Celestial Nav. - Sight Reduction with Calculator

[Gos2015]

I am having trouble calculating Z.

Text book question:
ALat. 48 degrees N
Declination 0 degrees, 19.4 minutes S
LHA 13 degress

Text book answer:
Hc 40 degrees 23 minutes
Z 163 degrees
Zn 197 degrees

I have a fx 991 Casio scientific calculator, using the shift key my Hc formula looks like this:

Hc=Sin-1((Cos A. Lat x Cos. Dec. x Cos. LHA) +/- (Sin A. Lat x Sin. Dec))=

Hc=Sin-1((Cos 48 x Cos 0 degrees 19.4 x Cos 13) - (Sin 48 x sin 0 degrees 19.4))= 40.37 converted to 40 degrees 23 minutes

So I get the correct answer for the Hc but then comes Z.

Formula for Z: (using shift keys for fx 991 Casio)

Z=Cos-1((Sin Dec. - Sin A.Lat x Sin Hc) / (Cos A.Lat x Cos Hc))=
Z= Cos-1((Sin 0 degrees 19.4 min. - Sin 48 x Sin 40 degrees 23 min) /
(Cos 48 x Cos 40 degrees 23 min))=

My answer:
Z=130 degrees
Zn=230 degrees

Text book:
Z=163 degrees
Zn=197 degrees

What is everyone else getting? What am I doing wrong?

[Snowpetrel]

I got the same as the textbook answers

[Snowpetrel]

Originally Posted by GoSailing

I am having trouble calculating Z.

Z=Cos-1((Sin Dec. - Sin A.Lat x Sin Hc) / (Cos A.Lat x Cos Hc))=
Z= Cos-1((Sin Minus -0 degrees 19.4 min. - Sin 48 x Sin 40 degrees 23 min) /
(Cos 48 x Cos 40 degrees 23 min))=

My answer:
Z=130 degrees strange, without the negative dec I get 158
Zn=230 degrees

Text book:
Z=163 degrees with the negitive dec I get 162.8
Zn=197 degrees
?

.......

[Gos2015]

So maybe for a contrary ALat and Dec, you make the Dec a negative figure.

This would explain why the formula sometimes works and sometimes it doesn't.

I know on other HC formulas, from the one I am using, that they make the Dec negative for 'contrary' situations and always add the figures in the first set of brackets to the second set of figures. Like this:

HC=Sin-1((Cos ALat x Cos -Dec x Cos LHA) + (Sin ALat x Sin -Dec))


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[Snowpetrel]

Yep. Thats the easiest way. Use negative for south and keep the Hc formula consistent. Hopefully this is giving you the right ans? Good on you for giving celestial a go. Cheers Ben

[Snowpetrel]

How did the calcs work out? still not sure how you got Z at 130? but just to clarify, it's easier to be very consistent with the naming conventions. North is +, South is - with both LAT and DEC. if you do this it all seems to work out in the wash. LHA doesn't matter, it does it itself being 360 as far as I remember. I'm all a bit rusty on it so might be wrong but thats how I remember it working for me...

[terrysandling]

Have you tried doing it without the calculator ,it's very quick and if the calculator malfunctions you have the knowledge ,sextant altitude to true altitude takes a few minuets , time GMT to GHA in your nautical almanacs ,plus or minus your assumed longitude depending or whether your longitude is east or west minus fore East and pluse for west gives you your LHA this takes only minuets , into your sight reduction tables with your LHA and there you have your HC D Z once you have calculated your declination and added or subtracted it from your HC ,you have what was once upon a time know as you height calculated,the difference as you probably are aware between your true altitude HO and the calculated altitude HC is your intercept, it takes us from start to finish about 15 minuets , i am almost sure it quicker than the calculator and if you make a slight mistake it generally show up very early, and the satisfaction is next to none as thoses who remember this great art will know------------The rewards of a life lived well is to plant trees under whose shad you do not expect to sit---------

[avid]

I am more than half way done with the Starpath Celestial Nav course. If you provide the full problem I will hand calculate. I can also run it through my Starpilot app on my iPad.

[Gos2015]

I have my celestial navigation certification the Canadian Yachting Assoc so I am quite comfortable in using the Ho 229 and Ho 249 sight reduction tables. In my mind, keeping no electronic items out of the fray is at the backbone of celestial navigation. However, always wanting to learn more and knowing that HO 249 tables (my preference) only work on Declinations up to 29 degrees, I thought I would teach myself the scientific calculator method.

