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    Re: Formulas to Compute LHA
    From: Gary LaPook
    Date: 2009 Jun 29, 02:53 -0700

     Chempro...Will Ross, PhD wrote:
    
    "Correct, except its the south pole your looking at. "
    
    
    Well, not so fast.
    
    A time diagram will work with either pole in the center as long as you 
    know what you are doing. With the north pole in the center, angles (such 
    as GHA) increase clockwise so westward is also clockwise. If you put 
    the  south pole in the center then westward is counterclockwise and 
    angles increase in that direction which is counter to every other way we 
    depict angles in navigation.
    
    Dutton, 1934, states:
    
    " Draw a circle to represent the equinoctial. P, its center, is the 
    pole." The accompanying illustration has westward clockwise so the pole 
    is the north pole.
    
    But, Dutton, 1942, states:
    
    "Draw a circle to represent the equinoctial. P, its center, is the 
    _south_ pole." The accompanying illustration has westward 
    counterclockwise so the pole is now  the south  pole.
    
    Weems, 1938, in describing the time diagram states:
    
    "It is assumed that the observer's eye is over the _north_ celestial 
    pole..." and the illustration shows westward as clockwise.
    
    But, Weems, 1942, states:
    
    It is assumed that the observer's eye is over the _south_ celestial 
    pole..." and the illustration shows westward as counterclockwise.
    
    H.O. 211, Ageton, 1937, has the diagram with the north pole and westward 
    clockwise.
    
    But, Ageton, 1942 has the diagram reversed, centered on the south pole 
    and westward counterclockwise.
    
    TM 1-206, Celestial Air Navigation, 1941 states:
    
    "The time diagram is a freehand picture of the terrestrial or celestial 
    sphere as seen from above the _north pole_" and the diagram shows 
    westward as clockwise.
    
    H.O 216, Air Navigation, 1967, show diagrams in both orientations and 
    states:
    
    "If, as in the continental United States, the sun is always south of an 
    observer, it appears to him to move from left to right. In this case, 
    the time diagram can appropriately be drawn from the_ north_ pole, 
    looking south."
    
    
    Mixter, 1960, states:
    
    "Westward counter-clockwise is in current accord with Bowditch, the 
    Almanacs, Dutton and all modern textbooks of _surface_ navigation. The 
    student should avoid confusion with the old custom which assumes 
    westward as clockwise, although either assumption is permissible."
    
    The earliest edition of Bowditch that I have is 1938 and it shows the 
    south pole orientation of the time diagram. It appears that about that 
    time many texts adopted the convention of the south pole, probably 
    following Bowditch. Can someone check their earlier editions of Bowditch 
    to see if it, also, had used the north pole depiction of the older 
    references.
    
    So, take your pick, north pole or south pole and then stick with it to 
    avoid confusion.
    
    gl
    
    
    
    
    
