Paul, the screen I used was 4 feet HIGH, not 4 feet WIDE. It's 88" wide, over 7'. Maybe 5' is still a wide viewing area for that size of screen, but others have built sucessful torii in that size range that used MUCH deeper curves. The curves in the spreadsheet were only about 2.5" deep on an 88" chord. If I'm figuring correctly, that works out to a radius of about 388" = over **32 FEET** !! How can that be right!?
Wait, I see. I guess the spreadsheet is aiming the screen such that the angles from the edges of the screen to the focal point bisect the required viewing width at the specified viewing distance. The attached not-to-scale picture will explain it better than my words can. Looking back at your spreadsheet, I see you do show this in one of your pictures -- I just didn't think it through.
That's a lot different from what I think most people are attempting, with their approximations of the string method. The string method focuses the whole screen on one spot, with a radius from that spot to the screen. That's effectively the same as specifying a zero-width viewing area with your spreadsheet -- which produces a top/bottom curve depth of almost 22 inches! Your spreadsheet is spreading the "sweet spot" across the whole requested viewing area. Makes sense.
I wonder what kind of gain curve results from this approach vs. the string approximation that everybody seems to be using? The ideal string approach would produce a huge gain spike right at the sweet spot, and it would drop off VERY rapidly as you move to the side. The "longer than string method radius" approach that most people use would probably produce a lower gain in the sweet spot but a reduced dropoff. I suspect your spreadsheet approach would produce fairly uniform gain across the width of the specified viewing area, but a much lower gain. Sound right to you?
Interesting spreadsheet! Thanks for sharing it.