NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: App or program to find Hc just from lat, dec and LHA?
From: Gary LaPook
Date: 2015 Dec 4, 17:17 +0000
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

From: Francis Upchurch <NoReply_Upchurch@fer3.com>
To: garylapook.net
Sent: Friday, December 4, 2015 8:25 AM
Subject: [NavList] App or program to find Hc just from lat, dec and LHA?
From: Gary LaPook
Date: 2015 Dec 4, 17:17 +0000
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

From: Francis Upchurch <NoReply_Upchurch@fer3.com>
To: garylapook.net
Sent: Friday, December 4, 2015 8:25 AM
Subject: [NavList] App or program to find Hc just from lat, dec and LHA?
To check the accuracy of my Bygrave and BN, I currently need to use the cosine formula with a calculator which is fairly tedious and time consuming. All the sight reduction apps I've seen need you to input sextant sight details etc. They are great for an actual sight reduction, but for a quick check of my my slide rule results, I really just need a quick app or program which gives me Hc from just Lat, Dec and LHA.
Could any of the experts recommend one or teach me how to program an HP 67 calculator emulator (free app) to do it? (by the way, I'm old enough to remember the HP67 from the late 70s. A dream machine which I could never afford ($600 then!)
Many thanks
Francis