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.  

Celestial Navigation for Dummies (in the Western Hemisphere)

Celestial Navigation is an utmost skill needed for any ocean voyager. Compasses can lie, electronic equipment can fail, but the stars will always be there! Yes, a cloudy day or night will obscure your view of the stars, but at some point, something will become visible in the sky and if you know how to use it, you can get a bearing on where you are.

The easiest way to find your position is to take a Noonsite. This will give you your latitude and your longitude with the least amount of math. All you need to get your noon site is a sextant and a clock (which is set at UTC time).

A noon site requires you to know how to use a sextant, which is really easy to learn. All you are doing is measuring the angle between the sun and the horizo.

When you take your noon site, you will receive two pieces of information that you will later translate into coordinates on a map. First you will have your time, which gives you your longitude. Second, you will have your sextant measurement, which will give you your latitude. 

Longitude

Longitude is a factor of time on Earth. To make this explanation simpler, we need to use an Earthcentric view of the universe.  

Remember that the Sun revolves around the Earth once every 24 hours. The Earth can be divided into 360 degrees of longitude, and in 24 hours, 360 degrees will pass by. 

360 degrees / 24 hours = 15 degrees per hour. 

At noon over Greenwich (where UTC is the time zone) the sun is directly overhead (their local noon).
In one hour, the sun will be directly over 15 degrees W.  
In two hours, the sun will be directly over 30 degrees W.
n three hours, the sun will be directly over 45 degrees W, and so on.

This means that the time of your noon site is going to b a cryptic form of your longitude, and with really simple math, can be converted into your East or West coorditantes.

When you take your noon site, look at the time (it is helpful to set a 24 hour clock to UTC so that you don't make any errors in calculation here, as each hour is 15 degrees!). Then you will simply subtract your time by 12, as this will give you the difference in time from Greenwich to your local noon.

Now take your time difference and separate it into two columns, hours and minutes. The hours will be multiplied by 15 and the minutes by 0.25; the answer will then be added to give you your coordinates.

Decimals are easy to convert into minutes by simply multiplying the decimal by 60.

So, for example, say its 4:55 PM UTC when the sun is directly overhead and you take your noon site. The math will be as follows:

   16  :  55
 -12. :  00

    4  :  55
x15   x0.2

   60  +  13.7     (0.75 degrees x 60 = 45 minutes)
  60* +  13*45'
  73*45'W

Just that simple, you now know that your latitude is 73 degrees and 45 minutes West.

Another example would be local noon (when the sun is directly overhead) at 2:38 PM UTC.

The math would be as follows:

  14  :  3
-12  :  00
   2  :  38
x15  x0.25
  30  +  9.5     (0.5 x 60 = 30 minutes)
 30* +  9*30'

  39*30'

Thats all there is too it! Longitude has nothing to do with the actual number that is displayed on your sextant but everything to do with "when" you measured the sun at its highest point in the sky.

Latitude

Ok, latitude is the North & South value of your coordinates and really weighs heavily on the reading you record with your sextant. To properly calculate your latitude using the sun (by day, obviously), you will need to use the tables in the Nautcal Almanac. These tables can seem long and complicated, and very confusing, but they are not all that bad once you learn what to look for. f you don't want to use a book, you can always download the latest Nautical Almanac for free! A simple Google Search will pull up a few options, and you will certainly be able to download your own copy.

I personally use a print version from 2017 (I bought it in late 2016 and have not updated my copy as of late 2018) as the angle of the sun over the horizon doesn't change all that much from one year to the next. Yes, your reading will not be as accurate as possible, but at the same time, you are measuring the sun on a pitching and rolling deck of a boat out in the ocean! There are going to be errors in your measurement, so a few tiny errors in your calculations will only compound into a slight bit of error in your final coordinates.

It is important to keep something in perspective here, the goal of basic celestial navigation is to ind land, not to find your exact position on the earth. Advanced celestial navigation will allow you to pinpoint your exact position by using three distinct celestial bodies and finding their intersected lines of position. That is very accurate and also a lot of work to do, which is why basic celestial navigation is just fine for ocean cruising.

The goal is to be less than 25nm off from your actual position. A GPS will tell you your true position, and you can then do some simple math to figure out how far off you are. It is good to practice that way you can get your error way down to less than 25nm. I personally tend to get us within 4nm of our true position with simple math and an outdated Nautical Almanac, meaning it can be done and it's not difficult to do. A 25nm error or less will allow you to find land, and once you reach land, you can then use visual navigation to get yourself in to port. By constantly practicing, you will know how good you are at celestial navigation should your electronic navigation equipment fail, forcing you to rely solely on your basic celestial navigation skills.

On the other hand, if you do not have a Nautical Almanac, you can also just measure the angle from the horizon to Polaris, the North Star, and that is your latitude; no math involved!

An important factor that your Nautical Almanac will tell you is a value called Declination. This is the angle of the sun relative to the horizon. You know how shadows are taller in the winter and shorter in the summer, this is because the sun is further overhead in the summer and lower on the horizon in the winter.

The Nautical Almanac is nothing more than an overfilled calendar. On the top corner of the page is the date range of that page, so simply leaf until you find today's page. Then look on the left side of the page for today's date. Then in the box of today, look for the hour you took your noon site. Don't worry too hard about the (time) minutes that you took your sight, simply round up or down to the nearest whole hour. Now, the declination will be displayed to you as Degrees, Minutes, and Decimal of Minutes.

