Direction-finding using only the sun and an analog watch is a trick that I remember first reading about when I was in elementary school. I think it was in one of Seymour Simon’s Einstein Anderson “science detective” stories, but I’m not sure; being a kid was a long time ago.

More recently, I saw it mentioned again in a shark movie that I happened to sit through, *The Reef*. In the movie, a sailboat runs aground and capsizes in shallow water; rather than stay with the boat, the people on board try to swim north toward a distant island. It doesn’t go well.

Before leaving the boat, one guy looks at his watch, looks at the sun, mumbles a few calculations, then says, “That’s north,” and off they go. I wondered if those calculations were correct, particularly since the movie was set in Australia– the Southern Hemisphere– and the method didn’t sound quite like I remembered it. After some additional searching on the web, along with some experiments and calculations of my own, I learned that descriptions of this “Boy Scout” survival trick are frequently incorrect, incomplete, or misleading. But more interestingly, such descriptions are almost never accompanied by a warning of just how *inaccurate* the method can be, even when it is used properly. My suggestion: keep your GPS-equipped smart phone with you at all times.

**How it works:** *If you are north of the tropics*, hold your watch face horizontal, and turn so that the hour hand points toward the sun. Then the ray bisecting the angle between the hour hand and 12 o’clock *noon* points approximately true south. (I will deal with the Southern Hemisphere later.) See the figure below for an example.

The first potential source of confusion is which direction is north and which is south: do you bisect the “small” angle or the “large” angle between the hour hand and 12 o’clock? Some sources suggest that “north will be the direction further from the sun”– that is, bisecting the *smaller* angle points south. Although this is usually the case, it can fail when the sun is up before 6:00 am or after 6:00 pm. It seems simpler to just remember that south bisects the angle that sweeps in time from the hour hand toward noon (clockwise in the morning, counter-clockwise in the afternoon).

**How well it works:** This is what I found most interesting about this problem. One survivalist blog (a somewhat amusing phenomenon, if you think about it) makes the strangely precise and grossly false claim that “the accuracy of this method is within 8 degrees (US and Canada).” In fact, the error in the estimate of direction quite often exceeds 30 degrees, and can even exceed 80 degrees depending on where– and when– you are.

There are two primary sources of error. The most obvious source of error is the accuracy of your watch. Several online sites state that “the direction will be correct if the watch is set for true local time, without adjustments for Daylight Savings Time [*sic*].” More precisely, the method is more accurate if your watch reads 12 o’clock when the sun is at its highest point in the sky, due directly south.

The problem is that “standard time” and “apparent solar time” rarely coincide exactly. Everyone in a particular time zone thinks it is the same time, despite the fact that those on the eastern edge of a time zone will see the sun rise approximately one hour earlier than those on the western edge. To make matters worse, the time zones in the U.S. are rather erratically shaped, resulting in even larger differences than would be the case if time zone boundaries were simple, straight lines of longitude, 15 degrees apart:

The second source of error is the latitude of your position: as several online sites suggest, “the further you are from the equator, the more accurate this method will be.” This is essentially true, and is by far the larger of the two sources of error. What is often left out, however, is that the method isn’t simply less accurate near the equator, it effectively doesn’t work “at all.” In the tropics– the band around the earth between about 23.5 degrees south and 23.5 degrees north– not only is the sun higher in the sky, making it more difficult to accurately estimate its direction in the first place, the sun’s motion is also not as well-behaved (why?), so that the error in your estimate of direction can approach 180 degrees, even assuming an accurate estimate of the sun’s direction.

So how well does it work? As approximately “best case” behavior, following is a plot showing the error in estimated direction over the course of the year 2012, at the Northwest Angle Inlet in Lake of the Woods, Minnesota (the northernmost point in the contiguous 48 states).

The general shape of this plot is typical; the method works best in the fall and winter months, with the worst case behavior in the middle of the year. Even this far north, errors can exceed 30 degrees.

At the other extreme, the following plot is for the Florida Keys, which suffer from being just north of the Tropic of Cancer, where errors are the worst. However, the method still works reasonably well during the “cold” months.

