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Why has Bygrave chosen his particular set of equations and his design?

The formula :

sin(hc) = sin(D)·sin(L) + cos(D)·cos(L)·cos(t)

can, in principle, solved with a conceptually simpler slide rule: one that has just one helical scale, namely log(cos(x)) scale or log(sin(x)) scale.  You'd also need at least 2 cursors that can be moved as a set and individually.  You would not have to match the scales on 2 telescoping drums as necessary for the Bygrave- a difficult requirement according to G LaPook's description. As cursors you'd print cross hairs on on each of two transparent cylindrical foils fitting each other and, as a set, the drum that is imprinted with the scale. A third set of cross hairs - fixed in reference to the first - could be printed on one of the foils. It would allow an automatic wrap around. The general set-up would follow the Fuller slide rule design.

If you want to be fancier you could have 2 copies of the same scale mounted coaxially on the same core. Since their diameters are identical lining them up would be easier. To see what I mean you might want to see USpatent 1,597,484 by Ritow.

Just like with the Bygrave you'd proceed in 3 steps: first sin(D)·sin(L) and then cos(D)·cos(L)·cos(t) and finally adding these. The fact that the second operation has three components is but a small complication as anyone who has used slide rules can confirm.

Now, before I rush into my garage to build such a thing please convince me that these are bad ideas!

Hanno