Calculator method

[pabrides]

The following paraphrased excerpt is from the 2018 Nautical Almanac:

Determine Hc using a calculator
Hc = asin[sin(Declination)*sin(Latitude) + cos(Latitude)*cos(Declination)*cos(LHA)]
As it would be entered into the Casio calculator
Sin-1(Sin(Ap Latitude) x Sin(Declination) + Cos(Ap Latitude) x Cos(Declination) x Cos(LHA)

 
Instantly one sees these two formulas are not the same.  The second formula is missing an operation bracket and one set of operations are transposed.  But that's only half the problem.  It is unclear which operation comes first.  Is cos lat added to sin lat before being multiplied to the first sin dec... is one question. 

I think you understand the operational problems here.  Some calculators dont take anything for granted, while some operate to the normal order of operations - as in multiply first then add.

Which of the following is right???  (I removed some brackets for clarity)

Hc = Sin-1 ((SinDec x SinLat) + (CosLat x CosDec x CosLHA))
or
Hc = Sin-1 (((SinDec x SinLat) + CosLat) x CosDec x CosLHA)
or
Hc = Sin-1 ((SinDec (SinLat + CosLat)) x CosDec x CosLHA)
or
Hc = Sin-1 ((SinLat (Sin (Dec + CosLat))) x CosDec x CosLHA)

Or something else???  My calculator shows an error using the original formula

Please be clear if you offer a formula in response.

joe

[craigsl]

Joe,

Both of the formulas you mention in the beginning of your post are correct and yield the same result. The Nautical Almanac specifies the second formula as entered in the Casio fx-300ES Plus calculator. The "Sin-1" is the arc-sin key.

Anyone using the second formula should understand that by comparing it to the first formula that the first "asin" (in the first formula) and "Sin-1" in the second formula are the same thing.

To get the Hc answer correct you might do it this way;

Get the sin of Ap Lat.
Get the sin of Dec.
Multiply those two answers together and write the result down (call the product "A").

Get the cos of Ap Lat.
Get the cos of Dec.
Get the cos of LHA
Multiply those 3 answers together (call the product "B")

Add "A" and "B" together (call the sum "C")

Get the Arc-Sin of "C"
That answer will equal Hc

Craig

[Rdutton]

Joe,

Take a look at these formulas- they're the same but may be of some help;

https://thenauticalalmanac.com/Formulas.html

Roland

[pabrides]

Joe,

Both of the formulas you mention in the beginning of your post are correct and yield the same result.  The Nautical Almanac specifies the second formula as entered in the Casio fx-300ES Plus calculator.  The "Sin-1" is the arc-sin key.

Anyone using the second formula should understand that by comparing it to the first formula that the first "asin" (in the first formula) and "Sin-1" in the second formula are the same thing.

To get the Hc answer correct you might do it this way;

Get the sin of Ap Lat.
Get the sin of Dec.
Multiply those two answers together and write the result down (call the product "A").

Get the cos of Ap Lat.
Get the cos of Dec.
Get the cos of LHA
Multiply those 3 answers together (call the product "B")

Add "A" and "B" together (call the sum "C")

Get the Arc-Sin of "C"
That answer will equal Hc

Craig

Thanks, I think I know trig notation well enough..  it was the sequence of operations I questioned....

So you say this is correct:

Sin-1 ((SinDec x SinLat) + (CosLat x CosDec x CosLHA))
 
This is exactly how I successfully enter it into my calculator:

Sin-1(Sin Lat x Sin Dec + Cos Lat x Cos Dec x Cos LHA)       just two brackets

To avoid confusion this might be an alternate notation (it works too when entered):

Sin-1 ((Sin Lat x Sin Dec) + (Cos Lat x Cos Dec x Cos LHA))      just 6 brackets

Original formula...   12 brackets.