Finally, back to the Southern Hemisphere. Here, the method is only slightly different: if you are south of the tropics, then point *12 o’clock* at the sun, and *north* bisects the angle between the hour hand and 12 o’clock noon (with the same “sweeping in time” sense described above). I found several different incorrect variations on this online; perhaps the most disappointing was an otherwise very cool interactive *Mathematica* demonstration on the Wolfram web site.

And the method used in the Australian shark movie? The description of the method turned out to be correct… but the action takes place at approximately 10 degrees south latitude, where all bets are off. At any rate, it wasn’t enough to escape a great white shark.

References:

- Meeus, Jean, Astronomical Algorithms (2nd Ed.). Richmond: Willmann-Bell, Inc., 2009.
- Muller, Eric, Shapefile of the Time Zones of The United States. [link]

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I found this web page after trying to explain to a coworker why using a watch as a compass is a bad idea. Do the different lines on each graph represent different times of day?

Sort of :). The “lines” that you see are actually just an artifact of the resolution of the times at which I computed the error. There is a single data point every 12 minutes, 120 points per day, which over the course of an entire year means there are almost 44,000 individual points on each of the two graphs. I didn’t “connect any dots,” so there are not really any actual lines on the graph. However, even within a single day, the error tends to swing through both extremes, so that the “envelope” or outer boundary of points that looks like one smooth curve is actually just the gradually-changing worst case that is experienced *every* day. And the error at a particular time of day changes only slightly from one day to the next, hence the appearance of “lines” on the plots.

Hi thereHello,

We are a charity and have been working in social housing estates across Cornwall ( UK) for 2 years aiming to get people living in disadvantaged neighbourhoods out and engaging with nature more. This is a Natural England funded project.

We are currently developing a website to house 4 new trails we have developed as part of the project. For this website we have developed a series of activity sheets and links to relevant websites to bring nature to life for families.

We have picked up an image ( using watch a compass in the northen hemisphere) that you have on your website that we would like to use for our Telling Time worksheet.

Would you give us permission to use the image, as we do not have funds to be able to purchase these photos from you? We can provide a link to your website by way of promotion of your project.

If you could let me know as soon as possible that would be appreciated.

Sure, no problem.

Thanks, I was wondering why I couldn’t verify the information I found on the web in the Southern Hemisphere … I also wondered why no-one proved their theory by showing a compass as well as the watch. Must verify what I read. Yours worked.

Much simpler method: All you need is a few oz. of water, a cork, and a needle or pin.

Cut the cork in half lengthwise, stick the pin or needle through it width-wise, set it in

the water, and it will always point to magnetic N/S. Use sun up & sun down to determine which is North.

A magnetic compass can definitely be useful, especially in the U.S., where even if you don’t know the actual variation from true north, the difference is at most 25 degrees or so, and less than 15 degrees in most of the country.

But I’m not sure the method you describe is necessarily simpler– I find that I have a watch available much more frequently (i.e., pretty much all the time) than I do a cork, a knife or other means of cutting the cork, a needle… and a magnet or other means of *magnetizing* the needle.

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Hello – I am trying to teach this method to Boy Scouts, and while researching the topic, I noted some issues with the method, which brought me to your page. While I am trying to understand your general rule about determining North or South on the N/S line, I do not understand what you mean by “… (S)ome sources suggest that ‘north will be the direction further from the sun’– that is, bisecting the smaller angle points south. Although this is usually the case, it can fail when the sun is up before 6:00 am or after 6:00 pm. It seems simpler to just remember that south bisects the angle that sweeps in time from the hour hand toward noon (clockwise in the morning, counter-clockwise in the afternoon).” — Isn’t there only one angle to bisect? (I.e., in the Northern Hemisphere, the hour hand – 12:00 angle?) I also do not understand the “sweeps in time” aspect of your description. Could you be encouraged to simplify the rule?

