The width of the penumbra on a surface is the distance from the style to the surface times the angular diameter of the sun in radians (about 1/107) divided by the cosine of the angle between the normal (perpendicular) to the surface and the sun's ray. So basically you are correct, although 1/107 would be a better value. The value varies by about +/- 2% during the year due to the elliptical orbit of the earth.
For the year 1999 the following web page gives a mean solar diameter of 1923 arc seconds, corresponding to 1/107.3 radians = 0.009323 radians.
The maximum is 1955 arc seconds, and the minimum is 1891 arc seconds. Angular diameters from http://www.astrosurf.com/taf/dim-ogg-neg/don-sole-eng.htm Gordon At 06:18 AM 6/15/02 -0700, you wrote:
Hello All Does anybody remember the exact ratio or multiplication factor that will determine the width of the a shadow's edge penumbra if you know the distance from the style to the penumbra's image? Isn't the penumbra's with about 1/100th the projection distance? And couldn't this ratio be viewed in graphic or tabular form? I ask because I'd like to be able to calculate the theoretical penumbra width at different points along the Kitt Peak Sundial perimeter timelines. John John L. Carmichael Jr. Sundial Sculptures 925 E. Foothills Dr. Tucson Arizona 85718 USA Tel: 520-696-1709 Email: [EMAIL PROTECTED] Website: <http://www.sundialsculptures.com> -
Gordon Uber [EMAIL PROTECTED] San Diego, California USA Webmaster: Clocks and Time: http://www.ubr.com/clocks -
