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. 

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. 

The Value of Effort

Sport sailing is all about getting the most out of every puff of wind. Coastal sailing is about getting from one place to the next as quickly and comfortably as possible. Ocean sailing is about making it to the other side.

While the goal in all three types of sailing involves getting somewhere, and quickly, the first two categories can be viewed as sprints where the latter should be viewed as a marathon.

Ocean sailing is an endurance sport, there is no way around it. Every action you take requires energy, and you have to be able to keep up that pace for the entire ocean! This leads to different decision processes as to sail selection and trim, as well as course.

If the winds are light, but you have clouds building around you, you are presented with a few options:

Option 1 would be to take down the working sails and put up the light air sails. When the winds change, then take down the light air sails and put the working sails back up.

Option 2 would be to grab a book and wait for the stronger winds to reach you so you can keep sailing with the sails you already have set.

This choice came up on our third day of ocean sailing, when our crew member got frustrated that we were ghosting along at 2 knots on a broad reach under mainsail and staysail. He suggested that we swap the sails out and put up the drifter. I attested that this would require a lot of energy and that it would be the same result in the end: we would move slow.

Being how he is rather Type A and in a rush all the time, I told him that we would do it as a learning exercise, to see when something is worth the work.

I was relaxing and reading my book as we ghosted along at 2-3 knots and recommended that he do the same. Instead, we all got up, sleepy and tired since we just finished our night watches, and swapped the sails over. The entire conversion took about 15 minutes to complete and a fair amount of effort. The light air filled the drifter and we began moving along once again, at 2-3 knots.

So, was it worth all that effort?

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.  

Reefing When Ocean Crossing

The biggest distinction between ocean crossing and coastal sailing is the lack of help. If something breaks close to shore, there are plenty of people around who can help you. They will tow you back to a marina where an army of skilled labor exists to get you back out there sailing! In the ocean, if something breaks, you better know how to fix it yourself with the supplies you are carrying on board your yacht because no one is coming to help you!

This lack of aid is precisely why you should reef early. If you see a storm coming, don't wait for it to hit you to then start adjusting the sail plan! Reef now and wait for it to pass over. Once it has passed and completely cleared you, then shake out the reefs! This will ensure that you and your gear are exposed to minimal risk during the ocean crossing.

Maddie and I sleep in the V-Berth up in the bow and our third crew member sleeps in the quarter berth. At night, we rotate watches accordingly. Maddie has first watch from 9 to midnight. I have second watch from midnight to 4:30AM and the third crew member has the morning watch from 4:30AM until we all get up. Since we are up in the bow, we hear the sound of the stem cutting through the water, and we can also feel how much we are heeling over. I have frequently poked my head out of the forward hatch to see dark and stormy looking clouds all around us and notice that we are full sail! I assume that the crew member on watch is keeping an eye on them and tracking their movements with the compass. A storm that is not coming at you is not a storm you need to worry about. Then we pick up speed and begin to heel over to an extreme angle and I hear a desperate cry from the helm.

"It's time to reef!"

Yes, it is time to reef, and it was time to reef a long time ago! The two of us run up to the mast and begin taking in the sails while Maddie works the sheets and helm to keep us safe. I quickly tuck in a few reefs in the main while he lowers the jib entirely. After all of this, he will usually say something like, "We reefed at the perfect time" and I don't understand what he is talking about.

Now, he knows how I reef. I track the storms on the horizon and if I find one that is coming at us, get ready to reef. I will also reef if everything looks fine but the temperature just dropped significantly. I will reef at the first hint of anything getting stronger, and the reefing is so easy to do!

The boat is stable, the winds are light and manageable, and I easily tuck in a reef or two in the main without really needing the winch handle. The jib is easy to pull over the deck by tugging on the lazy sheet and releasing the halyard. There is no fuss about it, this is the perfect time to reef!

Once we are reefed, we wait for the storm to strike and when it does, nothing happens! We do not heel, we do not panic, and most of all, we do not risk ourselves or our boat in the process.