The hour hand and a ray toward 12:00 always create *two* angles, that sum to 360 degrees. For example, at 10:30 am as in the figure in the post, there is a “small” angle of 45 degrees (sweeping clockwise toward noon), but there is also a “large” angle of 315 degrees (sweeping the other direction, counter-clockwise, effectively toward the previous midnight).

The complication is perhaps best described by considering what happens at *exactly* 6:00, when there are two 180 degree angles to choose from. For example, suppose that it is exactly 6:00 am in the morning, and you align the hour hand to point toward the risen sun. Is south the direction indicated by 9 o’clock or 3 o’clock? It’s 9 o’clock, right?

Now suppose that you conducted the same experiment just a few minutes *earlier*, say 5:57 am. South is still approximately in the 9 o’clock direction… but for us to get this right, we must bisect the slightly *larger* angle (still sweeping clockwise), not the smaller one containing 3 o’clock.

To make things worse, the situation will reverse later that evening: if it’s just a little before 6:00 pm at *night*, then south is at approximately 3 o’clock, bisecting the *smaller* angle sweeping *counter-clockwise*.

How can we keep this straight? As these examples show, it’s not enough to always choose the *smaller* angle; and we can’t always choose the “clockwise” direction, nor always the “counter-clockwise” direction. What *does* work is to imagine that one of the clockwise/counter-clockwise directions leads to 12 o’clock “noon,” and the other leads to 12 o’clock “midnight”, and we always want to choose the angle that sweeps toward *noon*, not midnight. This is what I meant by “sweep in time toward noon.”

Thanks for your reply. Then, considering your points, would this work to create a rule?

Northern hemisphere:

Point the hour hand in the direction of the sun. If it is before noon, measure clockwise from the hour hand to the 12:00 mark and bisect that angle with an imaginary line. If it is afternoon, measure counterclockwise from the hour hand to the 12:00 mark and bisect that angle with an imaginary line. In the Northern hemisphere, the end of the imaginary line you draw that is closest to the sun will point toward the South. The end of the imaginary line furthest from the sun will point North.

Southern Hemisphere:

Point the 12:00 position toward the sun. If it is before noon, measure clockwise from the hour hand to the 12:00 mark and bisect that angle with an imaginary line. if it is afternoon, measure counterclockwise from the hour hand to the 12:00 mark and bisect that angle with an imaginary line. In the Southern hemisphere, the end of the imaginary line you draw that is closest to the sun will point toward the North. The end of the imaginary line furthest from the sun will point South.

A simpler way to express this would be:

“Before noon bisect the angle before the 12, after noon bisect the angle after the 12, to find out where the sun is at noon.”

Some people can tell the time by looking at the sun. But I can never make out the numbers.

I can’t believe people are using this blog to teach the sun-watch compass method to Boy Scouts. Look at the title of the blog: Possibly Wrong. In this case, it should be “Definitely Wrong.” Look at the graphs. Error in the Florida Keys can be greater than 80 degrees at the Summer Solstice. If you don’t believe the graphs, do what I did — test the theory. I mounted a dowel rod in a flat piece of wood then measured the azimuth angle of the sun at several times of the day on the day after the Summer Solstice.

A simple calculation shows where the sun-watch compass method tells you South will be:

Call the angle A the angle between the sun’s azimuth and 1:00 on the watch face (because I’m presently in Daylight Saving Time). The value of angle A is simply 30(13 – t) where t is the time expressed as a decimal in 24-hour notation (i.e. 6:30 would be 6.5). Of course 30 is the number of degrees between hour marks on a 12-hour watch face (360/12).

The sun-watch compass method tells us that South will be halfway between the hour hand (which is pointing at the sun) and the 1 on the watch face (again because I’m in DST). So angle B would be A/2, or 15(13-t). To get the direction the sun-watch compass method tells you is South, simply add B to the sun azimuth angle you obtained using your compass.

The error (difference between 180 and angle B) was as high as 47 degrees in my experiment.

Please DON’T teach this method to Scouts. As a matter of fact I’ve pointed out the errors inherent in the method to the committee working on the next edition of the Boy Scout Handbook.

