NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
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/otherflightnavigationinformation/modernbygravesliderule
Or you can just try it out on a simple three memory calcualtor. . Here is the step by step process:
CHECKING YOUR COMPUTATIONS
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 colatitude 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 colatitude 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 TI30 with only 3 memory locations the key strokes are:

(colatitude = 90  Assimed latitude)
90

Assumed Lat
=
STO 1 (colatitude 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