Simply write this number down and begin to do your simple math!

You will take your sextant reading and substract it from 90 degrees, as the sun is directly overhead when you took your noon site. Then you will add or substract your declination to this number. The answer will be your coordinates for latitude.

You might be wondering what I mean when I say add or substract; which one is it? Well, it depends. If the sun is between you and the equator, you will add. If you are between the sun and the equator, you will substract. To keep the math and theory here simple, since this is just "Basic Celelstial Navigation" let's suggest that you do both and see which one is closer to where you actually are.

For example, you are sailing through the Bahamas, meaning that your latitude is somewhere between 27N and 22N. You get your sextant reading and you find today in the Nautical Almanac. It says your declination is 23*24.7' That is a pretty accurate value presented to you, but should you add or substract it from your recording? Well do both and see which one fits your assumed position best! One will be close to where you actually are and the other will be wrong by almost 24 degrees! Now you know for your present location that you should either add or substract next time.

This may sound really confusing, but I guarantee you that it is very simple to carry out this calculation. Lets do an example:

Declination is 23*24.7'
extant recording is 87*04'

We start by subtracting our reading from 90. Since each degree is 60 minutes, it makes the math easier if you just write out 90* as 89*60'

  89* 60'
-87* 04'

   2* 56'

Now, we aren't sure if we should add or substract, so lets do both!

     2*     56'
 -23*     24.7'

-21*      31.3'  A negative value would indicate that you are south of the equator, and thus in the Southern Hemisphere as you sail through the Bahamas. 

21*31.3'S

    2*   56'
  +23*  24.7'

25*    80.7'     (80.7' - 60' = 20.7') Each degree is 60', so to turn a number like 80 into degrees and minutes, simply substract 60 from it. The remaining number is minutes, and the 60 you took off becomes 1 degree.
25*    1* 20.7'    Now add the values together and that will be a possible N value for you as you sail through the Bahamas.

26*20.7'N

Being how you are in the Bahamas, the value of 26*20.7'N seems more plausible than 21*31.3S, so you know for the time being that you need to be adding your declination to the value, instead of subtracting it.

 

Finding Your Coordinates

It is important to know where you are before you leave, that way you have a rough idea of what the answer should be while you are doing your calculations. If you find that you are way off, you know you made some clerical error and can figure out how to make adjustments to erase this error in tomorrows noon site. 

Remember, Longitude is a factor of time, Latitude is a factor of the sun at noon with some minor addition or subtraction. 

With this, you can figure out where you are in the ocean using only a sextant and a clock! 

Speed While Crossing an Ocean

We picked up a third crew member to cross the Atlantic with us. This is his first ocean crossing and something that he has always wanted to do. He is a very competent sailor who knows his stuff (a huge improvement over the previous crew member). His background is in racing, meaning that he can trim and squeak out every last knot available. When he is approaching hull speed, he will imagine that there is still more power available and continue to trim. He obsesses over every tenth of a knot, making the boat sail as fast as possible.

This makes for fun and spirited sails over short distances, but this philosophy is very different from ocean crossing.

In ocean crossing, the goal is to get to the other side of the ocean with everything still working and as comfortably as possible. This means sitting back and relaxing as the sails and wind carry you from Point A to Point B. You are not going to be moving as fast as possible, but you are moving comfortably. This comfortable moving is what ocean cruising is all about. The trip is going to be several weeks, and if we wear ourselves out in the first day, we will be dead from exhaustion by the time we make our distant landfall. Instead, sailing comfortably is our goal, that way we arrive at the next destination rested and ready to explore!

This difference in philosophy came up when I saw a storm system forming. A massive thunderhead had been billowing up behind us with massive clouds climbing high into the sky. At this point, the system was only developing but I knew to keep my eye on it as it could start to come our way with devastating consequences.

All of a sudden, the massive cloud formation turned into an anvil cloud with the horn extending right over our boat. The cloud became so thick that it blocked out the sun! Instantly, I knew it was time to reef down. We were full sail with our Main, Staysail, and Jib flying; soon we would be only the staysail and trysail.

The concept of putting up the trysail in light airs perplexed our racing friend. "The winds are light, we can just switch the sail when the winds get here." I responded with, when the winds hit, no one wants to go up to the mast and wrestle with sails. The day was drawing to an end and the sun would be setting soon. Changing from full-sail to storm-sails is one thing, but doing it in the dark on a moonless night is completely different! To be safe, we simply set the storm sails and waited for the weather to reach us.

Our speed went from 5 knots to 4 knots. This meant that for every hour that we waited as the storm approached, we would theoretically lose 1 nautical mile of travel. That may sound like a significant loss in distance made good in a short course, but we are traveling 2800+ miles! 1 mile is 0.000357% of the journey, so not a significant issue to me, who is a comfortable cruiser and not a racer.

Late that night, the winds finally came, and we may have lost a theoretical 5 or so miles, but who cares! When the winds hit late at night, we were ready and relaxed. There was no drama caused by the boat pitching and rolling, instead the off-watch crew didn't even know it occurred.