Well, Unirac and Iron Ridge design tools force you into a large wind sail array configuration (3 panels high typically) and huge ballasts. They call for each ballast point to be about 1 cubic yard of concrete (~ 4,050 lbs) which is way overkill for what I want to do. I want a single panel in portrait vertically (77 inches) and 8 panels per row (~ 320") with 3 ballast points at 40 degree tilt angle. I doubt it would take 12,150 lbs of ballast to hold it down in a 110 MPH wind which is likely to never happen. I'm an electrical engineer, not a structural engineer so I could really use some structural formulas for this application, any links would be appreciated!
Edited concrete weight: ~2,000 lbs/yd for concrete rubble, 4,050 lbs/yd for a solid slab.
The stability is just moments, wind force x area x a coefficient x the height lever arm needs to be less than the mass of the ballast slab x the overturning distance.
Lets consider a 'slice' of your array:
-consisting of a section of PV, a single post, and ballast slab. See rough sketch attached.
The wind force wf is a function of windspeed and you can look this up from national tables.
The force will act on the net area of the panels (Apv)- you can reduce the area the wind acts on by tilting the panels more parallel to the ground for example. For this example we will just use the full area without reductions.
The applied force will act on the system as if concentrated at the centre of the PV array, we will assume the column height is this same central point
Putting this together: wf x Apv x h = the overturning force applied.
The base is a gravity block not attached to the rock below, it will resist overturning by gravity alone. This resistance will act at the centre of gravity of the block, we will call this distance from the leading edge to the centre of gravity 'd' - see the sketch.
The mass of the block we will call M, this mass will act as if it were concentrated at the centre of gravity point.
Putting this together: d x M = the resistance to overturning.
For your array to be stable we need the resistance to be greater than the overturing force, and to be 'safe' we usually go 1.5x for the resistance.
Lets run an example:
Say the PV area applicable to one post is 49 sqft, the post is 7 feet tall and the wf is 25 lbs per sqft. = 8575 ft.lbs
Lets also say the concrete base will be 6-feet wide, d=3 feet. how heavy does the concrete block need to be to not tip over?
3M > 8575 the mass needs to be at least 2858 lbs. but this would result in no factor of safety, which would normally be x1.5
so make the concrete block 1.5 x 2858 = 4287 lbs and now you have some safety margin for 25lbs/sqft wind force.
Remember this is just for one slice of the PV array - the panels associated with a single column, you can multiply by as many posts as you like, as long as you maintain the same geometry for each. Typical wf forces for exposed areas can be much higher than 25lbs/sqft so you should look up some data for your area and assess the exposure you have. ie a row of panels with a rock outcrop or trees sheltering them from wind can reduce the windspeed and thus lower the overturning force.
There are other failure modes, such as sliding, or if you were on soft ground the leading edge 'toe' of the ballast slab could sink instead of overturning on the corner, your post has to be stiff enough that is doesn't just buckle at the connection to the concrete ballast slab, and the array itself - if cantilevered ahead of the post can add to the overturning forces. Review your set up and check these items.