I hope I have not given the impression from the original post that I am advocating the use of this method. Indeed, my intent was to “warn of just how *inaccurate* the method can be, even when it is used properly. My suggestion: keep your GPS-equipped smart phone with you at all times.”

But I may have misunderstood your “definitely wrong” comment, to suggest that there was perhaps an error in my calculations? If it seems this is the case, your experiment from the Keys would be useful to compare with– any more specific data would be useful (e.g., time(s) of measurement, lat/lon position, etc.).

As far as I can tell your calculations are correct, as confirmed by my experiment. I am in Durango, CO, not in the Keys. And even here, on the day after the Summer Solstice, I saw an error of over 47 degrees.

Here are my numbers:

Date Time (H:M) Time (Decimal) Sun azimuth (Magnetic) Sun azimuth (True) Calculated South azimuth Error

6/22/14 6:59 6.98 65 74.63 164.88 -15.12

6/22/14 7:57 7.95 69.5 79.13 154.88 -25.12

6/22/14 8:29 8.48 72 81.63 149.38 -30.62

6/22/14 8:58 8.97 76 85.63 146.13 -33.87

6/22/14 9:58 9.97 89 98.63 144.13 -35.87

6/22/14 11:13 11.22 105.5 115.13 141.88 -38.12

6/22/14 11:51 11.85 112.5 122.13 139.38 -40.62

6/22/14 13:10 13.17 176.5 186.13 183.63 3.63

6/22/14 13:27 13.45 192.5 202.13 195.38 15.38

6/22/14 13:45 13.75 208.5 218.13 206.88 26.88

6/22/14 14:08 14.13 226 235.63 218.63 38.63

6/22/14 14:26 14.43 234.5 244.13 222.63 42.63

6/22/14 15:01 15.02 246.5 256.13 225.88 45.88

6/22/14 15:40 15.67 258 267.63 227.63 47.63

6/22/14 17:37 17.62 267.5 277.13 207.88 27.88

6/22/14 18:34 18.57 276 285.63 202.13 22.13

6/22/14 18:53 18.88 280 289.63 201.38 21.38

My magnetic declination, according to NOAA, is 9.63 degrees east, which is how I converted the magnetic azimuth to true.

Not to give away the actual location of my home, Durango itself is at 37.2686541,-107.8824657

It’s just a general method with the caveat that it isn’t very accurate (granted), and it is merely giving you a rough estimate. But, it is taught with caveats all the time, including by survival “experts” and militaries around the world. Thus, it seems better to state the caveats, and come up with a broadline rule-based method.

Over 80 degrees off is a very rough estimate indeed! The Scout Handbook of the Boy Scouts of America has no caveats. One edition I have handy says it gives you a “fair direction south.” Again, over 80 degrees error is NOT a fair direction.

Better to teach something that really works, like the shadow stick method. Stick a stick in the ground. Mark the tip of the stick’s shadow. Wait an hour. Mark the tip of the shadow again. Draw a line between the two marks. This a fairly accurate east-west line. If you do this all day you’ll see the shadow tip actually describes a very shallow arc.

That works at low latitudes, but the higher the latitude, the greater your error.

How accurate is this method, exactly?

mendel, I assume you’re speaking of the shadow stick method. The original poster is taking on a theoretical study of how accurate it is. The references I’ve seen online say to wait 10-15 minutes between measurements. For more accuracy measure shadow length before solar noon with a string then mark the shadow tip after noon when the length is the same. That should be dead on. The shadow tip does describe a gentle arc. Thinking about it, during Summer in the northern hemisphere the sun rises north of east then at some time during the morning the sun’s azimuth is due east, later still its azimuth is south of east. See for example my measurements below for Durango, CO on the day after the Summer Solstice.

