Solar panel row spacing calculation

[Aub]

hi
to calculate spacing for solar panel rows so the front row does not cast shadow on the second row is easy enough to calculate if the panels are on a flat surface but what is the sum to calculate the row spacing for solar panels on a negative incline (see attachment)
there are plenty of examples online for calculators for a flat surface but i can not find anything for negative inclines
i would appreciate if someone could show me the sum or even better a XLSX spreadsheet that i can add in factors..
Aub
Solar Business development

 

[blamocur]

This forum is not meant to provide final answers, but I thought I'd make exception and contribute to greener and healthier earth . First, the usual disclaimer: "trust but verify", since I've made my share of silly mistakes in the past.

The distance in question depends on the Sun's angle, which varies with seasons.

In the attached graph [imath]L[/imath] is the length of CD (length/height of the panel), and [imath]d[/imath] is the length of AB, i.e. the minimal obstruction-free distance.
[math]L\sin\alpha-d\tan\gamma = (d + L\cos\alpha)\tan\beta[/math][math]d\left(\tan\beta + \tan\gamma \right) = L\left(\sin\alpha - \cos\alpha \tan\beta \right)[/math][math]d = L \frac{\sin\alpha - \cos\alpha \tan\beta}{\tan\beta + \tan\gamma}[/math]
We have [imath]\beta = -7{^\circ}[/imath] (because the roof slopes away from the Sun), [imath]\alpha = 15^\circ[/imath] and [imath]L=1762[/imath].

At latitude [imath]44^\circ[/imath] the Sun's zenith angle [imath]\gamma[/imath] varies from 22.56 to 69.44 degrees, and the values of [imath]d[/imath] for those angles are 2272 and 261 respectively.

 

[Aub]

Thankyou Blamocur
"The distance in question depends on the Sun's angle, which varies with seasons."
in solar we always calculate for the worst scenario (it can only get better), so for us in the southern hemisphere on the 22nd June and at 44° latitude the sun position is 22° above the horizon
i will try entering your sum into a spreadsheet so i can alter a few parameters and work this out for different scenarios
have a good xmas

 

[blamocur]

in solar we always calculate for the worst scenario (it can only get better),

Interesting. I did not know that. But don't you loose a lot of space during summer time?