Celestial Navigation

Transatlantic: Day 11

Our friends on land tell us that the weather systems around us have normalized!

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With this glorious information, we await the 8pm transmission of Weather Faxes and anxiously download the information.

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The 1020 line has moved back towards us, the weird gales are gone, and the Azores High seems to dominate the North Atlantic.

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Looking at the wind/waves chart, you can really see how the weather patterns have normalized. There is a very nice and consistent flow of circulation in the North Atlantic. Winds are steady and seas are even. The weather is here! It is time to turn North and make our way to Westerlies!

How To Cross an Ocean: Navigation

You have sails, rigging, and steering; congratulations, you have a sailboat and can go anywhere. Where should you go?

This is where navigation comes into play. When you set out to cross an ocean, you need to know where you are going. Navigation can be as basic as looking at the sun and stars, or as technologically involved as GPS navigational equipment.  

In the most basic forms, a compass can give you an idea of your direction, a time piece will give you an indication of your longitude, and a sextant can be used to measure your latitude. Paper charts can identify dangerous areas and give you guidance to reach your destination.  

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Many people view paper charts as they view a chart plotter, but this is not the case. A chart will not tell you where you are or where you want to go; it merely tells you where things are located in the world, you need to do the rest! This lack of convenience is out weighed by the fact that a paper chart will never "not work". You will never open a chart to find that your subscription has expired, or it's battery is low, or that an update has occurred and you need to log in to unlock your chart. A paper chart will always tell you where land masses are located as well as hazards and depths. 

Electronic charts are convenient, but can decide "not to work" when you need them most. We personally like to have electronic charts available to us because at any point we can look at them and know where we are, how fast we are moving, and where we are going. We understand that this is a convenience and also rely heavily on paper charts with traditional navigational equipment. I use a sextant to take a noon sight where I then calculate our position. Then I plot our position on the paper chart and record the data in our log book. After all that, I compare my findings with the electronic charts and see how close I was to the "true value". During the rest of the day, we enjoy the convenience of the electronic charts. One of our favorites is when we are approaching a waypoint. We will use the electronic charts to know when we reach that point and then use it to set our new heading. 

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Yes, we rely heavily on them for their convenience, but should they fail, we know how to navigate without them and how accurate we really are.  

Electronic charts are "Really nice to have" but not necessary. Paper charts and the equipment to use them is mandatory to safely get you across an ocean. 

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While actual navigational equipment is critical to a safe passage, there is always the "Oh crap!" situation where everything goes wrong and your goal is to simply make it to shore. Your paper charts are gone, your log book washed overboard, and the waves ate your sextant. This is where situational awareness becomes very important. Imagine you are in the Atlantic Ocean and you just want to get home. You know you are close to the East Coast of the United States. Who cares if you show up in Florida or Maine, just head West! You will come upon land and can find a sea buoy to guide you into a port.  

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What if you have a Captain Ron moment where the compass falls overboard? This is where general awareness is important. The Sun rises in the East and sets in the West. By night, the Moon follows this same pattern and Polaris sits squarely in the North. The higher Polaris is from the horizon, the further North you are, and using the Sun and Moon you can find your way West to get back to a shore. The same holds true in any ocean in the world. The stars can be used as guides through the night sky and the Sun and Moon can guide you for East and West. 

In a moment of desperation, sail in the general direction of the largest landmass you want to find and deal with landfall as you get closer. The important thing is to make it back to shore where you can then get help and get food and fresh water to survive. 

The Goal of Celestial Navigation

GPS is a wonderful creation that has raised our expectations in positions to unrealistic but attainable levels. It is not uncommon to see a GPS touting an accuracy of a few feet! You might want to achieve these same results with a sextant, only to have your dreams dashed in the waves.

The goal of accuracy for a sextant is 25 nautical miles. Yes, not feet, but miles. While a GPS is considered good if it can place you within 10 feet of your true position, a person calculating their position with a sextant on a boat at sea is considered good if they can calculate their position to be within 151,903 feet! 

This might sound ridiculous, but the reasoning behind it is rather sound. Celestial Navigation is not to plot your position and get you to slip between a reef and a wreck on a chart, that is the realm of visual navigation. Celestial Navigation is to get you to your next landfall. Land can be spotted from very far away, and if you can get close enough to see it, you can then sail towards it, letting visual navigation take over from there. 

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When calculating your position, you can use very VERY precise measuring techniques which will let you calculate your position down to under 400 feet. The problem is this sort of refined measuring is done on land, which is not moving, and at rest, which is not sailing. The measurements can then be repeated daily to finally work down the exact numbers and find your precise position. 

On a yacht, you are sailing forward, so your measurements are off to begin with. Next, you are on a pitching deck, being rocked side to side as you ride up and down waves. You have to hold a sextant perfectly stable while being tossed around as your altitude changes constantly!  

If you take a course on celestial navigation or read about it in a book, it will typically have the calculations carried all the way down to the second (of time and location). 1 second of time is 1/60th of a minute. 1 second of latitude & longitude is 1/60th of a nautical mile in latitude, and 1/60th of a nautical mile at the equator to nothing at the North Pole. If you try to carry your calculations down to the second, you will find that your not going to gain much in accuracy for the amount of additional work you need to put in. It is best to take all of your recordings and calculations down the the minute (of time and position). 

