# NavList:

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

**Re: Formulas to Compute LHA**

**From:**Gary LaPook

**Date:**2009 Jun 27, 22:56 -0700

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 Rudzinskiwrote: > 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 0� to 360� 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 0� to 180� 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 0� to 90� and then back the other way, 90� to 180�. My > > > > implementation of the Bygrave eliminated the second set of markings on > > > > the scale, 90�-180�, to eliminate clutter so I added an extra step to > > > > bring hour angle into the range of 0� to 90� 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 90�, H > > > > = LHA; if LHA is greater than 90� but less than 180�, H = 180� - LHA; if > > > > LHA is greater than 180� but less than 270� then H = LHA - 180�; and if > > > > LHA is greater than 270� but less than 360�, H = 360 �- 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 �to GHA prior to subtracting ALon.) > > > > > If your AP is in east longitude: LHA = GHA + ALan. (if LHA then exceeds > > > > 360�, subtract 360� from the result.) > > > > > Using the first formula for your first two examples, GHA (55� + 360�) - > > > > 77� = LHA = 338�. > > > > > GHA 95� - 77� = LHA = 18� > > > > > 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 - > > --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---