15 July 2010

Plotting the Sights

If you've stayed with me this far, you are probably ready for your first set of sights!

I said last time that all sights consist of two numbers:

  • The date and time of the sight
  • The height of the celestial object above the horizon, at that exact time
For a noon sun sight we want to start taking measurements about 1/2 hour before the estimated time of solar noon.

Therefore, on 12 July 2010, a half hour before estimated Solar Noon, I positioned myself on a beach with an unobstructed view of the southern horizon (my exact location is what you are going to try to discover!) I had my inexpensive Davis 15 sextant, and a chronometer -- set to GMT of course!

Before you take your sights, you want to measure and note down two small errors that you will have to correct for, later:

  • the height of your eye above the water
  • the index error of your sextant
Since I was fairly close to the edge of the water, the height of the sextant above the water was approximately 6 feet. Ideally, you want to your sextant to be 0 feet above the water, because that way you have the most accurate view of the true horizon. I.e., you should be in the water with your eye half-submerged.

That's a bit inconvenient, though, particularly while sailing in shark-infested waters, so it is acceptable to take your measurements above the water. That slightly alters your view of the horizon, creating what is called a dip error. I'll discuss next time how to correct for this error.

Then I looked at the horizon through the sextant. Actually, at the two horizons, since you always look at two things at the same time through a sextant. I adjusted the vernier knob on the sextant until the two horizon lines were lined up, and then read the 'distance' between them.

What the two horizons look like through the sextant... sort of

Of course, the measurement should read exactly 0°, since I was lining up something with itself. However, the reading is never exactly 0°. This hopefully tiny error is called the sextant's index error, and in my case, it was 1.2' off the arc

I'll discuss next time what this strange but helpful 'off the arc' or 'on the arc' terminology means, and how to correct for this error.

Those two errors carefully noted down, I was ready to take some sights. It was coming up on 16:30 GMT. I expected solar noon to occur some time around 17:00 GMT. My plan was to take sights every 5 minutes, until 16:55 GMT, where I would start taking sights every 1 minute. I would do this until around 17:05 GMT, when I would go back to taking sights every 5 minutes until 17:30.

The usual way to take sights is for one crew to handle the sextant, and another to handle the chronometer and notebook. This is the way Helena and I mange it, if there are two of us. We swap positions every day so we both get practice with the sextant.

It's more difficult for a single-hander to juggle both chronometer and sextant, but it can be done. I cheat a bit by using a really useful iPhone application called 'Time Signal'. This app announces the time audibly every 10 seconds. With headphones, I can hear the announcements, even when it's noisy. It makes it very easy to know the time, even when your eye is glued to the sextant.

Here's a video that shows how it works... 

'Time Signal' iphone app
Great app, the music is NOT include (thank goodness!)

This app allows me to keep my eye on the sextant, while my ears take care of the time. You will note that all my sights are taken at :00 seconds. This simplifies the plotting process and probably makes it a tad more accurate. It's difficult to do this with a hand-held watch, but Time Signal makes it a snap. If you have an iPhone, iPad, or iTouch (the ultimate on-board navigation tools, by the way!), you should check it out.

At any rate, with the sextant to my eye, and Time Signal in my ears, here are the sights I took:

16:30:0070° 4.2'
16:35:0070° 25.8'
16:40:0070° 37.2'
16:45:0070° 48.4'
16:50:0070° 57.2'
16:55:0071° 1.6'
16:56:0071° 1.8'
16:57:0071° 2.4'
16:58:0071° 2.6'
16:59:0071° 2.6'
17:00:0071° 2.0
17:01:0071° 1.6'
17:05:0070° 59.8'
17:10:0070° 51.6'
17:15:0070° 41.0'
17:20:0070° 28.2'
17:25:0070° 13.2'

So, those are the sights. Note that each sight is composed of both a time, and an angle. The angle is the height of the Sun above the horizon at that particular moment. Now, what do we do with them?

After carefully putting away your sextant down in the cabin, you pull out a piece of graph paper and your favorite pencil, and you graph all the points, as I have done below.

Note the example below does not use the same sights as above. That would be cheating! You will need to make your own graph. I used a pen for this example because the ink shows up better in a scan. I actually do all my graphs in pencil, for obvious reasons! Click the image for a larger view.

The sights, plotted on graph paper

What you do is plot the time on the X axis, against angle on the Y axis. You should end up with a graph that looks something like the example.

Once you have plotted all the points, you must draw a curve that fits the points as closely as possible.

Neatness and accuracy counts! The more accurate the curve, the more accurate your position will be.

As you draw your graph, you will discover that there is a bit of science and a bit of art to it. The sights you will be plotting are 'smoother' than normal, because I was standing on solid ground when taking them. Yet you will see that drawing the curve still requires a bit of judgement.

That's okay! Don't let that stop you. As Capt. Pete Culler famously said, experience starts when you begin. Just do the best you can.

