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Re: Cylindrical Slide Rule tube poll
From: Gary LaPook
Date: 2010 Jan 25, 21:32 0800
From: Gary LaPook
Date: 2010 Jan 25, 21:32 0800
An easier way to check the computation on a Bygrave is to do the same
computationn on a calculator since this allows you to check the
intemediate steps.
Just use the standard Bygrave formulas in the three step process following along on the form I have posted and using my terminology.
First calculate co latitude and save in a memory on 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 since it will we used twice. If you are using whole degrees then this step is not useful.
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.
(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:
90

Assumed Lat
=
STO 1 (colatitude stored in memory 1)

Declination
tan
/
H
cos
=
inv
tan (computed W)
SUM 1 (X or Y now stored in memory 1)(change X to Y if necessary)
cos
/
RCL 1 (recalls Y from memory 1)
cos
x
H
tan
=
inv
tan (computed Azimuth angle)
cos
x
RCL 1 (recalls Y from memory 1)
tan
=
inv
tan (computed altitude)
2nd
D.D  DMS (changed Hc in decimal degrees to degrees, minues and seconds)
done
gl
Hein Bodahl wrote:
Just use the standard Bygrave formulas in the three step process following along on the form I have posted and using my terminology.
First calculate co latitude and save in a memory on 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 since it will we used twice. If you are using whole degrees then this step is not useful.
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.
(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:
90

Assumed Lat
=
STO 1 (colatitude stored in memory 1)

Declination
tan
/
H
cos
=
inv
tan (computed W)
SUM 1 (X or Y now stored in memory 1)(change X to Y if necessary)
cos
/
RCL 1 (recalls Y from memory 1)
cos
x
H
tan
=
inv
tan (computed Azimuth angle)
cos
x
RCL 1 (recalls Y from memory 1)
tan
=
inv
tan (computed altitude)
2nd
D.D  DMS (changed Hc in decimal degrees to degrees, minues and seconds)
done
gl
Hein Bodahl wrote:
On 24.01.2010 23:32, Hanno Ix wrote:Hein: These are nice scales. However, is there a way to check the accuracy? It appears to me computer generated scales depend on the accuracy and resolution of the particular printer one uses, no?Hopefully, an probably, any inaccuracy in the printer would be consistent enough over a few sheets. The resolution would of course have to be good enough to reproduce the scales with sufficient detail. I just realized that the separate scales I attached have different orientation. They should of course both be printed the same way as a printer most certainly deviates in accuracy in different orientations. As for testing I guess the easiest way is to test them against a calculator like this: http://www.coastalsailing.net/Resources/Navigation/Calculators/SunInformation.html I guess the greatest inaccuracy would occur in cos of a small angel and cot of an angle of about 45. Hein