    snav-coxn---.net wrote:
    > Correct, except its the south pole your looking at.         
    > Chempro...Will Ross, PhD
    >
    > ----- Original Message -----
    >
    > From: glapook---.net
    >
    > To: NavList
    >
    > Sent: Sun, 28 Jun 2009 05:56:13 +0000 (UTC)
    >
    > Subject: [NavList 8854] Re: Formulas to Compute LHA
    >
    >
    >
    >
    >
    > The "time diagram" is found in many navigational texts. It consists of
    >
    > a circle with the north posle as the center. You draw lines across the
    >
    > circle representing the Greenwich meridian, your meridian, and a line
    >
    > representing the GHA of the body (or of Aries if using H.O 249 vol.1).
    >
    > This diagram makes clear the relationship between all of these lines.
    >
    >
    >
    > gl
    >
    >
    >
    > On Jun 27, 6:38 pm, Greg Rudzinski wrote:
    >
    > > Andrew,
    >
    > >
    >
    > > I believe the time diagram refered to is the Weems & Plath celestial
    >
    > > slide rule. Google search this item for a description then look one on
    >
    > > eBay.
    >
    > >
    >
    > > Greg
    >
    > >
    >
    > > On Jun 27, 5:27 pm, Andrew Corl wrote:
    >
    > >
    >
    > > > I am interested in this diagram,  where can I find it?
    >
    > >
    >
    > > > Andrew
    >
    > >
    >
    > > > ________________________________
    >
    > > > From: chempro
    >
    > > > To: NavList
    >
    > > > Sent: Saturday, June 27, 2009 11:00:31 AM
    >
    > > > Subject: [NavList 8849] Re: Formulas to Compute LHA
    >
    > >
    >
    > > > Why dont you learn to use a TIME DIAGRAM? It simplfies ALL of the
    >
    > > > concepts.It can universally used for all reduction methods from Ageton
    >
    > > > to NASR. Chempro-Dr Will
    >
    > >
    >
    > > > On Jun 24, 8:07 am, Gary LaPook wrote:
    >
    > >
    >
    > > > > To see that you can use hour angle and LHA equally well, you 
    > just have
    >
    > > > > to look at H.O. 249. Look at the LHA columns at each edge of the 
    > page
    >
    > > > > and you will see that you get the same Hc for two values of LHA. 
    > Look at
    >
    > > > > LHA 10 and LHA 350 on this example page:
    >
    > >
    >
    > > > >http://www.fer3.com/arc/img/106576.2007-page%20152.pdf
    >
    > >
    >
    > > > > LHA 10 is the same as hour angle 10 west., LHA 350 is the same 
    > as hour
    >
    > > > > angle 10 east.
    >
    > >
    >
    > > > > This relationship is not so evident if you just look at H.O 229 
    > due to
    >
    > > > > the arrangement of the tables.
    >
    > > > > gl
    >
    > >
    >
    > > > > Gary LaPook wrote:
    >
    > > > > > Remember, LHA is in the range of 0º to 360º and is always 
    > measured to
    >
    > > > > > the west from the assumed longitude (ALon). It is the angle 
    > measured
    >
    > > > > > westward from the meridian of the ALon to the meridian 
    > containing the
    >
    > > > > > body's grographic position (GP). There is no such thing as 
    > easterly LHA.
    >
    > >
    >
    > > > > > In the past, various computations methods and tables (e.g H.O. 
    > 214) used
    >
    > > > > > "hour angle," (abbreviated "H.A." or "H" or "t"), which is the 
    > angle
    >
    > > > > > measured between the meridian of the ALon and the meridian 
    > containing
    >
    > > > > > the body's GP measured the shortest way, either west or east. 
    > Using this
    >
    > > > > > notation, hour angle ends up in the range of 0º to 180º only 
    > and is
    >
    > > > > > denoted "east" or "west." Because of the the way the trig 
    > formulas work,
    >
    > > > > > using either method computes the same Hc and the same "azimuth 
    > angle"
    >
    > > > > > ("Az" or "Z"). The only thing affected by choice of notation 
    > is the
    >
    > > > > > method used for the final determination of Zn,(azimuth used 
    > for plotting
    >
    > > > > > the LOP.)
    >
    > >
    >
    > > > > > The original Bygrave used hour angle, not LHA, and the scales were
    >
    > > > > > marked from 0º to 90º and then back the other way, 90º to 180º. My
    >
    > > > > > implementation of the Bygrave eliminated the second set of 
    > markings on
    >
    > > > > > the scale, 90º-180º, to eliminate clutter so I added an extra 
    > step to
    >
    > > > > > bring hour angle into the range of 0º to 90º only and provided the
    >
    > > > > > necessary rules for the final computation of Zn. This is what is
    >
    > > > > > happening on the top of the form I provided. If LHA is less 
    > than 90º, H
    >
    > > > > > = LHA; if LHA is greater than 90º but less than 180º, H = 180º 
    > - LHA; if
    >
    > > > > > LHA is greater than 180º but less than 270º then H = LHA - 
    > 180º; and if
    >
    > > > > > LHA is greater than 270º but less than 360º, H = 360 º- LHA.
    >
    > > > > > Conceptually, this is the smallest angle measured from either 
    > the upper
    >
    > > > > > branch or from the lower branch of the observer's meridian to the
    >
    > > > > > meridian containing the body's GP.
    >
    > >
    >
    > > > > > See the revised form at:
    >
    > >
    >
    > > > > >http://www.fer3.com/arc/img/108719.revised%20form%206-18-09.pdf
    >
    > >
    >
    > > > > > The formulas for calculating LHA are:
    >
    > >
    >
    > > > > > If your AP is in west longitude: LHA = GHA - ALon. (If 
    > necessary, add
    >
    > > > > > 360 ºto GHA prior to subtracting ALon.)
    >
    > >
    >
    > > > > > If your AP is in east longitude: LHA = GHA + ALan. (if LHA 
    > then exceeds
    >
    > > > > > 360º, subtract 360º from the result.)
    >
    > >
    >
    > > > > > Using the first formula for your first two examples, GHA (55º 
    > + 360º) -
    >
    > > > > > 77º = LHA = 338º.
    >
    > >
    >
    > > > > > GHA 95º - 77º = LHA = 18º
    >
    > >
    >
    > > > > > The third example you bring up makes no sense since GHA is never
    >
    > > > > > measured to the east, it is always measured west from Greenwich.
    >
    > >
    >
    > > > > > gl
    >
    > >
    >
    > > > > > Andrew Corl wrote:
    >
    > >
    >
    > > > > >> All,
    >
    > >
    >
    > > > > >> I need some help.  I am attempting to work the problem in Ocean
    >
    > > > > >> Navigator using the Lapook-Bygrave Slide Rule.  I am 
    > uncertain how to
    >
    > > > > >> compute the Local Hour Angle (LHA).
    >
    > >
    >
    > > > > >> In the following cases I am assuming my longitude to be 77 
    > degrees
    >
    > > > > >> west of Greenwich.
    >
    > >
    >
    > > > > >> 1. The GHA of the Sun is 55 degrees west of Greenwich
    >
    > > > > >> 2. The GHA of the Sun is 95 degrees west of Greenwich
    >
    > >
    >
    > > > > >> In the following cases I am assuming my longitude to be 120 
    > degrees
    >
    > > > > >> west of Greenwich
    >
    > >
    >
    > > > > >> 1. The GHA of the sun is 170 degrees east of Greenwich.
    >
    > >
    >
    > > > > >> Also what is the formula if my position is east of Greenwich 
    > and the
    >
    > > > > >> sun has a GHA of more than 180 degrees?
    >
    > >
    >
    > > > > >> Thanks
    >
    > > > > >> Andrew- Hide quoted text -
    >
    > >
    >
    > > > > - Show quoted text -
    >
    > >
    >
    > >
    >
    >
    >
    >
    >
    >
    >
    > >
    
    
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