Tuesday, March 26, 2019

Improvised Direction Finding Using A Clock, Some Math and A Pocket Friendly Chart

It's 10:42am last Sunday and the sun is shining brightly. I'm curious how closely I can calculated my direction using the sun and my watch. I snap these pics as a control:

Both my compass and cell phone agree: the sun has a current heading of 128°.

If I plug my location and precise time into the formulas to calculate solar azimuth the result matches my field readings:

If I create a chart with the day's azimuth's calculated on the half our, I can derive an accurate estimate:

While reassuring (yay, math and my programming works!), both these approaches aren't ideal. If I have the means to execute the full series of solar math calculations, then I probably have my cell phone which has a compass and GPS built in. Using the sun to verify these readings is handy, though not essential. The daily cheat-sheet is useful for specific days (say, we're on a weekend backpacking trip) but requires planning to be of use.

A more general solution is a chart like this one:

This chart provides the sunrise time and azimuth, hours of daylight and solar sweep for an entire year. It does so in 1 week increments. The chart is small enough that I can tuck it in my pocket notebook and ignore it until needed. Using this data and some basic math, I can estimate the solar azimuth for March 24th at 10:42am:

I start by estimating sunrise time, azimuth, hours of daylight and sweep for March 24th. This day isn't on the chart, but the 26th is so I interpolate from there. I then calculate solar noon. This is the point where half the hours of daylight have been consumed, and the azimuth is 180°. I convert the target time of day, 10:42am, to a number of hours after sunrise. Using a simple proportion I can now solve for the number of degrees the sun has traveled between sunrise and 10:45am:

6.015hr             3.5hr
-------       =     -----
  92°                 x°

x = 53.5°

Adding the number of degrees the sun has traveled since sunrise (53.5°) to the sunrise azimuth (88°); yields my estimated position: 141°.

My first thought was: yikes! 141° is quite a ways off from 128°. However, looking at a compass convinced me this error is acceptable. Both approaches suggest that the sun is in the South-East on March 24th at 10:42am. If I had no GPS or compass to go off of this information would be invaluable.

I wouldn't want to survey property or search for hidden treasure using this chart, but as a zero-weight, battery-less, method for calculating direction I think it works.

Here's the Google Spreadsheet that powers this chart.

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