Navigation
By the stars and otherwise
Updated Series
On my last website, I had a series of blog posts about mapping (Mapping Adventures) and celestial navigation (Star Math). There was a lot of overlap and muddling in the information, so I have retooled it and included it all on one page. Please use the links to navigate your way through each of the articles, or have a scroll through.
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If I omitted your favorite joke or info tidbit in my streamlining, please let me know.
Where Am I?
Wherever you are, looking in all directions around you will help you determine where you are, in relation to your surroundings. But you’re probably here to learn about where you are on our big globe, so let’s talk about more universal directions.
Compasses
To orient ourselves in a common direction, most compasses point North, and North is marked on maps, so we can turn ourselves and our maps in that direction, and plot our route accordingly.
North
There are three Norths, believe it or not.
True North
North is considered by many to be the top of the world, because it is at the top of nautical maps, and sailing used to be the only international method of transport. Historically, however, most of the directions have taken a turn at being the popular top of a map, for various cultural reasons. For example, Mecca to the East was considered most important, so that area should go up top. Or North is on bottom because that’s where darkness is and who would want to go there? Then came European imperialism.
European sailors relied on Polaris, which they called “The North Star” to largely guide their night navigation, since it is the only relatively fixed point in the sky. It’s super important to navigation, and important goes at the top… Of course I have some Southern Hemisphere friends who have never even seen Polaris, so who’s to say that it’s really the most important factor?
From Earth’s perspective, Polaris is Astronomical True North. Geodetic True North is the land right under where Polaris sits (It’s not perfectly right under the star, but to such a small degree that we don’t have to worry about it). If you want the top of the world, this is it!
Map North
There’s a fun experiment where you pretend Earth is an orange, and you peel off its crust. Then you try to make that formerly round peel into a flat 2D representation of the round Earth. No matter how hard you try, either the peel will dome up, or the presentation of the globe will be distorted.
Every map has some level warping or distortion, so North isn’t always where it’s drawn to be, and sometimes not even perfectly at the top of the page, depending on the map’s printing.
Map North (or grid north) is where the arrow or grid lines on your map are telling you that North is. You’ll usually just rotate the map to line up with where North is in reality or on your compass.
Speaking of compasses, we’ll move on to the most bizarre North: The one that you fall prey to every time you pop open your compass.
Compass North
Earth is a planet, spinning around in a void full of harmful rays, emitted from a star that we’re just far enough away from that it doesn’t burn us alive, but close enough to that we don’t freeze to death.
So it shouldn’t come as a surprise that Earth has a shield of sorts. A geomagnetic field, generated by the movement of the earth’s liquid core. It protects us against charged particles that can damage the ozone layer that protects us from harmful space radiation.
How does this affect navigation? Magnetic or Compass North, points to the strongest point of this magnetic field (this location is also slightly shifting over time, but it’s minor, don’t worry about it).
Magnetic North is not in the exact same spot as True North, so your position on Earth determines how far off your compass will read. All you have to do is look up the Local Declination (how many degrees off your position is) online or in a book, before you head out, and adjust your compass so you don’t have to think of it again. If you’re using a compass app, you can just set it to the True North option.
Types of Wayfinding
I have always understood that compasses point generally Northward, or that East is in the direction of sunrise, but… I never really knew how to use that information. I just felt like “hey, we’re going North. What a thrill!” Eventually I discovered three different ways to make my way around:
Method #1: The Course Plotter
Works when you have directions to a specific location:
1. Say you’re a pirate looking for a great tea shop that was recommended to you.
2. You’ve been told (or maybe you have a map) that the shop is 30 paces West.
3. It’s late afternoon, so you turn toward sunset and start walking!
Method #2: The Levelheaded Wanderer
Works when you have a starting point you need to get back to:
1. Note the surroundings of where you start
2. Pick a major long running “hand rail.” A hand rail is a long, visible landmark like the road you’re on (if you’re in a city, get the street name too!), a river or a long, straight fence line.
