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: Bill B
Date: 2006 May 4, 00:15 -0500
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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From: Bill B
Date: 2006 May 4, 00:15 -0500
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
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to NavList@fer3.com
To from this group, send email to NavList-@fer3.com
-~----------~----~----~----~------~----~------~--~---
