator’s graph itself. This makes it easy for me to find my location – I simply use the <Intercept> function to find where the lines meet. Below is a real intersection, or fix of my location, from two sextant sights that I did.
Another technique of sight reduction, based on the same principles, allows one to sight the sun and calculate the local time that the sight was taken – without the use of a watch. This trick was useful to American explorers with inaccurate timepieces.
I took the time sights with the quadrant, because using the sextant would have required dark solar shades (to protect my eyes from the sun’s image). I didn’t look directly at the sun; I used the sighting tube’s shadow to reverse-‐sight the sun’s altitude. By this, I mean that I aligned the sighting tube backwards; when I could see the light from the pinhole sight’s hole in the shadow, it meant that the tube was
perfectly aligned with the sun’s rays. (In the picture below, you can see the hole’s speck of light on my thigh, in the middle of the tube’s shadow.) I then read the angle.
I programmed the necessary trigonometry for the method into a third program; it uses the sight taken, your latitude, and the declination of the sun on that day to provide the local time. Because this “local apparent time” is not CST, I needed to add several corrections to check my accuracy.
Below is a picture of a sample calculation page – it shows the various corrections I make for each time sight that I do. I start by recording the sun’s angular height and the exact time I took the sight. (Recording the time is purely to determine my error – if I were actually trying to figure out the local time from scratch, I would obviously not have access to a watch!) I then record the day’s mean values of the sun’s declination and the equation of time. (These values are defined below.) Using my third program, I calculate the local apparent time based on my approximate latitude, the sun’s declination, and the recorded height of the sun. To this time (2:57:22 in the example) I add the equation of time value for that day (+00:05:11) to get the local mean time. If I didn’t have a watch and were truly lost, I would stop here; however, I’m in a city full of clocks and appointments, so I do some more corrections to convert that time into CST. By adding the correction for daylight savings time (+1:00:00) and compensating for my longitude west of the CST zone line
(+00:21:58), I get the time of my sight in CST, which I then compare to my watch recording to get an error.
Without a nautical almanac on hand, the sun’s declination and equation of time value are difficult to know precisely. (The sun’s declination is how far north or south of the equator the sun appears to be on a certain day of the year; the equation of time is a correction for the Earth’s elliptical orbit and its tilt, both of which affect the sun’s position in the sky.) To address this, I wrote a fourth program; it uses trigonometric equations to approximate these two effects, thus calculating the two values for any day I wish.
Below the sample time calculation is a screenshot of my declination/equation of time value calculation program.
Conclusions:
Through research, careful instrument construction, and programming, I am able to practice celestial navigation with respectable accuracy (by pre-‐GPS standards, at least).
I can sight the altitude of stars to within a fourth of a degree, using my homemade sextant and artificial horizon. For less precision, I can use my quadrant to measure angles to within a degree. Both instruments are made from household materials, too.
With the sights, I can use my own calculator programs to plot lines of position and achieve location fixes. I have actually located myself to within a tenth of a degree of latitude and longitude!
I can find the local time and CST using only a quadrant and a graphing calculator. My average error, decreasing with experience, is 2 minutes 20 seconds. That’s about as accurate as most people’s watches!
I now have a profound appreciation for the navigators of the cultures mentioned, made stronger with every measurement I’ve taken over the past three years. This pursuit has been truly intellectually fulfilling; I never dreamed it would take me this far, so I can’t wait to see where it will take me next.
This site teaches some basic theory behind celestial navigation, specifically how the stars appear to move as one’s location changes. Discusses other Polynesian techniques.
http://www.northwestjournal.ca/dtnav.html
This magazine article discusses the reconstructed and reanalyzed techniques of the North American explorer David Thompson. Provides several worked-‐out and explained examples of various sextant and navigational procedures. This is where I sourced the formulas for local time sights.