Steve – PW, the shadow stick method is fine, but not expedient during travel. Let’s say, for example, that the proper caveat is made to check this method against the shadow stick method first, determining whether the watch method will work for you for your area and, for example, not near the Solstice (etc., etc.). Then, the user could rely on the general direction the watch method (quickly) gives. Yes, it’s a very good idea to make sure you have your GPS with you, with fresh batteries at all times, a back-up compass, and your own commandos to make sure you never go astray — but the entire reason you would use even a roughly accurate (depending) method is quite simply because you do not have those things. Thus, and again, I would ask whether the above rule I wrote would work for people who are in areas where the error is fine enough to be used as a general direction finder — pure and simple.

I’m not going to argue with you, Mike. It’s best to go out in the woods with the ten essentials, of which map and compass with optional GPS is right at the top. See my reply to “possibly wrong” (the owner of this blog) for the numbers I obtained on 6/22/14 at my home in Durango, CO. The error is negative in the morning (method gives a direction east of south), goes to zero very quickly at solar noon, then goes quickly again to positive numbers in the afternoon. So you could never come up with a general rule to correct the method’s “south” to actual south. Far better to make sure you have a map and compass with you, together with the knowledge of how to use them, when you go out in the woods.

Steve – I am not saying this is a very accurate method. In a perfect world, everyone is properly prepared for survival. As you know, ours is not one of those worlds. What I ask is – can it ever be useful (for its intended purpose), and if so, under what conditions? Your dismissal of the entire method seems not to take into account that it does, actually, work under certain conditions. We are not talking about navigating from a map with this method. So, Steve and PW — is it ever useful, and if so, when/where?

Seems to me the method would work perfectly at the Arctic and Antarctic Circles on the equinoxes IF the watch was set to the local solar time. At those times the sun would be skimming the horizon all day and would be due east at 6 AM, due south at 12 noon, and due west at 6 PM. PW’s graphs show it works best February and November, with much smaller errors than the rest of the year both for extreme northern and extreme southern contiguous US locations.

An interesting observation is that the error curves shift down in the Spring and up in the fall. The answer might lie in the Equation of Time (which is the difference throughout the year between apparent solar time and mean solar time). It can be though of as the time error of a properly setup sundial.

http://en.wikipedia.org/wiki/Equation_of_time

Steve and PW – what if you set your watch to apparent solar time by observing the shadow of a vertical stick (i.e., when the shadow is shortest, that would be solar noon) – and set your watch to 12:00 at about that moment. After setting the watch by this method, wouldn’t that alleviate a lot of this gross error?

It would remove the difference between time zone time and local solar time and the error introduced by the Equation of Time, but there would still be a lot of error. My mind turns to jelly when I try to think about 3D geometry, so I went back and plotted Sun Azimuth (True) vs decimal time. Going back to the sun at the equinoxes on the Arctic and Antarctic Circles, that’s simple, you can almost visualize it as a 2D geometry problem. As the hours progress, the azimuth vs time plot would be a straight line. But the actual azimuth vs time plot in Durango near the Summer Solstice is not linear, it’s s-shaped. It could be approximated as three straight lines, with a shallow slope from sunrise to 12:00 MDT (which would be 11:00 MST) and from 14:00 MDT (13:00 MST) and sunset, and a steeper slope between 12 MDT and 14 MDT. The errors change quickly during the steeper-sloped portion of the s-shaped curve dropping to zero at approximately 13:00 (solar noon).

Steve, thanks for your reply. I think I understand what you are saying: depending on your locale, the more length in time away from solar noon introduces substantial error, correct? But now, let’s take the 80 degree Florida Keys error example: does the setting-solar-noon method reduce this error substantially — enough to determine general direction? See, what I am searching for is some kind of additional step or steps one could take to minimize the error enough to get the general directions — bearing in mind the caveat of less accuracy towards the equator, etc. Do you think this step would do that, and if not, would this, in combination with another step perhaps, work to resolve the error enough in order to have the method function more accurately under general conditions, and in most locales (keeping in mind the different methods between N/S hemispheres?)

Mike, to finally respond to your initial question, yes, your interpretation of the method discussed in the original post is correct– that is, it accurately reflects the clockwise/counter-clockwise sense of which angle to bisect to find “south.”

