Comments on Solar Radiation on a Tilted Surface


Dear Christiana Honsberg and Stuart Bowden,

First of all I really appreciate your work for very complete information
about photovoltaic system in this site.
After I read about "Solar Radiation on Tilted Surface", I've tried to apply
the equation to get best tilted angle for optimum PV system output. In that
article, its said that S module = S horizontal (sin (a + b)/sin a).
From that equation, we can see the optimum S module will be got if (sin (a +
b)/sin a) is maximum (Because S Horizontal is given data). Then I've began to
get maximum value of (sin (a + b)/sin a).
These are what I've done :
Given data :
Latitude : -6 (S)
Longitude : 106 (E)
GMT : +7
Type of Module : Fixed
Daily solar radiation - horizontal : NASA data.
From data above a (elevation angle - at noon) is got from day 1 to 365, then
I've calculated value of "(sin (a + b)/sin a)" where data of b (tilted angle
of module) are varied from 0deg - 90deg (interval 1deg).
After all data calculated and summarized in one year (day 1 to 365), the
maximum output of PV is got when tilted angle of module b = 17.

But in the other hand, that article also said that : "For a fixed tilt angle,
the maximum power over the course of a year is obtained when the tilt angle
is equal to the latitude of the location". SO from that statement, the best
tilted angle for latitude = -6 (S) should be b = 6 (different with what I've
got from calculation, b =17).
Can u explain this matter?

In another references, it also said that "the maximum power over the course
of a year is obtained when the tilt angle is equal to the latitude of the
location", how can we prove that this statement is true and can be accounted.

Hope you can reply soon because I really need your answer. Thank u for your

Dear Christiana and Stuart,

First thank you a lot for this wonderful website, it really helped me understanding the fundamentals of solar radiation calculations.

I am trying to get the grasp on tilted PV module aspects and to do so have modeled a sample year on a hourly basis. Using S_module=S_incident*sin(alpha+beta) and S_horiz=S_incident*sin(alpha) on a daily value for S_incident I get the same response that you show in the [Solar Radiation On a Tilted Surface] page. However I have alternatively calculated the hourly radiation profile for each day of the year using the infra-day variation of zenith angles both for horizontal and tilted planes as a function of latitude,mass air and time. When I integrate the hourly values over each day I get a significantly different and lower result than yours for both tilted and horizontal daily radiation sum. After double checking my equations it seems everything is correct (also the results looks sound). I must say I am a not 100 percent confident on how to interpret this mismatch. My intuition would say that the relation you provide only accounts for daily maximum elevation at solar noon and neglect course of day variations, thus overestimating the sum. Is it right?

Thank you for your attention and time. It would be great to have your comment on this aspect.

This is correct. It is a simplification for solar noon. A more accurate method is to adjust through out the day as you suggest. The solar noon is easier to explain and it works reasonably well since the suns intensity is lower at other times and the modules are generally pointed towards the equator.

First of all, thanks for your wonderful website.

However, I was wondering if the solar azimuth will have any effects on the surface. Say for example, if i have a surface placed vertically facing east and the sun altitude is 0 degrees and azimuth is 90 degrees. Suppose this is the best placement for the surface to receive the maximum solar radiation. However, if I placed the surface vertically facing north and the sun condition remain the same, wouldn't the surface recive no energy? Then does that mean I also need to take account of the solar azimuth instead of only take account of the solar altitude?

Sorry for my bad english by the way.

I am a Plant Biologist. I am very interested in photosynthesis of epiphytes on trees such as mosses and lichens. I want to model PAR (400-700 nm)photons on a vertical surface.
I have a EXCEL routine that uses SMARTS data to model a horizontal surface quite well.
Your equation gives the direct beam. How do I model skylight? I know that the colour temperature of skylight (7600 K?) is different to the sun.

How to estimate

1) Global tilted irradiation (GTI) on a tilted surface from the Global horizontal irradianion
2) How to compute power of a PV panel from GTI

Hi! Thank you very much for this great material.
I am trying to find the "correction factor" that should be applied to the radiation on horizontal surfaces to get the real radiation over a tilted surface as a function of latitude, tilt angle and month of the year.
In other words: I am looking for the numbers you used to build the simulation at the bottom of this article. Is it possible to get this info?
My e-mail:
Thank you in advance and greetings from Argentina,