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Re: Traditional navigation by slide rule
From: Paul Hirose
Date: 2016 Oct 25, 09:36 -0700
From: Paul Hirose
Date: 2016 Oct 25, 09:36 -0700
On 2016-10-20 12:43, Bob Goethe wrote:
>
> Scale ST, which currently deals in values from tangent values from 0.01 to
0.1, would - if extended - deal in values of 0.0096 to 0.105.
> Not as clean for the hypothetical-slide-rule-novice for whom I am trying to
design the rule and write the manual.
Did you notice how it's done on the Deci-Lon? The trig scale labels
ignore the extensions. They show only the nominal scale ranges. E.g.,
the SRT scale is marked "0.01 to 0.10," though its true range is .00960
to .1047.
Also, scale extensions need not go out to the next numbered graduation
as on the Deci-Lon. They could extend only to the next convenient
graduation. A danger there, however, that the additional graduation
could be perceived as an index. That won't happen on the Deci-Lon since
the extensions are so obvious.
In the Mark 1 user manual, there's an arithmetic error in Step 3 at the
top of page 49. The minutes in the result are wrong. However, the next
line uses the correct value.
There's a mistake or omission in the Bygrave rules, or I'm doing it
wrong. Please check this southern hemisphere example:
L = S 27, d = S 21, LHA = 79, H = 79
approx correct az, el = 255, 19
1. W = atan( tan d / cos H ) = 63.6
2. X = (90° - L) ± W
– if contrary name
if meridian angle > 90, X = 90° - L - W
Take absolute value. X = 126.6
3. If X < 90°, then Y = X
If X > 90°, then Y = 180 - X = 53.4
4. Az = atan(cos W / cos Y * tan H) = 75.4
Use N if Dest. is N of Your DR
Use E if Dest. is E of Your DR
Az = N75.4W = 284.6
5. Hc = atan(cos Az * tan Y) = 18.7
That's the correct altitude, but azimuth is wrong. It should be about
15° south of west, but my value is north of west by the same angle. What
do you get?
The Bygrave simulation in my Monte Carlo accuracy measurement software
works correctly. But its computations are arranged differently from
yours. For one thing, azimuth angle is always measured from the elevated
pole (south, if the assumed latitude is south of the equator) and
increases east or west up to 180°.
https://navlist.net/m2.aspx/Bygrave-formula-accuracy-10-inch-slide-rule-Hirose-jul-2009-g8985
