# Math Help - Irradiance onto a flat plate at certain orientation

1. ## Irradiance onto a flat plate at certain orientation

Suppose I want to measure, say, sky or solar radiation incident upon a flat plate. The maximum irradiation will be achieved when the plate surface normal is parallel to the direction of irradiation (but in the opposite direction obviously). If I know what this irradiance is (in Watts/m2) how do I calculate the irradiance incident upon a plate at a certain orientation (i.e. what value between 0 and 1 do I need to multiply the maximum irradiation by)?

Given the tilt (-90deg is face down, 90deg is face up) and rotation angle of the plate I can work out the zenith and azimuth angles of radiation relative to the plate normal. I also suspect that this question is analogous to finding the projected surface area on a two dimensional image plane.

I began with something like cos(Az)*sin(Zen) but when the tilt was 90, I was getting an azimuthal dependence when I really shouldn't have been.

Can anyone help?

2. Originally Posted by jl5000
Suppose I want to measure, say, sky or solar radiation incident upon a flat plate. The maximum irradiation will be achieved when the plate surface normal is parallel to the direction of irradiation (but in the opposite direction obviously). If I know what this irradiance is (in Watts/m2) how do I calculate the irradiance incident upon a plate at a certain orientation (i.e. what value between 0 and 1 do I need to multiply the maximum irradiation by)?

Given the tilt (-90deg is face down, 90deg is face up) and rotation angle of the plate I can work out the zenith and azimuth angles of radiation relative to the plate normal. I also suspect that this question is analogous to finding the projected surface area on a two dimensional image plane.

I began with something like cos(Az)*sin(Zen) but when the tilt was 90, I was getting an azimuthal dependence when I really shouldn't have been.

Can anyone help?
You need the area of the plate projected onto the plane normal to the
line of sight to the source.

If you have the unit vector n which is the normal to the plate (in the
direction that the plate is sensitive to incomming radiation), and the
unit vector m in the direction of the line of sight to the source then the
projected area is:

A n.m,

where A is the area of the plate.

RonL

3. Edit: Never mind.