It’s an interesting question whether we can refine this method somehow, by introducing a hopefully simple additional “correction” or two, to reduce error. I’m not sure, and I admit I don’t have any great ideas here– as Steve points out, this could be tough, since the error varies widely even over the course of a single day.

To see this more clearly, instead of showing error over the course of an entire year as in the figures in the original post, let’s use Steve’s very helpful example data and “zoom in” on Durango, CO, over the course of the single day 22 June 2014. Here is a plot that shows the error using the method over the course of the day (my prediction in blue, Steve’s actual measurements in red).

PW — thanks for the data. PW — would this change at all taking into account adjustment to solar noon?

It does, but not by much– as mentioned earlier, not by nearly as much as some sort of correction for latitude would. Here is a plot showing the worst case error over the same day, as a function of our choice of time offset. For example, the original data used MST=-7, with a worst case error of about 43.5 degrees… by adjusting our watch we improve this by at best a few degrees.

PW – thanks for your reply. Would there be a relationship between your latitude, and some kind of field expedient shadow method that could be used to correct the watch method based on one’s latitude? I’m not suggesting there is a fix for this, but it seems to me that there must be some correlative effect we can take advantage of in order to make the watch method useful enough to be without very large error swings.

As I was drifting off to sleep last night it occurred to me that it would be interesting to calculate the solar azimuth required for the method to work. It’s a simple algebraic manipulation to get from my equation for angle B = 15 ( 13 – t), solving for azimuth + B = 180. Plugging in the equation for B, collecting terms, and solving for azimuth, we get azimuth = 15t -15. This means the sun-watch compass method we’re discussing requires that the sun’s azimuth must be linear with time, and it’s just not. It’s the s-shaped curve I discussed above. The curve and the line intersect at solar noon, but that’s not very useful because we know that if we’re in the northern hemisphere and north of the Tropic of Cancer the sun will be due south at solar noon.

Steve and PW — OK, so it doesn’t seem as though there exists an “easy” fix for this method. Therefore, I ask you both: is the shadow stick method, by and large, more accurate? If so, could you brilliant mathematicians estimate its accuracy? I state that question broadly, knowing full well you both could probably fill volumes on error dynamics. Finally, if you were lost in the woods with no modern conveniences of navigation (including a magnetized needle, or the ability to magnetize a needle, etc., ad infinitum) what method(s) would you suggest, in order of accuracy, ease of use, etc. Again, I appreciate your time on these questions and acknowledge your expertise. Thanks.

Mike, I had a spreadsheet years ago that incorporated an equation that could give you the azimuth and altitude of the sun for any place on Earth at any date and time. This was many years and many computers ago. I can’t remember the details, seems the equation was from a book on passive solar design. At any rate, I ran some calculations for both the sun-watch method and the shadow stick method, and the shadow stick came way out ahead. Fuzzy memory tells me the maximum error for the shadow stick was a few degrees, maybe three. IIRC the shadow tip follows a gentle arc with the convex side of the arc facing South.

Ever since then I’ve felt like a modern-day Don Quixote tilting at the windmills of the sun-watch method. I’m so glad that PW published this blog with his great plots, and any time I see a mention of sun-watch in the popular press (most recently the June issue of Popular Mechanics in an article about the 25 things a father should teach his son) I try to educate the author on the fallacy of depending on the “old outdoorsman tale” that is the sun-watch method.

Steve – thanks for your reply. If you ever have the time; coming up with your data on the shadow-stick method’s reliability would be of great use to me. Also, pardon me, but what is IIRC? Thanks.

Internet jargon. If I Recall Correctly.

You have posed an interesting problem. Let me take some time this week to work on it, and I will try to post analysis of some hopefully useful alternatives (including Steve’s shadow-stick method).

Briefly, I would think there are some interesting trade-offs to consider, such as: (1) How quickly can you determine direction (immediately, in an hour, over several hours spanning noon, etc.)? How dependent is the accuracy of the shadow-stick method on the “local-levelness” of the stick and the ground on which its shadow is projected? Etc.

PW – that sounds great! Yes, please let me know what you find out. I think it would be a very useful study.

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