# the disk of the sun

Hi All -

I'm working on a project in which the brightness of the disk of the sun has become a discussion topic.

Using gendaylit set for California's central valley, a view toward clear (smoggy-ish) sunny skies at 8am on September 1 reveals a disk luminance of 987,365,074 cd/m2.

This seems perfectly reasonable, although when I find myself commenting "oh yes, it's about a billion..." I can't help but pause.

Does anyone know of a handy reference for disk luminance based on location and climate? Or better yet, anyone out there with greater math skills than I know how to derive disk luminance from direct normal radiation found in a weather file?

Thanks!

Mike

Hi Mike,

See page (number) 60 in chapter 3 here for a description how to derive the luminance of the sun from direct normal illuminance:

http://www.iesd.dmu.ac.uk/~jm/doku.php?id=resources:thesis

Includes a little discussion re: the inconsistency of applying a measurement taken with an acceptance angle of, say, 6 degrees to a source - the sun - that has an angle 0.5 degrees. Note that the discussion is couched in terms of predicting illuminance.

Best
John Mardaljevic

Institute of Energy and Sustainable Development
De Montfort University, The Gateway, Leicester, LE1 9BH, UK
Tel: +44 (0) 116 257 7972

Hi Mike, I think John's equation may be an equivalent equation - but here
is how I have gone about it using these two equations:

E = L * w * cos(theta)

where w is the solid angle of the sun and theta is the incidence angle on
the illuminance plane; 0 for direct normal illuminance.

Then the solid angle can be determined using this:

w = 2 * pi * (1 - cos (half angle) )

This uses the half angle of the solar disc cone, so roughly .25 degrees.

Cheers,
Zack

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On Tue, Mar 6, 2012 at 3:41 PM, John Mardaljevic <[email protected]> wrote:

Hi Mike,

See page (number) 60 in chapter 3 here for a description how to derive the
luminance of the sun from direct normal illuminance:

http://www.iesd.dmu.ac.uk/~jm/doku.php?id=resources:thesis

Includes a little discussion re: the inconsistency of applying a
measurement taken with an acceptance angle of, say, 6 degrees to a source -
the sun - that has an angle 0.5 degrees. Note that the discussion is
couched in terms of predicting illuminance.

Best
John Mardaljevic

Institute of Energy and Sustainable Development
De Montfort University, The Gateway, Leicester, LE1 9BH, UK
Tel: +44 (0) 116 257 7972

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