# NavList:

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

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From: Gary LaPook
Date: 2020 Apr 30, 14:43 -0700

Something to keep your brain cells active, learn the Bygrave method. You can access all the information on this here:     https://sites.google.com/site/fredienoonan/other-flight-navigation-information/modern-bygrave-slide-rule

Or you can just try it out on a simple three memory calcualtor. . Here is the step by step process:

An easy way to check the computation on a Bygrave is to do the same computation on a calculator since this allows you to check the intermediate steps.

Just use the standard Bygrave formulas in the three step process following along on the form I have posted.

First calculate co-latitude and save it in a memory in the calculator. If you are using a value for hour angle that is not a whole number of degrees you might want to make the conversion to decimal degrees and save it in a memory since it will we used twice. If you are using whole degrees then this step is not necessary.

Then you calculate "W" using the formula:

tan W = tan D / cos H

and sum it to the memory where you have saved co-latitude which is then X and then make any adjustment necessary to convert X to Y. (If you are just making trials you can avoid this step by your choice of the trial values.) There is no reason to store W itself since it is not used again. You can then convert W to degree and minute format to compare with the Bygrave derived value.

Then you compute azimuth angle using the formula:

tan Az = (cos W / cos Y ) x tan H.

If you want you can also convert Az to degree and minute format to compare with the Bygrave.

The last step is to calculate altitude with the formula:

tan Hc = cos Az x tan Y.

Then convert to degree and minute format to compare with the Bygrave result.

(When entering values in the format of degrees minutes seconds, change decimal minutes to seconds, 6 seconds per tenth of a minute, in your head  before punching in the assumed latitude, declination  and hour angle if necessary.)

Using whole degrees for declination, assumed latitude and hour angle, using a TI-30 with only 3 memory locations the key strokes are:

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

(co-latitude = 90 - Assimed latitude)

90
-
Assumed Lat
=
STO 1  (co-latitude stored in memory 1)

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

(tan W = tan D / cos H)

Declination
tan
/
H
cos
=
inv
tan    (computed W)
SUM 1  (X now stored in memory 1)(change X to Y if necessary)

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

(tan Az = (cos W / cos Y ) x tan H)

cos    (of W from prior step)
/
RCL 1  (recalls Y from memory 1)
cos
x
H
tan
=
inv
tan (computed Azimuth angle)

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

(tan Hc = cos Az x tan Y)

cos    (of Az from prior step)
x
RCL 1  (recalls Y from memory 1)
tan
=
inv
tan  (computed altitude, Hc)

2nd
D.D - DMS (changes Hc in decimal degrees to degrees, minutes and seconds)

DONE

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