3. Start heading out perpendicular from your starting from, noting the direction you’re heading in. For this example, let’s say you’re starting off Westward
4. Squirrel around the city/forest as much as you want.
5. Once you’re done, you just turn in the opposite direction that you started in and head back to your hand rail. In this case, turn East and walk until you get back to the road you started on
6. Walk along your handrail until you see something that’s familiar to your starting point
Method #3: The Fastidious Record Keeper; or, Dead Reckoning
Most of us will be more like the Levelheaded Wanderer, but if you want to really keep control over where you are, you can:
1. Track which direction you head in, the duration, and make a note of every time you change directions. If you also happen to note your surroundings as you go, this is a great way to make a map!
2. When you are ready to head back, you can either retrace your steps, or head out to the handrail, but this time you’ll know which direction to head in to find your starting point, and for roughly how long!
I feel like most people hear about dead reckoning in connection to Christopher Columbus who was… not a good navigator. This doesn’t mean dead reckoning is a poor navigation method! Far from it. Columbus just used it poorly, in addition to trying to experiment with celestial navigation which he was much worse at, not knowing much about it. A cautionary tale: Try things at home before using them in the middle of the ocean.
How it works for sailors: Instead of using the stars to navigate, you note the direction in which you’re travelling, and record for how long and at what speed, then calculate the distance of travel, noting it on your map, if you have one. It will definitely get you in the right general location.
The calculation is: Distance = Speed x Time
Now we know how to get around, let’s talk about how we note where we are, more precisely.
Coordinates
Ever looked up a location and seen something like this: 41.2565° N, 95.9345° W or this: 41° 15' 23.4", - 95° 56' 4.2"? These numbers are telling us how far the location is to the north or south (Latitude), and east or west (Longitude).
Latitude
Latitude measures how far north or south a point is on Earth. On a map or globe, it’s drawn like Earth is wearing a horizontal-striped shirt. Imagine the core of Earth. Lil’ buddy:
And now imagine Earth’s bellybutton: The exact center of the world (basically, I am aware that the Earth is super lumpy and the core is liquid, but apparently math has figured out some “good enough” measurements that make this allll okay).
Drawing a straight, horizontal line from the bellybutton to Earth’s surface, you get The Equator or 0° latitude.
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​Drawing another line out at an angle to Earth’s surface, gives you another line of latitude, parallel to The Equator.
We name these lines based on their angle in relation to The Equator. Since each line of latitude is parallel to the others, they are referred to as Parallels (we hear a lot about parallels when it comes to historic American wars, because they were often fighting about border disputes).
These angles are how we refer to how far North or South we are on the globe.
Longitude
This number notes how far East or West we are, starting from a universal point. Believe it or not, it’s calculated using time, more specifically time zones. This necessitates we first talk a bit about time.
The Artifice of Clocks and Calendars
The history of clocks and calendars is so significant that it has its own subdivision in the Library of Congress book organization system. There are two major things that wonk up our ability to accurately track time according the sun: Year Lengths and Daylight Saving Time.
Leap Years
If you’re really keeping track of the sun, you’ll notice that each day is a liiiittle bit off. By the end of the year, you’ll note that a year, in our common calendar, is actually 365.2422 days long. Different calendar systems handle this differently, but the common Julian calendar accounts for that extra quarter day, by having three years of 365 days, then a year of 366. There are a few other rules, but that’s the jist.
Daylight Saving Time
Daylight Saving Time is the practice of shifting the time forward, or backward one hour, depending on the season. There’s actually an interesting background to DST.
To the best of my research, back in 1784, Benjamin Franklin wrote a satirical (read: hello, it was a JOKE) essay, entitled “An Economical Project” suggesting that rising with the sun, rather than using artificial means of lighting, would save Parisians tons of money on candles. He went on to jokingly detail how this could be enforced.
