# Math Help - What is the hitting angle between my (flat) solar collector and the rays from sun?

1. ## What is the hitting angle between my (flat) solar collector and the rays from sun?

I have an excel calculation which gives me the angles for the horizontal direction and vertical elevation to the sun, for a given time at given longitude/latitude coordinates.

I also know my solar collectors horizontal direction (194,5 degrees) and tilt angle (45 degrees). In other words, I can very easily count the relative horizontal angle between the solar collectors and the sun, likewise also the the vertical relative angle.

However, I'm interested to count the combined angle. What could be the equation for this?

2. ## Re: What is the hitting angle between my (flat) solar collector and the rays from sun

Originally Posted by kiqz
I have an excel calculation which gives me the angles for the horizontal direction and vertical elevation to the sun, for a given time at given longitude/latitude coordinates.

I also know my solar collectors horizontal direction (194,5 degrees) and tilt angle (45 degrees). In other words, I can very easily count the relative horizontal angle between the solar collectors and the sun, likewise also the the vertical relative angle.

However, I'm interested to count the combined angle. What could be the equation for this?

I'm not sure that I understand your question correctly ...

In vector geometry the angle between a straight line (= sun ray) and a plane (= solar panel) is defined as the angle between the straight line and the normal to the plane.

If you have an equation describing your solar panel and an equation of the sun ray (with respect to the day time) then the angle $\alpha$ between the normal vector $\vec n$ and the direction vector of the straight line $\vec a$ is calculated by:

$\sin(\alpha) = \frac{|\vec n \cdot \vec a|}{|\vec n| \cdot |\vec a|}$

3. ## Re: What is the hitting angle between my (flat) solar collector and the rays from sun

Thank you.

You did understand it correctly.
I guess it's possible to choose any length for vectors n and a (for example 1), since the distance to sun or the length of the normal are not interesting?

Let's see if I'm able try to turn the equation above into excel..

4. ## Re: What is the hitting angle between my (flat) solar collector and the rays from sun

Let's say for example that the relative horizontal angle is 8 degrees, and the relative vertical angle is 26 degrees.
Would you mind help me to turn the above equation into numbers?

Please, this is difficult! It's a long time ago since I've calculated with vectors.