# Thread: Hi ALL, Need help with vector mathematics for a complex light sensor

1. ## Hi ALL, Need help with vector mathematics for a complex light sensor

I'm an older engineer, rusty on math, building a complex sensor to characterize Sun's energy at solar power arrays.
It is an assembly of 9 sensors, mounted on a funnel; with one pointing straight up, 8
Others spread evenly in 8 directions, tilted at 30 degree above horizon. One points due
North.
I'm struggling with vector formula giving a summation of dot-ptoducts of these 8 directional
Signals with the normal vector of the solar panel, which is specified with azimuth and tilt angle.
Thanks for any assistance, or suggestion.
-Steve

2. ## Re: Hi ALL, Need help with vector mathematics for a complex light sensor

Try to convert your directions in cartesian coordinates, this allows to calculate the dot product quite easily.

Using z for "up" and x for "north" (=> y is "west") and the notation (x,y,z):
(0,0,1) is pointing upwards
(sqrt(3/4),0,1/2) is pointing N, as y=0, z=sin(30°)=1/2 and the vector should be normalized.
(sqrt(3/8),sqrt(3/8),1/2) is pointing NW, calculated similar to the N-sensor just with the requirement x=y.
The other 6 sensors just have signs and coordinates swapped.

3. ## Re: Hi ALL, Need help with vector mathematics for a complex light sensor

Thanks mfb,You got me a good start, I should be able to carry on and figure out the rest of photosensors,and the Normal vector to the solar panel.I represent a solar array's attitude with azimuth and tilt. For instance, an array points South, slightly to the west, its Azimuth is 195 degrees and tilt is 20 degree.The challenge is to define this array in a form as follows...I found a representation of plane intersecting x-y-z axes:NORMAL FORM FOR EQUATION OF PLANE P:xcosα + ycosβ + zcosγ = p, γ where p = perpendicular distance from O to plane at P and α, β, γ are angles between OP and positive x, y, z axes.α ~ 90-20 =70; β =0?; γ ~ 15? I'm stuck here and unable to proceed. Any suggestion?Thanks again,-Steve

4. ## Re: Hi ALL, Need help with vector mathematics for a complex light sensor

You can find the normal vector in a similar way to the sensor coordinates:
South is negative x, slightly to the west is positive y, using the coordinate system from my previous post.
For a horizontal orientation, this gives $\displaystyle (\cos(\phi),-\sin(\phi),0)$ with your angle $\displaystyle \phi=195°$. The signs are arranged to combine the definition of azimuth with my coordinate system.
With 20° tilt, you get a z-coordinate of sin(20°) and have to normalize the horizontal components with cos(20°) accordingly. Therefore, the normal vector is $\displaystyle (\cos(\theta)\cos(\phi),-\cos(\theta)\sin(\phi),\sin(\theta))$ with the tilt $\displaystyle \theta=20°$ and the azimuth $\displaystyle \phi=195°$.
It is possible to do this more formal with rotation matrices, but I think it is easier to understand (and quicker to calculate) like this.

You can get the normal form by simply using $\displaystyle \cos(\alpha)=\frac{1}{\cos(\theta)\cos(\phi)}$ and analog equations for the other two components.