Bop forward to 1895, New Zealand where entomologist (he was a bug man) George Hudson proposed a two hour time shift, so he could get in more daylight hours after work for bug hunting. Because that’s not at all selfish.
1902, England, builder William Willett (with props from Winston Churchill and Sir Arthur Conan Doyle) felt that we could save so much productive daylight, for things like horse-riding, by shifting time around. Parliament didn’t go for it. Because why would they.
1916 (World War I), the German government starts trying to save more energy… AND THEY DID IT. Of course, this move influenced most of the countries involved in WWI to do the same, with the US jumping on board in 1918.
Now, of course, we don’t depend so much on coal to fuel our lives, and the shift in time doesn’t actually save much (or any) energy (depending on where you live, of course). Some places have reverted back to not observing DST at all, and some places never observed it to begin with. This makes it difficult to know what natural time it really is!
Time Zones
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Looking at Earth from the top, if it’s noon where I am, and midnight on the exact opposite side, then it follows that halfway ‘round, it must be 6pm and 6am, respectfully. That continues to get subdivided into hourly increments, resulting in zones of time. This is how I know that I can pick up the phone in the Pacific Northwest at noon my time (Local Noon), and call my relatives on the East Coast of the USA, and they will be three hours into the future.
But I’m not so egotistical as to think that the world should base all of timekeeping relative to where I happen to be at any given time. So time got standardized, and the world got sliced into specific, wiggly wedges of time.
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Though the time zones fit within these broad lines, I have grossly oversimplified exactly how they are drawn in the image above. The details of where a time zone begins and ends are determined largely by property boundaries, and boundaries are decided by what? Politics. The answer is always politics. My home state in the US is actually divided in half, one side in one zone, the other an hour ahead. Craziness.
We also have to remember though, that the world is in constant motion. Technically, if I travel West a few miles, I’ve technically gone a few minutes or seconds back in time.
These time zones are noted in UTC (Coordinated Universal Time. I know, that acronym seems wrong. It seems to be a compromise between the US’ CUT and French’s TUC (Temps Universel Coordonné) because humans cannot manage to amicably coexist without shenanigans). We just count how many hour slices we are away from the Prime Meridian in Greenwich, with movement toward the West being noted in negative hours, and movement toward the right being in positive hours. But why Greenwich?
Prime Meridian
Have we already talked about politics? Yeah, that again. Literally any line could have been drawn ’round the world, through the North and South pole and we could have called it the spot at which we base time–called the Prime Meridian. But we picked Greenwich, London, England. And when I say ‘we’ I really do mean a group of 26 delegates from around the world, during the International Meridian Conference in 1884, decided that this was the most agreeable spot. Most of England’s sea charts were already based on it, and the US had accepted it as its prime meridian. So, much like Daylight Saving Time, I guess this is one that we all agreed on!
The Chronometer
Once upon a time (hah!), clocks were not so fancy. Between transporting a very accurate clock from Greenwich to my launch, and the pendulum-like motion of the ship rocking on the waves, a clock would have been an unpredictable amount off from what time it actually was in Greenwich.
In the early 1700’s British government started a competition of sorts, giving rewards to people who could create an accurate marine clock. Several attempts were made, but the most successful of them were the chronometers made by John Harrison. He was a clockmaker and carpenter, and he submitted three chronometers over his lifetime.
We didn’t have a fantastic system for pegging a location at sea until 1762. Later than I would have thought. There’s no wonder that world maps were a little wonky!
Visualizing Longitude
Unlike the time zones, however, longitude is noted in degrees, much like slicing up a circle. Because we’re slicing up a circle.
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Looking at the world from the top again, it’s split in degrees from 0 to 180 in the Easterly and Westerly directions.
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Being in the Pacific Northwest, I’m at about -122° or 122°W.
Let’s say I don’t have a GPS and I need to know where I am. What shall I do?
