Paulsan, - - I don't know such a formula off the top of my head, - - but I'll give you a sure-fire 'barn-yard' method that I would use in this situation, - - (even under close scrutiny), - - first of all lets take for granted you were going to use what I'll call the '8-rafter' method (48 total), - - I would cut each header with a 22 1/2 degree bevel on each side, - - and whatever (compound) angle it takes so your rafters will be 'plumb-cut' (where they meet the header), - - just making sure the shortest measurement of the header is at least a 7 1/2" minimum (so it can recieve five 1 1/2" rafters) - - then install all 8 headers, - - then on any one header mark 5 evenly spaced lines (representing the rafter locations), - - now tap 5 nails down into the outside edge of your top plate, representing the bottom end of your rafter locations, - - now pull a string from the nails to the apex, - - and measure and record your height difference between your string and your header at each corresponding location, - - you only need to check location #'s 1, 2, and 3, - - because #1 will match #5, - - and #2 will match #4. Now from those recorded measurements you can determine your arc onto a piece of plywood, - - then just go ahead and use that for a template to make the other 7. Something tells me that if you were to draw an octagon, - - with each of the sides being the same length as your headers (plus 1 1/2", representing your rafter thickness), - - then found your middle and drew that circle connecting the points of your octagon, - - that would be your correct radius/diameter for your plywood 'arc-caps'.

OK, - - it's getting late, - - I've confused myself enough now.