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:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-p7j91DJBylkHt_-cR2AzbydT4HNosS-6D1K6fZaKdeQrakkFkl-ajfvphSi3AdNdhC3S7GCeSwc-1ZrporIp5A_ZEwUOrPtVNp5k5qPCAxdYS1KoB0q25ODlfXRwdKq7njHa/s200/20190324_104309.jpg)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhn0b2LOClCamYYSFjfOchGzxKSO13CLODlxehWOuaZTWNE6zeDnHa9fgNs-JFbPB6qljvvjNAjaCts22I7-UfexVGUMn33cdy2crtDYnuC75DT-00gXaKDRnFk2Xhpgr1mUAyM/s200/20190324_104247.jpg)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilNhEgAws9PMxz0rbgWsVeZ2gn-PEIPorNPF_RAFPC_-9x7LuKi52jkxAuAgOFxVnlIm8QoIW3JOjIA8uV6ur_ww1NKDHmTa4EHTroiVGUBr4bfgFhqTwH01i-wANjAipm4KPJ/s200/Screenshot_20190324-104259_GPS+Test+Plus.jpg)
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:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFDTYv8WZkdYFm1eeivzHl8N79gPLfrODMvNAStMfoGLb0y0IXD5ZGE6ZtOKRu4behycjphy07gyGiH0ukVWFkjpSsuVxHodTidkQ0kxtqSw72tln8nEAwzEpsHsS1oy1qaoAe/s400/exact-calc.png)
If I create a chart with the day's azimuth's calculated on the half our, I can derive an accurate estimate:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPnlOr1mXASXbzzZZSSoRTNY7Fw1YKpAXk55eaTqbT5IsFZiUBYiDh3YslRwTnJwx-qAnHDh6S5g6iB9vhqO5w8Ep3_UzXzdO0eh6PhhpWdHvoRrPoNSChIryVcPLAOpaazVLU/s400/daily-calc.png)
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:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhA0GBzQSkx49BtR6GkXoL-rjMOdS1k7uc2e_Ic9TKHuIYEh4VQeH-YHMzhyphenhyphenY0HcCVwtAh3xqevJ3qZJtWAccg_MhI00eVLE77glMF-yUS6eJTJgYBqEnXAzfu28M96oD68rPTA/s400/20190325_205104.jpg)
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:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipOy5t5fvbbNr2U4NOJAyI-3CT5-iDSA9XoAq2D_zMDwIR62VtOOgfMLIJdMXFQ7Pm5zFjmqnU5ZDawArDbhdRYbaRQoNzz3o82flY_dHVqGn22o9INaUVYrPD7H4aI1i7RFIo/s400/20190325_205042.jpg)
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.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1MQTbF3j1_j1-OKhAOXwvaO6w79awzRmB0XbeIlX0XqItaXEDOvjBpbSFQk68s56dKPupwHUWQGPle7GRIPsat-0kgiVmtgfop4-Zsxl_RPHXf_upZu798g0vXONaGIw_D4BF/s400/20190325_205056.jpg)
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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