# NavList:

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

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Re: New compact backup CELNAV system RENAMED Accuracy of Bygrave Slide Rule
Date: 2009 Apr 11, 16:48 -0700

```Hi Gary

The MHR-1 has the instructions printed on the rule itself, so they are right
where you need them.  Naturally, they are in German.  I fiddled around and
came up with this translation (using online word by word translation.

Begin Translation

Special case: with azimuth between 85 degrees and 90 degrees, the calculation
is repeated with the permutation of latitude and declination. Instead of
latitude in the second step, use declination and calculate b=90 ?
declination.  In the third step, Azimuth is the helper angle that is used
only for the calculation the altitude.  Don?t use the slide rule when the
hour angle and declination is between 0? and 20?, as well as when the hour
angle is close to 90.

End translation.

Azimuth => helper angle, but not a valid Azimuth at that point. I think you
are supposed to get the azimuth by running the calculation TWICE.  In the
first instance, you get the azimuth close to 90.  In the second instance, you
solve for altitude.

-------------

The MHR-1 also permits the use of hour angles beyond 6 hours or 90 degrees.
So, if you were beyond the arctic or antarctic circle and wanted to calculate
the alitude of the sun as it runs around the sky in 24 hours without setting,
you can do so.  I have done just that.  It took a bit of thought to see how
the MHR-1 was to be manipulated, but it does clearly word (and compares well
with calculator comparison).  In addition to the black numbers printed by the
lines, there are also red numbers that extend the scales to 180 degrees.

-------------

In answer to your querry regarding the Flat Bygrave compared to the
Cylindrical Bygrave, we have only to look to the printing process, assuming
that you did follow the equations.  The modern person, like you or I, will
print our scales directly on a one to one basis.  That is, the print size is
the final size.  We will be subject to the resolution of the printer.  300
DPI (dots per inch) will look just fine but you may wish to jump to the
highest resolution possible.  No matter which resolution you obtain, this
will force the ticks on the Flat Bygrave to one line of pixels or another, as
a function of the printer resolution.

For the cylindrical Bygrave, I will have to resort to a bit of speculation.  I
wasn't around when the original English Bygraves were made and I certainly
wasn't in Nazi Germany for the MHR-1 construction.  However, the general
principal is to make one huge master and photo reduce it down.  This
principal was used to great advantage.  The creator spends alot of time with
a massive scale, measuring off and marking lines where they are to be.  Then
the image is reduced for production.  You essentially have infinite
resolution, since each line is individually created, one at a time.  Any
small errors in tick creation are masked when the photo reduction occurs.

The benefit of the directly printed scale is the speed at which it is
initially created and the lack of creation errors (assuming those equations
are right).  The draw back is the pixelation.

The benefit of the photo reduction method is the infinite resolution for the
tick marks.  Slow as molasses in creation though.

I strongly feel that there will be little if any affect on the resultant
reductions.  The Bygrave does not depend on precise alignment of the tick
marks, merely the closest one, by eye.

Best Regards

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```
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