NavList:

Dear Trammel,

Nice tools — you have done an excellent job composing these!

I played with them a bit, and it was a real joy. I didn’t build them myself, only used the online versions.

If you don’t mind, I have a few comments on the haversine disc, which could be a great tool for fast celestial calculations when moderate accuracy is sufficient.

Easy readability is essential for such tools, and I found it a bit inconvenient that the natural hav and logarithmic hav scales increase in opposite directions. Late-period slide rules had a very good convention: left-to-right increasing scales were printed in black, while right-to-left increasing scales were printed in red. This makes readout consistent and fast, less error-prone, and requires no mental gymnastics. Let me recommend reversing the rotational direction of the Log Hav scale (and perhaps flipping the text labels on the outer disc to preserve their meaning, although those scales are interchangeable). You would be able to read out the values much faster.

In the past, I was thinking about building a similar haversine calculator to the one you made. I got the idea from Poor’s computer but never put it together. Your approach with the outer cosine/secant rings is superior to my plan of using a single spiral cosine scale. The biggest problem with spiral-type haversine scales is carry handling, which is a real struggle and can easily lead to errors. In special cases, you may need to jump two scales, not just one or none, and the direction is yet another factor. It’s difficult, hard to remember, and error-prone.

I had a plan to overcome this problem that could be implemented on your disks as well: a “rough computer” with no ambiguity (see the attached image). Before using the main scales, one could calculate a rough result on a condensed haversine scale (one full turn covering the entire domain). Rotate Lat over LHA, read transfer angle below Dec. Let’s say one reads an estimated result of thirty-some degrees. Then the detailed scales could be used as you demonstrated, but without struggling with carries — simply reading the result closest to the estimated thirty-some value. Easy, fast, and with little room for error.

This rough-computer scale could be implemented as the innermost scale of your upper disc and would probably require a third disc above it (perhaps attached to the cursor for easy handling?). Of course, different rough computers would be needed for the natural hav and log hav sides.

Cutting the cosine/secant scales at 60° is a clever trick to divide the long logarithmic haversine scale into segments, but this also limits the latitude and declination selection to a maximum of 60 degrees. The latitude limitation is not a big problem for me and for most of us I guess, but Dubhe and Kochab are also excluded from computation as popular navigation stars. A few southern-hemisphere stars are excluded as well — though unfortunately I have little chance to observe them anyway.

Would it be possible to extend the declination scale up to 75° beyond the 60°? (The 60° mark could complete the full circle and then continue on a separate ring.) And perhaps the latitude scale as well — who knows…

Nice disks! However, I am a bit skeptical about its usability for lunar calculations. The precision of this tool is too limited for rigorous methods; I estimate that the final longitude uncertainty could be on the order of half to one degree.

Although I am skeptical about its suitability for lunar calculations, it could nevertheless be a very effective tool for everyday LOP work, even under time pressure. It might even compete with Bygrave, without requiring the recording and calculation of intermediate values.

Regards,

Tibor