# Navigating by the Sun

September 12, 2016 2:02 AM Subscribe

I was messing about while building a floor on my boat and got distracted by a sunbeam (because I am very easily distracted) and started wondering how much information could be determined by this pattern of sunlight.

To expand on this a little, given the pattern of sunlight seen here, and the words scribbled on the floor what can you determine about the location and orientation of the boat.

Assumptions:

The portholes are perfectly circular.

The boat is completely stationary (it's actually grounded at this point)

If you had more information (size and location of portholes say?, another sunfix?) what more information could you determine.

To expand on this a little, given the pattern of sunlight seen here, and the words scribbled on the floor what can you determine about the location and orientation of the boat.

Assumptions:

The portholes are perfectly circular.

The boat is completely stationary (it's actually grounded at this point)

If you had more information (size and location of portholes say?, another sunfix?) what more information could you determine.

If you don't know what time it is and don't know the heading/orientation of the boat, a single sunfix gives you the angle of the sun above the horizon. You could get it by measuring the a and b lengths of the oval or using a measuring tape to get the rise and run distance from the porthole.

Having the angle of the sun above the horizon would through geometry tell you ... that you're within a (northern/southern) band of latitudes where you can see the sun at that angle, at some time in the day.

Getting enough sunfixes would let you get your latitude by fitting a curve in the space angular measure verus time, where you could deduce the maximum angle at high noon, even if you don't get a sunfix at that time. But you need a timepiece, even if the timepiece doesn't know what time it is at some port.

Or a single sunfix at high noon would give you your latitude. And it would allow you to draw a vector in the direction of North.

To get your longitude, you need to set your timepiece's time at some port. Then later if you're on the equator you use your porthole-based-sextant to measure the angle of sun above the horizon at time t and that gives you your longtitude. If you're not on the equator you need a tiny bit more math, but you can still get your longtitude.

It's basically a sectant, in other words, you still need a marine chronometer.

posted by sebastienbailard at 3:38 AM on September 12, 2016 [1 favorite]

Having the angle of the sun above the horizon would through geometry tell you ... that you're within a (northern/southern) band of latitudes where you can see the sun at that angle, at some time in the day.

Getting enough sunfixes would let you get your latitude by fitting a curve in the space angular measure verus time, where you could deduce the maximum angle at high noon, even if you don't get a sunfix at that time. But you need a timepiece, even if the timepiece doesn't know what time it is at some port.

Or a single sunfix at high noon would give you your latitude. And it would allow you to draw a vector in the direction of North.

To get your longitude, you need to set your timepiece's time at some port. Then later if you're on the equator you use your porthole-based-sextant to measure the angle of sun above the horizon at time t and that gives you your longtitude. If you're not on the equator you need a tiny bit more math, but you can still get your longtitude.

It's basically a sectant, in other words, you still need a marine chronometer.

posted by sebastienbailard at 3:38 AM on September 12, 2016 [1 favorite]

Also, with a calendar and map of the heavens, you can figure out where you are. At local midnight on June 1, a given constellation is precisely overhead only at one point on earth. Similarly, with some starfixes and a knowledge of the date and local time you can figure out where you are. Basically celestial navigation.

posted by sebastienbailard at 3:45 AM on September 12, 2016

posted by sebastienbailard at 3:45 AM on September 12, 2016

Contrary to the twitter comment a straight line between the centre of the two spots will only point east-west at one particular time of the day.

posted by Mitheral at 5:09 AM on September 12, 2016 [2 favorites]

posted by Mitheral at 5:09 AM on September 12, 2016 [2 favorites]

In John McPhee's book Looking for a Ship, there's a story about a ship captain who woke up from a nap and the sunshine through the port in his cabin told him that the junior officer on watch had turned the ship 180 degrees off course by trusting a defective compass and failing to think about where the sun should be at that time of day at that location.

posted by Bruce H. at 5:15 AM on September 12, 2016

posted by Bruce H. at 5:15 AM on September 12, 2016

As the speed the sun moves is known, if you give us the distance between the porthole and the plane I

(When I say "we" I mean "somebody smarter than me").

posted by Leon at 6:26 AM on September 12, 2016 [1 favorite]

*think*we can calculate the size of the porthole.(When I say "we" I mean "somebody smarter than me").

posted by Leon at 6:26 AM on September 12, 2016 [1 favorite]

The spot of light on the deck would have a shape of an oval (allowing for a circle to be considered a special case of an oval) which would give you the angle of the sun relative to the porthole, but since the sun's bearing, as well as the angle above the horizon, changes all day, this would be slightly difficult to extract; you might get away with measuring two lengths of the oval, vertical and horizontal (parallel to the plane of the porthole), and the angle of your deck in two dimensions (which is another variable to complicate all this). You'd have to feed in the ship's measured bearing from the compass or whatnot.

In short, this is simpler to get information from in a fixed building with a porthole at a fixed angle. With a maneuvering vessel with a rolling deck? Fuhgeddaboudit. It would be humanly impossible to measure all the necessary information at once to produce a useful result.

If you had a gyro-stabilized compass-driven sundial which always pointed south/north (as appropriate for the hemisphere), you could get the local time all day, for what it's worth, and you could use a round window in place of a gnomon if you want, I guess.

posted by Sunburnt at 7:21 AM on September 12, 2016

In short, this is simpler to get information from in a fixed building with a porthole at a fixed angle. With a maneuvering vessel with a rolling deck? Fuhgeddaboudit. It would be humanly impossible to measure all the necessary information at once to produce a useful result.

If you had a gyro-stabilized compass-driven sundial which always pointed south/north (as appropriate for the hemisphere), you could get the local time all day, for what it's worth, and you could use a round window in place of a gnomon if you want, I guess.

posted by Sunburnt at 7:21 AM on September 12, 2016

*Emergency Navigation*goes into the minimal information and ad hoc devices to make a reasonable estimate of your position in a variety of situations. But I think a bit more information is needed than a marked shadow, a compass heading and heeling angle at the minimum in this case.

posted by sammyo at 8:18 AM on September 12, 2016

What can you learn from a sun dial (which is approximately what you have)?

Given enough time and sunny days, you can determine the points of the compass, the approximate latitude, and the local sun time. If you have a separate source of time, you can determine your longitude.

posted by SemiSalt at 10:34 AM on September 12, 2016 [1 favorite]

Given enough time and sunny days, you can determine the points of the compass, the approximate latitude, and the local sun time. If you have a separate source of time, you can determine your longitude.

posted by SemiSalt at 10:34 AM on September 12, 2016 [1 favorite]

If you had a Sextant then you could do the classic pose for photos.

posted by ovvl at 6:12 PM on September 12, 2016

posted by ovvl at 6:12 PM on September 12, 2016

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posted by colfax at 2:29 AM on September 12, 2016 [2 favorites]