Lastspikemike
The formula is useful if you're drawing a layout plan.
If you actually have a layout and a roundhouse or kit for one you just need two lines on your layout.
Take the longest floor piece for one stall. Place that floor piece on your layout. Mark the back wall position of the roundhouse. Draw two converging lines, one along each long side of that roundhouse stall floor piece. Where they intersect will be the center of your turntable.
It doesn't matter how big the roundhouse is, how wide the doors are nor how large the turntable is. The location of the back wall of the longest roundhouse stall determines the location of the center of the turntable. That point depends only on the angle of the stalls.
The formula is always useful even on existing layouts. It may well be that someone is contemplating the purchase of a turntable and roundhouse but doesn't yet own one in which case he won't have the stall floor at hand.
Also, at least on the Walthers Cornerstone roundhouse, all of the stalls are the same length. Some kits include a few extensions for longer locomotives, but it is sufficient to measure the length of the standard stall.
The data derived from the formula is also useful in determining overall space for both the roundhouse and turntable. For example, using the 130' turntable and the Walthers Cornerstone Roundhouse, a space of 38.5" would be required from the back of the roundhouse to the far edge of the turntable. A space of 26.3" would be required if using the 90' turntable.
Rich