Just a minor point: the f-number is the focal length divided by the diameter of the entrance pupil, not by the diameter of the iris opening (unless the two are equal, of course). This is a fairly important concept to understand, particularly when you are trying to comprehend zoom lens specifications.
On a lens that is stopped down the two are basically the same when shooting LF.
What you are doing with Bellows Factor is working out what the
effective aperture is as it will differ from what is indicated on the aperture ring*.
For example a marked aperture of f-8 would behave as if it were f-11 when the bellows are extended to twice the focal length of the lens, and as f-16 at an extension of 4x the focal length.
It worked well enough for me in the studio
*Note: f-numbers are a convenient way to simplify and standardise exposure calculations across lenses of different focal lengths.
f8 on a 85mm lens gives the same level of illumination on the film as f8 on a 300mm lens.
The aperture on the 300mm is wider at f8 than that aperture on the 85mm to compensate for light loss caused by the greater distance of the film from the lens. That is to say, f-numbers are constants (calculated by the formula above) that take into account the effects of the Inverse Square Law.
But f-numbers assume the focal length of the lens remains constant (for primes).
Extending the bellows more than the focal length of the lens (or the use of extension tubes) brings the Inverse Square Law back into play so that the f-numbers are no longer accurate indicators of illumination levels on the film.
Bellows Factor is nothing more than an adjustment to compensate for this effect.