Using a Watch as a Compass

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.

Example of using a watch as a compass (Northern Hemisphere, 10:30 am).

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 time zones in the contiguous 48 states.

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).

Compass error in Lake of the Woods, MN, for the year 2012.

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.

Compass error in the Florida Keys for the year 2012.

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:

  1. Meeus, Jean, Astronomical Algorithms (2nd Ed.). Richmond: Willmann-Bell, Inc., 2009.
  2. Muller, Eric, Shapefile of the Time Zones of The United States. [link]
This entry was posted in Uncategorized. Bookmark the permalink.

10 Responses to Using a Watch as a Compass

  1. Pingback: Prepper Life Skill: Finding North Direction « preppernextdoor

  2. Pingback: Prepper Life Skill: Finding North Direction | The Prepper Next Door Blog

  3. Steve Harmony says:

    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.

  4. karen says:

    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.

  5. Jude says:

    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.

  6. J.R. Johnsson says:

    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.

  7. Pingback: Computing positions and eclipses of the Sun and Moon | Possibly Wrong

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s