# NavList:

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

Message:αβγ
Message:abc
 Add Images & Files Posting Code: Name: Email:
Re: Scales used on Bygrave
From: Wolfgang Hasper
Date: 2010 Feb 19, 21:31 +0100

```I'll try a quick translation of page 166 / �80.
You may judge if it can compete with google's...
I will try to keep it as literal as possible, so
everyone can follow the original text if they want

BEGIN

[end of �79] The altitude slide rule manufactured by
Dennert Pape has proven useful and was introduced to
navy and air force.

�80. The position-fix altitude slide rule

The position-fix altitude slide rule is based on the
following considerations: The basic celestial triangle
of pole-zenith-star (fig. 105) is divided in two
rectangular spherical triangles by drawing a
perpendicular from the star S to the meridian, the
base point of which shall be A. Denoting the side PA
of the triangle PSA "90-x" and the side ZA of the
triangle "90-y" one can derive the following group of
formulae to calculate altitude and azimuth from these
two triangles.

cotan x = cotan delta *cos t
cotan Az=cotan t*cos y/cos x
cotan h=cotan y/cos Az

In doing so x is to be taken greater than 90� if the
hour angle t is greater than 90�. y equals 90�-phi+x
if phi [latitude] and delta are of same name. If of
contrary names, y=90�-phi-x The azimuth Az on the
northern hemishere counts from the South Point, on the
southern hemisphere from the North Point and is to be
assumed in the same quadrant as y, thus greater 90� if
y is greater than 90�.
These formulae consist of the trigonometric functions
cotangent and cosine only. This allows to build the
slide rule with only two sliding scales, with which
all three formulae can be solved. To achieve the
required precision (1 minute of arc) the two scales,
divided with log cos and log cotan respectively, are
fitted in a spiralling manner on two concentric
cylinders. Thus they can, naturally, be very much
longer than on on a linear arrangement, without making
the slide rule bulky. The log cotan scale fitted to
the inner cylinder would unwound be about 7 metres
long, the log cos scale unwound from the outer
cylinder would be about 4 metres long. The scales
cannot, however, be set next to each other to make a
reading as on a conventional slide rule. A pair of
cursors, fixed to a small outer ring [here the
description does in my eyes fail] compensates for
that. It resembles the hair line of an ordinary slide
rule. Setting of the zero mark on the log cos scale is
simplified by a fixed zero-stop for the cursor-pair.-
the scales do not only show markings from 0-90� but
also the respective complements, thus cumbersome
side-calculations can be omitted, if one only follows
the sign-rules as given above.
The use of the slide rule in detail unfolds from the
instructions for use printed on the device.

END

Well, google would have been a lot faster!

Wolfgang

Am Freitag, 19. Februar 2010 01:35 schrieb Gary LaPook:
> A while ago we had an ongoing discussion of what
> scales were actually used on the Bygrave and the
> German version, the HR1. Wolfgang just posted an
> excerpt of a book in German which supplies
> additional information on this issue. I am attaching
> pages 166 and 167 of this book. Even without
> speaking German I think it is clearly stated on page
> 167 that the inner scale is a log cotangent scale
> and the other scale is a log cosine scale. Also page
> 166 states the formulas that are actually solved
> with these slide rules which identify the scales as
> a cotangent scale and a cosine scale.
> ----------------------------------------------------
>-------------- Some of you may be interested in the
> Bremen 1943, volume II
> They show different aircraft sextants and describe
> their use and properties. (in German...)
>
> Most intersting is the last paragraph on mechanical
> calculation devices for the celestial triangle,
> including HR1.
> "The altitude slide rule manufactured by Dennert &
> Pape has proven useful and was introduced to navy
> and air force."
> Another hint that MHR1 is not likely to mean
> "marine" HR
>
> Wolfgang
>
> Pdf documents, zip compressed are linked ~ 5MB
> ----------------------------------------------------
>------------ NavList message boards and member
> settings: www.fer3.com/NavList Members may
> optionally receive posts by email. To cancel email
> delivery, send a message to NoMail[at]fer3.com
> ----------------------------------------------------
>------------
>
>p
>
>
>
> ----------------------------------------------------
>----------------
>
>
> gl
> ----------------------------------------------------
>------------ NavList message boards and member
> settings: www.fer3.com/NavList Members may
> optionally receive posts by email. To cancel email
> delivery, send a message to NoMail[at]fer3.com
> ----------------------------------------------------
>------------
>
> http://www.fer3.com/arc/imgx/SKMBT_C25010021719592.p
>df

```
Browse Files

Drop Files

### Join NavList

 Name: (please, no nicknames or handles) Email:
 Do you want to receive all group messages by email? Yes No
You can also join by posting. Your first on-topic post automatically makes you a member.

### Posting Code

Enter the email address associated with your NavList messages. Your posting code will be emailed to you immediately.
 Email:

### Email Settings

 Posting Code:

### Custom Index

 Subject: Author: Start date: (yyyymm dd) End date: (yyyymm dd)