Shading limit angle for collector field in sheds

[Ruslan]

Please help me find my mistake with calculation of Shading limit angle or give formula for it.

For horisontal basis I receive formula :

θ = arctg ( sin β / (Pitch/L - cos β))

where β - Tilt of table

L width of table = const = 3.3 m (2 portrait modules)

My calculation for θ (Pitch, β), degree :

θ (5, 30) = 54.7 PVsyst : 38.0

θ (5, 36) = 64.0 PVsyst : 40.1

θ (9, 30) = 17.1 PVsyst : 15.2

θ (9, 36) = 20,4 PVsyst : 17.2

θ (11, 30) = 12.7 PVsyst : 11.5

θ (11, 36) = 15.2 PVsyst : 13.2

looking forward to hearing from any who knows why I receive different results.

Regards,

Ruslan

[unilhexio]

I think your formula is wrong. This is the one I obtained:

θ = arctg ( L*sin β / (Pitch - L*cos β))

Regards,

[Ruslan]

Dear unilhexio,

Our formulas is same :

L*sin β / (Pitch - L*cos β) = L*sin β / L ( Pitch/L-cos β ) = sin β / (Pitch/L - cos β )

Please give another variant. But if You and me have same formulas, error in the PVsyst?

[unilhexio]

Dear Rusian,

Your formula is the following:

θ = arctg ( sin β / (Pitch/L - cos β))

And the one I obtained is:

θ = arctg ( L*sin β / (Pitch - L*cos β))

These are not same.

Be aware that you are subtracting 'L - cos β' (this is, a distance in meters and cos β with no units)...

I have tested my formula and it leads to exactly the same result than PVsyst do.

Regards.

[Ruslan]

Dear unilhexio,

Our formulas is same. My dont has expression L-cos β. Only Pitch/L - cos β.

θ = arctg ( sin β / (Pitch/L - cos β)) = arctg ( L*sin β / (Pitch - L*cos β))

and gives same results (Im checked out now)

Please give me your arguments and results will be same. For example I'm calulated :

L=3.3 m

Pitch = 9 m

β = 36 degree.

for my formula θ = 20.38 dergree, for yours formula θ = 20.38 degree, PVsyst gived 17.2

If Yours result is different, please write me to eynesr@gmail.com, I will send You my excel - file with all calculations.

Best regards,

Ruslan

[unilhexio]

Dear Ruslan,

I think you are doing something wrong.

Our formulas are different. You are substracting cos β (it does not have units) and L (its units are meters).

I think the following image can clarify the problem:

https://s28.postimg.org/4ufl2kv8p/20170110_173439.jpg

For your example (β=36 and L=3.3):

θ = arctg ( L*sin β / (Pitch - L*cos β))

Then:

θ = arctg ( 3.3*sin 36º / (9 - 3.3*cos 36º)) =

= arctg ( 3.3 * 0.58779 / (9 - 3.3 * 0.809) =

= arctg ( 1.93969 / 6.33024) = arctg (0.3064) = 17.036º

If you do not find the problem, then tell me and I will write you an email to receive your excel calculation.

Are you converting the tilt angle into radians in excel calculation?

Regards.

[Ruslan]

Dear unilhexio ,

I'm found error. Its convertation rad-grad and grad-rad. I'm forgot multiply Pi() for grad to rad.

and our formulas and pictures is same :

θ = arctg ( sin 36º / (9/3.3 - cos 36º )) = arctg ( 0.58779 / (9/3.3 - 0.809))= arctg (0.58779 / 1.91827) = arctg (0.3064) = 17.04º

Many thanks for Your time,

Best regards,

Ruslan

[unilhexio]

Dear Ruslan,

I am glad we found the mistake. It is very common to skip the radians conversion to operate with trigonometric operators in excel.

Best regards!