# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Please help me with the math Re: learning sight reduction**

**From:**Lu Abel

**Date:**2006 May 4, 10:22 -0500

It's okay to use LHA in the formula, even if the body is east of the

observer and therefore LHA will be between 270 and 360. The reason for

this is that cos (x) is the same as cos (360-x). For example, cos (10)

is the same as cos (350).

I've never seen the formula expressed with a dlo, but I suspect it's

simply the difference between the observer's longitude and the body's

GHA without worrying about who is east of whom. Simplifies the picture

of the spherical triangle and makes it easier to understand. But if one

is doing sight reductions with a calculator, why insert an extra step

(changing a large LHA to a small dlo)? Every extra step is a potential

source for error. A calculator is quite happy to calculate (and get the

correct answer) using LHA!

Lu Abel

Bill Burchell wrote:

> Guy wrote:

>

>

>>OK so here is the formula I have sin

>>(Hc)=sin(dec)sin(lat)+cos(dec)cos(lat)cos(dlo)

>>question 1 is dlo the same as LHA? if not what is dlo?

>

>

> Not certain. I think of dlo as the smallest angle (absolute value) that

> expresses the difference between two longitudes.

>

> LHA is the angle measured WESTWARD from the observer's position to the body

> (GHA). If the body is west of the observed, that will be the same as dlo.

> If the body is east of the observer, you will have to go all the way around

> to get to the observer.

>

> Example:

>

> AP lon 80d W

> Body GHA (lon) 60d W

> dlo = 60 - 80 = |-20| = 20

> LHA = 60 - 80 = -20 = 340

>

>

>>question 2 is this formula telling me to mutiply sin(dec) by sin(lat) and

>>then add it to multiplication of cos(dec) by cos(lat) by cos(dlo)

>

>

> Yes. sin Hc = (sin dec * sin lat) + (cos dec* cos lat * by cos LHA)

>

> Order of operations: Please excuse my dear aunt Sally. PEMDAS

>

> P parenthesis

> E exponents

> M multiplication

> D division

> A addition

> S subtraction

>

> Do anything within the () first, as ordered above.

>

> No. You need LHA, not dlo

>

> NOTE: If you are careful to always subtract AP from GHA, most calculators

> will not mind if you feed it -20 instead of +340 as LHA.

>

>

>>question 3 if my methodlogy of question 2 is correct, then how do I get the

>>result back to degrees and minutes for the answer Hc?

>

>

> Sine of the equation to the right of = is your answer in decimal degrees.

> Read the manual, do what it says to convert decimal degrees to ddd/mm/ss.

>

>

>>question 4 what is the difference in accuracy of HO 240 Vs Ho229 Vs

>>calculator?

>

>

> Your almanac explanation section will give you the range and probability of

> error for daily data. Using almanac tables for dip, refraction, time-to-arc

> etc., could shift you an additional 0.1', maybe 0.2' worst case.

>

> 229 table errors for figuring d, v, d (adjustment to tabular Hc) and Z might

> be another 0.1' to 0.2" (rarely) over calculator. Most of the time these

> rounding errors will pretty well cancel out or be smaller than sextant

> accuracy (+/- 0.15 to 0.3') and operator/refraction/dip errors on the water.

>

> NOTE: The calculator carries a lot of digits past the decimal point, that

> in theory are not significant digits anyway given the input.

>

> NOTE: If you really want to be picky, find a v factor for the sun by taking

> the GHA difference for 24 or 48 hours and dividing by 24 or 48 and adding or

> subtracting from 15 (sun) to get a real angular speed. Won't matter much at

> the 10-minutes-past the-hour mark, but can shift you 0.1' at the 40-50

> minute mark.

>

> I think 249 tables (solving the spherical triangle etc.) are less accurate

> than 229, but cannot speak to that from experience. 249 table books are

> smaller, but have limits on the stars you can use.

>

> Of any help?

>

> Bill

>

>

> >

>

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