[TowerTalk] And now for something completely different (True North)

Jim Lux jimlux at earthlink.net
Mon Aug 28 12:46:39 EDT 2006

At 07:15 AM 8/28/2006, Rajiv Dewan, N2RD wrote:
>The stick at high noon is a very good method and a lot more useful
>than stars at night.  You do not have to live exactly at the time
>zone meridian.  You just have to find the sunrise and sunset for
>*your* location and date.  So here are the steps:
>1.  Find the sunrise and sunset time for the location and day you are
>going to do the experiment.  You can find that in your local
>newspaper or visit
>http://aa.usno.navy.mil/data/docs/RS_OneYear.html and type in the
>state and city.   (For even greater accuracy and greater generality,
>you can enter the exact latitude and longitude instead of using the
>city/state combination)  The web site has the times in ST without the
>daylight correction.
>For example it lists the sunrise and sunset times are 0530 and 1852
>EST for Rochester, NY on August 28, 2006.   With the daylight
>correction the times are 0630 and 1952 EDT.
>2.  Compute the mid point which is high noon for the day and location
>specified.  The duration of the day is 19:52 - 06:30 = 13 h 22 min.
>Half of that is 6h 41 min.  Adding that to 6h 30 min (sun rise time),
>I get  1:11PM EDT.

Meridian transit (when the shadow points north) is NOT always halfway 
between sunrise and sunset (although it's certainly good enough for 1 
degree kinds of accuracy)
a) most (good) calculations of sunrise and sunset make corrections for 
atmospheric refraction, which may be different in morning and afternoon 
(the temperature profile is different)
b) The sunrise time is calculated for a position of the earth that is 12 
hours or so earlier than the sunset time. For example, if you're in the 
spring, when sunrises are getting earlier and sunsets are getting later, by 
a couple minutes per day, the time from meridian transit to sunset will be 
a minute (or so) longer than the time from sunrise to meridian transit. 
You're basically interpolating between two points on a sinewave.  Near the 
solstices, this is less of an issue, because the slope is low, likewise on 
the equinox, because the sine is close to linear

As long as you're going to the usno website, why not just use the transit 
time, which is given as well as sunrise and sunset times.

By the way, the same site gives az and el for the sun at 1 minute ticks, 
which provides a nice illustration of why the "wait til the shadow is 
shortest" approach is difficult:  For today for my location, the elevation 
of the sun is above 65 degrees from 11:38 until 12:15, reaching a peak of 
65.3 degrees from 11:47 until 12:06.  I doubt that anyone could accurately 
discern the difference of 0.3 degrees in a shadow length, especially 
considering that the shadow itself has a 0.5 degree wide border. (the 
shadow difference is a few mm if you have a  1 meter high stick)

>3.  The shadow of a vertical stick (use a plumb line for greater
>accuracy) at 1:11PM on August 28, 2006 at Rochester, NY points due

The same site gives the following interesting information (for today, 

Time          El           Az
12:09       56.4       178.8
12:10       56.4       179.3
12:11       56.4       179.7
12:12       56.4       180.2
12:13       56.4       180.6

So you can see that if your clock is off by a couple minutes, you're still 
within a degree.


Just to get a feel for the impact of screwing up your position:

Here's 119W, 34N
Sunrise                   05:27
Sun transit               11:57
Sunset                    18:27

and here's 119, 10'W (roughly 8-10 miles west..)
Sunrise                   05:27
Sun transit               11:58
Sunset                    18:28

So it looks like a 10 mile position error at mid latitudes in late summer 
is worth about a 1 minute error in timing (probably less.. I think there's 
a roundoff/truncation thing too), which, in turn, is about 1/2 degree 
azimuth error.

Jim, W6RMK 

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