Question

Find the direct-beam solar radiation I_B normal to the sun's rays at 10:00 a.m. solar time on a clear day in Vancouver, BC (latitude 49N) on March 1.

Find the beam insolation on a collector I_BC that faces 15 degrees toward the southeast and
tipped up at 40 degrees at 10:00 am March 1 (Latitude 49N).

Answer 1

Ignoring sunspots, the day-to-day variation in extraterrestrial solar insolation is the following:

where SC is called the solar constant and n is the day number. The solar constant is an estimate of the average annual extraterrestrial insolation. Based on early NASA measurements, the solar constant was often taken to be 1.353 kW/m2, but 1.377 kW/m2 is now the more commonly accepted value.

Consider the following table with optical Depth k, Apparent Extraterrestrial Flux A, and the Sky Diffuse Factor C for the 21st Day of Each Month;

For computational purposes, it is handy to have an equation to work with rather than a table of values. Close fits to the values of optical depth k and apparent extraterrestrial (ET) flux A are as follows:

where n is the day number.

For finding solar declination refer to this table:

Now moving on to the given problem:

Number of days on March 1, n = 60 (29=february + 31=january)

So,

Now optical depth k ,

From the third table, on March 1 solar declination is 0.0◦ , so the altitude angle of the sun at solar noon is

L is the latitude, so L=49 here.

So the air mass ratio

So the direct-beam solar radiation is

Putting the values we get IB= 1051.93 w/m^2.

The angle of incidence θ is a function of the collector orientation and the altitude and azimuth angles of the sun at any particular time.The solar collector is tipped up at an angle zeta and faces in a direction described by its azimuth angle φC (measured relative to due south, with positive values in the southeast direction and negative values in the southwest). The incidence angle is given by

Refer to the following figure:

So putting the values in this problem:

Beam radiation on collector is given by

Hence these are answers for both parts of the question. Thank you!!