 ... :)

By the way, the first two formulas provide different results - however, you may be getting the same results if you dont ask for a solution to the left side first before multiplying the last two cosines...   ((SLxSD)+CL)=A
                            AxCDxCLHA=B
Sin-1 B does not equal Sin-1 ((Sin Lat x Sin Dec) + (Cos Lat x Cos Dec x Cos LHA))

This is more fun than the law should allow.
joe

---

Joe,

Take a look at these formulas- they're the same but may be of some help;

https://thenauticalalmanac.com/Formulas.html

Roland

Thanks, Roland

I must have missed that page... :)

joe

[craigsl]

Gentlemen,

For more clarification and help, Bowditch Chapter- 22 Calculations and  Conversions page 331 covers both Hc and Zn.  The way it's written might be more confusing.

https://thenauticalalmanac.com/Bowditch-...pdf#page=3

See if that does you any good.

Craig

[pabrides]

Gentlemen,

For more clarification and help, Bowditch Chapter- 22 Calculations and  Conversions page 331 covers both Hc and Zn.  The way it's written might be more confusing.

https://thenauticalalmanac.com/Bowditch-...pdf#page=3

See if that does you any good.

Craig

There it is, Craig... plain as day.  If i had seen this before this thread would never have been an issue

thanks
joe.

[pabrides]

Hello shipmates.

I like to frequent Professor Herning's Youtube page because within short videos he explains the use of slide rules and sometimes uses calculators as comparison tools.  

Recently I decided to start looking for another calculator because the Chinese no-name brand I bought cheap has developed some problems... not only that, but the numbers and characters on the buttons and face have always been hard to read.

I wrote to the Professor about the present day flimsy and hard to read calculators and asked him for some recommendations.  I said that all I want in a scientific calculator is heft and readable characters.

This is what he said:

"I've found unreadable font colors and flimsy construction to be big issues on modern calculators. It's just not worthwhile for companies to care about quality construction (and details) anymore. Case in point: the original TI-89 vs the TI-89 Titanium. The former has very nice high contrast color printing on the keys. It was replaced by the "improved" Titanium model which has an unreadable keyboard (although TI had already shifted production to China, reducing reliability over the Taiwanese made revisions). I'm no expert, but here's a couple to consider: 

The TI-30Xa. Also <$10. I've heard the newer production versions no longer suffer from the infamous "logarithm bug." I think this old one-line design still makes a great basic scientific. It has a bit of contrast trouble with the shifted functions, but it makes my most-used functions primary functions (including pi, 1/x, square root, and square!). In most other cases the 2nd key simply gets you the inverse of the primary function, so there's no actual need to read the secondary printing anyway. My college's math lab has a bunch of them that have taken a beating over the years and still work (although production quality can always go downhill -- TI seems to always look for ways to cost-cut). -

The HP-35s. If you can stand RPN and the cost, this is one of the best-constructed currently available calculators, even if it pales in comparison to calculators from the glory days. The main keys (arrow keys excepted) are amazing for a modern calculator and overall it actually has some heft. Downsides though are the dot-matrix display, complexity (it's programmable), and the contrast on the blue printing."

We corresponded a few more times and I decided to go with the HP-35s - if I can find one here in the Philippines.

The HP's RPN (Reverse Polish Notation) system of calculation is not new and may predate the Algebraic system found in most contemporary calculators... Even so I felt drawn to it having never used it.  I suppose it just seemed like a worthy challenge.   Soooo, I downloaded the HP-35s user manual and started to study - WOW!  What Ive missed over the last 5 decades astounds me... now I want an RPN HP-35s almost as much as a decent 10inch slide rule.... and I told my wife as much seeing as how its my birthday in a few days. 

So here are my questions:

1)   Does anyone have some advice or information regarding the HP?

2)   Has anyone had experience with said calculators suggested?

3)   Does anyone have an old HP-35s they are not using anymore?

4)   Are there any other calculators that might fit my qualifications (heft and readability)?

5)   Has anyone designed navigation or nautical computation programs for the HP-35s?

Thanks in advance
Joe