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
>North.
The same site gives the following interesting information (for today,
Rochester):
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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