Think about it, when you take your noon site and record the time. If you record to the second, you will then have a very accurate reading. If you take it to the minute, you could be off by as much as 59 seconds! But what does 59 seconds come out to be in the grand scheme of things? The boat is moving, you are pitching around, and if all you need to do is get a general idea of where you are, why do all the extra math?! 

If you take your noon site at 16:00 vs 16:01, the difference in your longitude will be minimal

 16 : 00
  -12 : 00

   4 : 00
x15 x0.25

60*0'W 

 

 16 : 01
 -12 : 00

  4 : 01
x15 x0.25

60 + (0.25x60) 

60*15'W 

What this means is that your longitude is going to be calculated as one of these two positions. If you were to measure the time of the noon site down to the second, your answer would fall somewhere in between 60*0'W and 60*15'W. Yes, that would be a much more accurate calculation, but you can assume that your true position is somewhere between 0' and 15', which means that you are not that far off!  

Imagine that the true time of the noon site was 16:00:30, this would mean that the true position would be around 60*07'30". Your calculations would only have been around 7.5 nautical miles off. Not bad for skipping an entire section of calculations! 

You might be wondering how you can verify what your true position is out at sea and how you would then calculate your error, and the answer just makes it more logical to stop the calculations at the minute. You check your calculated position with a GPS reading of your present coordinate at that time. The GPS, which is accurate down to a few feet, will tell you where you actually are; so why go through all the extra headache and math to figure out your position to a few miles closer when at the end of it all, you will verify it with a GPS? 

In practice, I have found that I am usually within 4nm of our true position. This is far lower than the acceptable 25nm radius of error, and this lets me know that should all the GPS's in our yacht fail, I can trust my calculated coordinates to get us to land. At first, you might find that you are way off, but with practice, you will zero in on a very accurate noon site while only taking your measurements and calculations down to the minute. 

 

Theory Behind Latitude

Latitude is your position on the surface of the Earth in a North/South direction. Unlike longitude, which is pinched together at the poles and spread out at the equator, latitude is a set and constant distance between degrees.

Each degree of latitude is 60 nautical miles, and each minute of latitude is 1 nautical mile. This makes calculations of distance when traveling up and down the coast of the United States very easy to do in your head! 

In a previous post, we discussed the simple math to find your latitude using a noon site and none of the reasoning or theory that went behind it. Now, we will do just that. 

The easiest way to confirm that your latitude calculations are correct is to check your work at night by sighting Polaris. Polaris, also known as the North Star, will not let you calculate your longitude, but it is a very easy latitude indicator. The angle from the horizon to Polaris is your latitude. This is because Polaris sits practically directly above the North Pole, and your angle to it is equivalent to your latitude. So, if you are unsure if your calculation of your latitude from noon was accurate, double check your work by sighting Polaris at night and it will tell you right away if you are one the right path. 

The Sun, on the other hand, is not as obvious to calculate. As you know, the sun climbs higher in the sky during summers and stays lower on the horizon during winters. This is caused by the Earth having a tipped axis, which means that the sun doesn't sit directly over the equator. Instead, the sun is above the equator during the summer and below the equator in the winter. This change in position to the equator is called Declination. 

Now, the calculations to find your latitude are rather simple. You measure the angle of the sun to the horizon and then substract it from 90. This number is then added or subtracted by the declination to give you a result which is your latitude. The math is pretty simple, but how do you know if you should add or subtract? 

The decision is simple and based on the relative position of you, the sun, and the equator when you took your noon site. If the sun is between you and the equator, then you will add the declination. If you are located between the sun and the equator, then you will subtract. 

As stated in the simplified version, if you are unsure, simply do both and figure out which one gives you a more reasonable answer. If you have no idea where you are; as in, you woke up one day floating on a raft with only a sextant, a current Nautical Almanac, and an accurate time piece that is set to UTC time (a very likely scenario) you could easily do both (adding and subtracting) to figure out your posible latitude coordinates. Once the sun sets and the stars come out, you could then site Polaris and see what your actual latitude is. The correct answer could be used to decide which mathematical process to follow and used to calculate your position on the Earth as you slowly drift along this giant ocean! 

From experience, I have yet to subtract the declination from my reading, as you would only do this if you are very close to the equator. If you are sailing anything higher than say, 24 degrees North, you will be adding the declination in your calculations. 

The Theory Behind Longitude

Your coordinates while at sea depend on two dimensions, Latitude and Longitude. Latitude is your position on the surface of the Earth based North/South, while Longitude is your position on the Earth based East/West.  Previously, we have discussed the math and simple calculations to find your Longitude without going into the theory behind the calculations.

Longitude is time dependent, and longitude will also make time zones make sense as well. As with before, a Earthcentric view of the solar system makes longtitude easier to explain, but do remember that it is the Earth that revolves around the sun (Heliocentric Solarlarsystem). So, back to the Earthcentric view:  The sun revolves around the Earth in 24 hours, and the Earth is a sphere.

