# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Centring Error Detector
Date: 2014 Jan 26, 21:48 -0500

Peter

The repeatability is due to all the faces meshing at the same time.  So 360 teeth vs 360 teeth. All teeth engage, every time.  The accuracy is due to the precision of cutting the teeth.  You could cascade them but it will be a mighty expensive sextant.  I'll leave it up to you to calculate how many you would need to stack up to get to 0.1 arc minutes (6 seconds) steps, throughout a 120° range.

The Hirth interface probably could be 3d printed, but I'm unsure if 3d printing can achieve the surface finishes required.  Additionally, the steps are discrete steps.  There's no way to get a mid-step position.

On Jan 26, 2014 9:32 PM, "Peter Monta" <pmonta@gmail.com> wrote:

Could this technique be used for sextant construction?  With these face-meshed gears one can make highly repeatable angle settings.  With several in cascade, one could have high resolution too.

For example, imagine a 3D-printed plastic or metal plate with 360 ridges on the top surface, something like the lines of a protractor, but more extended radially.  (With a plate radius of 60 mm, the pitch will be 1 mm, quite doable with FDM 3D printers.) It will mesh with a similar network of ridges in an adjoining plate, and under a suitable preload and with kinematic averaging over such a large surface area, repeatability will be good.  Now put two of them in cascade, the second with 361 ridges/teeth.  Now the settability goes from 1 degree to 10 arcseconds, small enough that one could just set it close and wait for a touch of a celestial body.

The index mirror would be mounted on the top plate, there would be a thin "idler" plate sandwiched in the middle, and the bottom plate would carry the horizon mirror and scope and shades as usual.

To calibrate, make several sextants and run them against each other, perhaps under autocollimation with a camera doing the measurements.  With enough (random?) angle settings on each sextant, an error model could be estimated.  (Yes, that's pretty hand-wavey.)

Could be better than a vernier plastic sextant, and cheaper too.  Could think about a hybrid construction with thin plastic or metal plates bonded onto a high-stability platform like carbon-fiber honeycomb.

Cheers,
Peter

ps: best to "skew" the ridges so they're not radial but instead canted something like a herringbone gear, the better to smooth out any printer anisotropy.

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