Plastic French Curves, available at any office supply store

If you are a really crummy draftsman (like me) you can try using a set of French Curves. You can find them in the States at any office supply store for a few dollars. I imagine they are just as inexpensive, elsewhere.

I'm not sure they make the curves more accurate, but they look more accurate, and save a bit of time. Try them, if you like.

Free hand or not, have your curve drawn for next time. You're going to need it for the next step.

Speaking of next time... if you'd like to be notified when I post a new 'lesson' (erratically, about 3 times a week), you can sign up for my super-sophisticated Automatic Notification Process. Actually, it's just an email, but Automatic Notification Process sounds better. I won't spam you, and you can de-sign up at any time.

>>> Next Episode: Latitude - Correcting the Sight

If you enjoyed this episode of the Unlikely Boat Builder, please consider telling a friend about it, or posting a link on Facebook. Thanks!

Get Notified Automatically

I hope you're enjoying "The Unlikely Boat Builder" as much as I enjoy writing it. Over 250 people have asked for a way to be notified automatically when I post new episodes. I've figured out how to do this, so if you'd like to be notified, please click on the link below. I promise I'll never spam you (and Google will have my head if I do.)

Thanks for your interest!

-- John

Follow me on Twitter! My son Chris has been bugging me for a few weeks to use Twitter to make short, more frequent posts from my iPhone, for when I don't have the time for longer blog posts. I don't know how it will work out, but I'm willing to give it a try! My Twitter ID is UnlikelyVoyager (UnlikelyBoatBuilder is too long, apparently), and the URL is http://twitter.com/UnlikelyVoyager. Twitter me back, or leave a comment below, if you think this is worth while. Thanks, Chris!


  1. Hi John, I am enjoying this part of you blog almost as much as cabin boy build. John, how did the oldy days captain get and maintain GMT and also, will a $50 sextant off ebay do the job? and get me where I want to go. Good on you John your blog has become some of my favorite reading.
    cheers from the south

  2. Dan: that's an interesting question with a long answer! For most of human history, they couldn't keep accurate time at all, which made finding your longitude impossible or very difficult.

    After marine chronometer's were invented, their error rates would be carefully measured *before* leaving port. For example, a particular chronometer might lose 1 second every week.

    Once at sea, the captain would not try to adjust the chronometer. He would just use the known error to correct his times by calculation.

    For example, he would know that when he left port the clock was slow by 56 seconds, say, and would lose 1 second per week while at sea. If you know the errors, it's easy to correct for them.

    Of course, once radio was invented, radio time signals made checking the chronometer much easier.

    There are lots of interesting books on this subject, including "Longitude" by Dava Sobel. A great read.

  3. John did you ever use an Excelspreadsheet for drawing the grafics? Excel has a tool that can draw perfect curves through any number of points. Thank you very much for these lessons.

  4. Dan, you asked about $50 sextants on fleaBay... I'm no expert, but I'm dubious. Most of the cheap sextants seem to be 'collectibles', meant as accents for your nautical theme lounge. Real sextants seem to go in the multi-hundred dollar range.

    If you could find an Astra IIIb in good condition for under $300, I'd consider that a good deal. Problem is, how do you know it wasn't dropped? A sextant with a bent frame is no good. You either need to be very smart, or deal only with a reputable dealer who knows what he's talking about.

    I couldn't find one, so I plunged for a new Davis 15. It's good enough for what I use it for.

  5. Gerard, I didn't know that Excel could do curve fitting. That would be pretty cool.

    Just be careful that you are not using the simple 'line graph' drawing, where Excel just connects the data points with straight lines. That kind of graph is not what we need.

  6. If you battle through the tourists at the Greenwich Observatory in London you can see the original chronometers that were invented to allow mariners to keep GMT at sea. As you say, read Sobel's "Longitude" for the whole fascinating story, before you go to the observatory. The chronometers are works of art.

  7. Problem with buying ANYTHING on ebay is that you are buying sight unseen, from a person or persons unknown. There are honest sellers on ebay, and there are the other kind.

    Personally speaking, I bought a Davis MK. 15 second hand on Ebay, it came with a leveling device no longer made. From what I can tell, it was essentially as represented, lightly used and in proper operating condition.

    I've shot the sun and the moon with it, getting acceptable fixes, navigational errors turning out to be something that "I owned". One thing about plastic sextants, actualy two things. They aren't as stable as metal frame instruments, though with care, they are useable. They are significantly less expensive than metal sextants

    The Astra 111B, currently goes for, see celestaire.com, $659 plus shipping. They have gone up in pricse over the last several years. The Davis MK. 25 goes for $195, the MK 15 for $125, discounted prices from Celestaire's 2011 catalog. Ken Gebhart the proprietor had been helpful to me re a couple of things. Other sextants run higher, much higher. You pay your money and take your choice.

  8. More on plastic sextants, check out the EBBCO. It is/was English made, and by some people has been well spoken of, others not so well.
    For mysaelf, I have neither ever, in the flesh, seen one nor have I ever used one.


I'd love to hear from you. Please comment!