# NavList:

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

**Re: Formulas to Compute LHA**

**From:**Will Ross

**Date:**2009 Jun 28, 15:13 +0000

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 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 Corlwrote:

>

> > 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 LaPookwrote:

>

> > > 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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----- 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

> 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

>

> > 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

>

> > > 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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Navigation List archive: www.fer3.com/arc

To post, email NavList@fer3.com

To unsubscribe, email NavList-unsubscribe@fer3.com

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