On this list we have had a good discussion on using Google Earth to determine
wall declination. Jim Tallman described the simple technique using Google
Earth's ruler tool.
"In Google Earth there is a function that allows you to measure headings and
distances. I don't remember what it's called, but it will give you true compass
bearing of the line you draw with it. Check out the tools at the top of the GE
window. I click on each end of a roof ridge, or the gutter line of a building
and then convert the heading to the standard sundial declination convention for
whichever side of the building that I need".
I use this ruler tool routinely to determine wall declinations of remote
sundials. It works well but how accurate is it?
Remember the rule of thumb for angle x, measured in radians. For small angles,
Angle x = Sin x = Tan x. Whether you measure along the arc, on the
perpendicular from the the horizontal or the perpendicular from the hypotenuse,
the answers are much the same for small angles. For 1°, x, sin x and tan x are
all about 1/57, 2?/360. The error in the perpendicular from a wall displaced by
1° is about 1 in 57. Let's call it 1 in 60.
When you place a line on a Google Earth image, along a roof edge or whatever,
can you place in within 1 ft in 60? If the picture is clear and taken from
directly above, of course you can. Given good pictures, Google Earth can
determine wall declinations with an accuracy well better than 1°. This is why I
use it routinely. Just remember +/- 1° is about 1 in 60.
How does this matter for the lines on a sundial? Where does the shadow hit the
wall? Consider the triangle of the real wall, the assumed wall and the error in
the base of the perpendicular. That is where the shadow hits the wall. The
error in where the shadow falls is generally much less that the difference
between the walls. It all depends on the specific geometry. Everything is
exaggerated as the solar azimuth approaches the wall declination. Tangents
racing to infinity are always a problem. Don't divide by zero!
My bottom line is to trust Google Earth. Pictures don't lie.
Believe that and you will believe anything!
Regards,
Roger Bailey
Walking Shadow Sundials
PS. Wearing another hat, I have used Google Earth images to estimate Iran's
progress towards nuclear bomb capability, specifically the route involving the
production of heavy water and the construction of heavy water moderated
reactors to produce Plutonium. My assessment based on GE images and a specific
knowledge of nuclear technology predicts 2017. The U235 route can get them
there quicker. Details on request. Google Earth is an amazing resource.
Sundials, nuclear holocaust whatever. The Google Earth resource is open and
transparent.
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