As a sphere, the earth can be divided into degrees, and we all know from geometry class that a sphere (and a circle) is divided into 360 degrees. 

This means that the sun revolves around the entire Earth in 24 hours, and therefore makes the journey of 360 degrees in 24 hours. This can be simmered down to a speed of 15 degrees per hour, and 0.25 degrees per minute of time. This is where the "Hours x 15" and the "Minutes x 0.25" comes from.

Now, the sun, while visible from sunrise until sunset over a vast expanse of the Earth, is only actually directly overhead in one very particular position. This position is called the "Meridian" and it is where the sun is directly overhead, also known as "Local Aparent Noon". Noon is a very important part in this story, and leads to the reason that the sighting is called a "Noon Site"

When viewed from the suns perspective, the Earth is slowly turning beneath it, and there is only a small sliver of Earth that is located directly under the sun. This small sliver is called the Meridian and it is the small segment of Earth that is currently experiencing "Noon". Every minute, this meridian moves 0.25 degrees to the West, slowly making its way around the Earth until it reaches its starting point for the day.  

The starting point, which is degree 0 and known as the Prime Meridian, is located over Greenwich, which gives the reason behind the name of that time zone of Greenwich Mean Time, also abbreviated as GMT. In the name of science, and to move away from any places name, this very same meridian and timezone is also called UTC which stands for Universal Time Coordinated.  

Now, you are not standing on the sun looking down on the Earth slowly rotate under you. Instead you are standing on the Earth, watching the sun slowly rise in the East, move directly overhead, and then set in the West. At some point in the day, the sun will be located directly overhead, and that very moment will be when the sun's meridian is shining down on your little sliver of Earth. At this point, the sun is at it's zenith (highest point) in the sky and this time is your local noon.  

You don't need a sextant to figure out your longitude, only a clock and a shadow, but a sextant does help. 

When your shadow is pointing directly at True North (not magnetic North) the sun has made its journey from 0 degrees to be directly overhead of you. The time it took to reach you is proportional to the number of degrees you are from 0 degrees. So, if it took exactly 1 hour for the sun to be directly overhead, then you are exactly 15 degrees to the West of 0 degrees. This would mean that your longitude is 15W.  You would also be located in the next timezone, known as UTC-1.

If your local noon occurs at 1 hour and 1 minute after the sun has left 0 degrees, then you would be located at 15.25 degrees West of the Prime Meridian. Now, you won't see coordinates listed as decimals, instead they are listed in the format that is Degrees:Minutes:Seconds; where 60 seconds is 1 minute, and 60 minutes is 1 degree.  (it's easy to think of it in the same format as time, Hours:Minutes:Seconds, but since its coordinates, the Hours are called Degrees). 0.25 degrees can be multiplied by 60 to convert it into minutes: 0.25 x 60 = 15 minutes. This means that if your local apparent noon occurs at 1 hour and 1 minute after the sun has left 0 degrees, then your longitude would be 15 degrees and 15 minutes West (also written as 15*15'W).

Now, thinking of the time as "Time since the sun has left 0 degrees" may be helpful at first, it doesn't help with the actual calculations. To make the math easier, simply have a 24 hour clock set to UTC time and look at that clock at your local apparent noon. 1 hour and 1 minute after the sun left 0 degrees would be 13:01. If you are located further West, local noon will occur later on the clock. If you are located in the Eastern Hemisphere, then your local noon will occur before the clock says 12:00.

I know this might seem rather simple, and that is because it is. The sun moves across the sky at a set and specific speed of 15 minutes of longitude every 1 minute of time. If you check the time of your local noon, you can easily find your longitude. 

All you need to do is measure the time difference from your local noon and Noon of UTC. The difference in hours is multiplied by 15, and the difference in minutes is multiplied by 0.25.  

If your local noon occurs at 16:55, then your difference from 12:00 is 04:55.  
04 x 15 = 60 degrees
55 x 0.25 = 13.75 (the whole numbers are degrees, the decimal is going to be minutes) 

13.75 = 13 degrees, 0.75 x 60 = 45 minutes

60 degrees + 13 degrees + 45 minutes = 73*45' W

 

If your local noon occurs at 08:47, then your time difference from 12:00 is 3 hours and 13 minutes (03:13). 
03 x 15 = 45 degrees
13 x 0.25 = 3.25

3.25 = 3 degrees, 0.25 x 60 = 15 minutes

45 degrees + 3 degrees + 15 minutes = 48*15'E

 

Just that easily, with an accurate measure of time, you can find your longitude on this large round Earth. 

There was mention of timezones earlier, and this is how they come into play. Every hour, the sun is generally overhead an area of 15 degrees. So, at 12:00 UTC, the sun is over the area of 0*W to 14*59'W.  
At 13:00, the sun is over the area of 15*W to 29*59'W
At 14:00, the sun is over the area of 30*W to 44*59'W

Every hour, the sun has moved over 15 degrees, so the Earths 24 timezones are divided up into 15 degree increments. Every hour, the sun has moved 15 degrees West, and a new timezone is experiencing their Noon.