Calculating Longitude
You will need:
- Your current time
- The current time in Greenwich (if you know your time zone, you can just make the calculation)
Right now, it’s 11:52am where I am. A quick Google search tells me that it is 6:52pm in Greenwich. But I also just entered into Daylight Saving Time. So though the clock would lead me to think I am -7 hours from Greenwich Mean Time, I am, in fact -8 hours GMT. This would get me a ballpark longitude. I’ll talk about methods for exact longitude in a moment.
Then we plug into the equation:
Longitude = -(8 x 15°) = -120° or 120° West
Therefore I’m somewhere about 120° to the West of Greenwich!
More specific calculation
If you want to know your exact longitude, you need to know how many hours, minutes and seconds your local time is off from Greenwich. I did mention before that time zones are nice hour chunks so our brains can more easily parse the movement of time but… there’s minutes and seconds difference between different locations. The only real way to figure this out is by using an instrument to figure out the exact time that the sun is at its peak height in the sky, like a gnomon or astrolabe.
I did this experiment with a homemade gnomon and astrolabe. Let’s say that I observed the sun to be at its highest height at exactly -7hr 45min off from GMT. I’d calculate it this way:
Longitude = -[(8 x 15°) + (45 / 60 x 15°) ] = -(120° + 11.25°) = -131.25° or 131.25° West
Degrees (°), minutes ('), seconds (")
Expanding on the sun appearing to move 15° in an hour, by that same math/logic, it appears to move 1° every 4 minutes. Now… I’m sorry about this, but when you subdivide a degree, it’s split into… minutes. Degree minutes, not time minutes. So the sun appears to move 15' in one minute. When you subdivide a degree minute, it becomes a degree… second. So the sun appears to move 15' in 4 seconds, therefore moving 1" in 1 second.
131.25 is the Decimal Degrees version of the longitude representation. If I wanted to look cool, or use it for other purposes, I could note it as:
131° 15' 0" or 131 degrees, 15 minutes, 0 seconds.
If I was eagle-eyed enough, we could also calculate seconds, but honestly, you’ll be close enough without them, if it’s just for a roughing it, or for fun navigation jaunt!
Latitude
NOTE: This is a very broad overview. My past explanation was more detailed, but a bit confusing. If you want more nuts and bolts, I recommend David Berson's Celestial Navigation: A Practical Guide to Knowing Where You Are, for a plain-speak rundown of precise calculation.
Definitions
Sextant
A very fancy, compact protractor that we use to measure the angle between us, the ground and a heavenly body.
Ground Point
I called this "star's house." The ground point is the area directly below where a heavenly body is in the sky, mapped onto the Earth. If the star is right overhead (the point above the observer's head is the Zenith), then you are standing in the star's house. If we take a measurement with a sextant, it would read 90°
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Nautical Almanac
There is actually a book of charts that contains the Ground Points of more celestial bodies than you can think of, at any time of any day throughout the year.
Circle of Position
If we walk 100 feet away from the star's house (ground point), and take an angle measurement, it will be something less than 90° for example, 70°. It doesn't matter which direction we walked away from the ground point, if it was the same distance, the angle would be 70°. This forms our circle of position.
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Bearing
The direction we're heading. Knowing our bearing helps us determine where we are on the circle of position.
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General Celestial Navigation Method:
1. Pick a heavenly body
2. Using a sextant, measure your angle from the body
3. Note the time
4. Calculate how far away you are from the body's projected position on Earth. If using the sun at local noon, the formula is basically: Latitude = 90 – Sextant reading at local noon + solar declination
5. Use a compass to decide what direction you're pointed in to determine your precise location
Visualizing the Star Math
I've buried the lead a little here, but Star Math is just very fancy trigonometry.
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Why all of this works requires a lot of explanation! I once went through it all very sloppily, but rest assured that with a lot of jazz hand and diagram drawing, it all makes sense!