# NavList:

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

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Re: recommendation for slide rule ?
From: Gary LaPook
Date: 2009 May 20, 15:59 -0700

```Computing Hc and Zn on a slide rule takes 16 steps. It will be easier to
explain with an example, using 34 for the latitude, 20 for the declination
and 14 for LHA, the same values used in my previous example with the Flat
Bygrave, see http://www.fer3.com/arc/m2.aspx?i=107414&y=200902

I will use a K&E 4080 for the illustrations.

Using the sine- cosine procedure we first calculate Hc using the formula, sin
Hc = (sin Lat sin Dec) + (cos Lat cos Dec cos LHA).

First line up the sine (S) scale with the D scale, see IMAGP5888.

Second move the cursor to the latitude, 34, on the S scale, see -98.

Since the sine and cosine values are all less than 1 we know that when we
multiply these values that the product will be smaller than the original
numbers which on a slide rule means that the result is found further to the
left on the scale. So, third, line up the 90 mark on the S scale with the
cursor, see -00.

Fourth, move the cursor to the declination, 20, on the S scale and read out on
the D scale the product of sine latitude and sine declination, .1915. see -
02.

Fifth, line up the S and D scale again, see -88.

Sixth, move the cursor to the latitude, 34, on the cosine scale, red numbers
on the S scale increasing right to left, see -04.

Seventh, line up the 90 mark on the S scale with the cursor, see -05.

Eighth, move the cursor to declination, 20, on the cosine scale, see -07.

Ninth, line up the 90 mark on the S scale with the cursor, see -09.

Tenth, move the cursor to LHA, 14, on the cosine scale and read out the
product of cosine latitude, cosine declination and cosine LHA on the D scale,
.755, see -11.

Eleventh, add the two products together, .1915 plus .755 equals .9465.

Twelve, line up the S and D scale again and locate .9465 on the D scale and
read out Hc on the S scale, 71.1º , see -13.

Next we calculate Az using the formula (sin LHA cos Dec)/ cos Hc rearranged as
(sin LHA/cos Hc) cos Dec. Az will be in the range of 0 to 90.

Thirteen, move the cursor to LHA, 14, on the S scale, see -15.

Fourteen, line up Hc, 71.1, on the cosine scale with the cursor, see -26.

Fifteen, move the cursor to declination, 14, on the cosine scale, see -27.

And finally, sixteen line up the S and D scales and read out Az, 44.5º, on the
S scale under the cursor, see -28.

gl

,
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