The text book I am using provided me with the two formula, one for Hc and the other for Z.

Thanks to the help of SnowPetrel I have been able to solve my issue - which stems from the fact that the text book failed to mention to change the Dec. from + or - if Lat and Dec. are contrary in the formula.

So a big thanks to SnowPetrel for you help and I appreciate all the other comments I received.

Les

[Dsanduril]

Snowpetrel is right on. For a little background, think of declination as the latitude of the sun. It is the latitude at which you would be when the sun is directly overhead at noon.

The formula is looking for the difference between your (assumed) latitude and the latitude of the sun. If both are north (or both are south) then it's easy, you subtract. If one is the opposite sign from the other then you have to add (48 degrees to get to the Equator, then another 19.4 minutes to get south of the Equator to the sun).

The "traditional" way to handle this (at least for us northern hemisphere folks, don't know how they handle this down under) is to always have southerly latitudes/declinations be negative, that way the formula stays the same. Again, just as Snowpetrel pointed out.

[roland stockham]

If you are using a calculator why not use an app that contains the almanac data as well and gives you a position. You are still reliant on an electronic device but it is an independent position fix not reliant on GPS. Same as checking using a radar fix in coastal waters. I am trying to learn manual astro nav but so far not got much practice in, either no sky, no horizon or been hand steering so no time (auto pilot broke!)

[PDA1]

Zn is 197 degrees 10min.

I'm using the Casio FX-300Es Plus.

Zn was determined using the following formula;

Z = tan-1 (sin (LHA) / (cos (LHA) x sin(AP Latitude) - cos(AP Latitude) x tan(Declination))


Then to put az into the right quadrant, apply the following rules-


If answer is negative, add 180 degrees to az.
If LHA was less than 180 degrees add 180 degrees to az.


Part of your trouble was that you didn't put a minus sign before the Declination....since it's a South declination it should've been entered -0 degrees 19.4 min

For determing Hc I use the following formula;


Sin-1(Sin(Latitude) x Sin(Declination) + Cos(Latitude) x Cos(Declination) x Cos(LHA)

Again, make certain to put a negative sign before the Declination if it's Contrary to your Ap Latitude.

Besides calculators, using HO-249 could answer your question almost as fast.

[Gos2015]

Hi Roland, actually trying to stay away from things like apps. The calculator was just an add on to my preferred way using a sextant, almanac and sight reduction tables. I just can't see sitting in a life rate trying to keep my calculator dry to keep it working and then make something like 40 entries to just figure out the Hc. Not knocking anyone who chooses to use the Starpilot, any of the numerous apps or software programs around.

Thanks again Snowpetre - save me a lot of hassel trying to figure why things weren't working especially when they would work sometimes (when Lat and Dec the same)!but not other times (when Lat and Dec were different)!

For those wanting to refresh how to do celestial nav - old school, the book by David Burch out of starpath has the best book I have found and I have read, I am sure over 6!texts dedicated to celestial navigation.

If there are enough people interested, maybe as a group we can put up celestial navigation questions for fun and practice.


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[PDA1]

Originally Posted by GoSailing

If there are enough people interested, maybe as a group we can put up celestial navigation questions for fun and practice.


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Count me in- I love doing celestial problems.
Doing it on paper is much more enjoyable than using a calculator. In doing Sun sights all I need are about 3 sheets of paper;

1 for GHA and Declination determination found in HO 249 (it's Table 4- GHA and Declination of the Sun for the years 1981-2016

1 for the Latitude I'm generally in (from HO 249)

1 for Table 5 "Correction to Tabulated Altitude for Minutes of Declination"

For Stars....you need a few more pages...maybe 5.

[avid]

Originally Posted by GoSailing

For those wanting to refresh how to do celestial nav - old school, the book by David Burch out of starpath has the best book I have found and I have read, I am sure over 6!texts dedicated to celestial navigation.

That is what I am using although I am actually signed up for the Starpath course through an ASA sailing school. Plenty of problems to satisfy. Actually quite fascinated by StarPilot as well. Have it on my iPad and thinking of purchasing it for my TI-86. I have read the book about the StarFinder but haven't put in any time on it other than to look at the discs.