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There is a method of finding north with a watch described here

So you point the hour hand of your watch at the sun. Halfway between your hour hand and the noon mark is south.

How accurate is this method of finding north?

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TLDR: Its accurate at solar noon which probably won't correspond to noon on a watch and is inaccurate otherwise without more information.

Reasons for it not corresponding to noon on your watch.

  • Failing to account for Daylight Savings Time
  • The difference between solar time and the time zone.
  • Going east or west within a timezone (solar noon is 16 minutes later on the western border of Wyoming compared to the east)

Reasons for needing more information,

  • The sun's speed across the sky is not constant, its faster at solar noon and slower at dawn/dusk.
  • Equation of time, depends on the time of the year.

With all of that said, it is possible to find north using the sun with a solar compass and can be more accurate in areas with lots of iron, but in order to use one you need to know,

  • Set the sun's declination for that day, obtained by means of tables, on a scale attached perpendicular to the time dial.

  • Set the latitude on a scale in the alidade.

  • Set the approximate local time on a dial that rotates on a polar axis.

Solar Compass

These inaccuracies are also why it is difficult to tell time other than solar noon with a compass, the direction of the sun's shadow can't directly be correlated to a time without more information.

  • While finding the true north from the sun, with a watch or just from knowing the time and judging the shadows is hard to impossible, it is quite easy to learn to judge which way to go on a road or path where there are but two options. – Willeke Jun 28 '18 at 14:48
  • @Willeke I think you are underestimating the pedantry that goes on around here :) Yes just the sun will be useful, but its not very precised – Reinstate Monica Jun 28 '18 at 14:50
  • Do you have any estimate on how inaccurate this method could be (worst case scenario etc.)? – JeroendeK Jun 28 '18 at 14:52
  • @JeroendeK It depends on the latitude, but around 15 ° / 1 hour at certain times assuming you knew the correct solar time – Reinstate Monica Jun 28 '18 at 15:16
  • @CharlieBrumbaugh wow that's quite a lot. Thanks! – JeroendeK Jun 28 '18 at 16:16
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In short:
Not completely reliable but good enough for emergencies. It may give you north-east or north-west, but it will not give you south instead of north if you do it right. A compass used by an inexperienced person might send you 180 degrees off. See the last bit of this answer.

While the watch method is not good enough to find the north in an area where there are many options, like in an open field or in a forest with many roads that might go north, it has its uses and it is worth learning for emergency use.

The 'watch' method or just learning to read the shadows will help you when you are out in the wilds without a proper compass and you want to walk roughly one direction or when you are in a place where you know that the road you are on runs north-south or east-west.

The watch will work with any watch with a twelve hours system, an hours hand an a reliable 'twelve' spot.
Learning to read the shadows will work without any tools, like when your only watch is a digital one or when your watch has stopped working. But it does depend on your ability to read the shadows.

You will never be sure to get the proper north from reading the shadows and early and late in the day it will be worse, but it will help you not walking in circles when you pay attention to the shadows, as long as there is enough sun to get shadows to read.
And when walking in a (city) park and reaching a simple straight road from walking off road, knowing which way the road runs, a quick look at the shadows will often be good enough to confirm your direction.

And having trained for using your watch and/or reading the shadows in a 'safe' area, you will have a life skill that will help you when you ever get in a real difficult situation, where you are without proper tools (like lost your compass and your GPS ran out of power,) to get back to a place where you can work out where you are.

And while a good compass will give you the true north, I have seen several people using the tail end of the needle so they see south as north. Second checks with the sun (if visible) or shadows (if the sun is strong enough) will help to avoid that mistake. (And even with a good compass you will have to allow for a few degrees off the true north.)

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