(g) altitude-intercept method 1

8/10/2019 (G) Altitude-Intercept Method 1

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One way of fixing position is by means of altitude-

intercept method and the Navigator must be familiar on

identifying the celestial body, starsin particular..


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Identification of Stars

Although no formal star identification tables are

included in Pub. No. 229, a simple approach to star

identification is to scan the pagesof the appropriate

latitudes, and observe the combination of arguments

which give the altitudeand azimuth angleof the observation.

Thus the declinationand LHA of Ariesare determined directly.

The stars SHA is found from:

SHA of the star = LHA of the star LHA of the Aries.

From these quantities the star can be identified from the

Nautical Almanac.


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Altitude-Intercept Method

Learning Objectives:

Comprehend the concept of the circle of equal

altitude as a line of position.

Become familiar with the concepts of the

circle of equal altitude.

Know the altitude-intercept method of plottinga celestial LOP.


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Circle of Equal Altitude

Imagine a pole attached to a flat surface, with

a wire suspended from the pole.

If the wire is held at a constant angle to thepole, and rotated about the pole, it inscribes a

circle.

This scenario is depicted on the next slide...


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Now, lets make two changes to oursituation:

make the pole infinitely tall make our surface spherical

Now we have something similar to the

earth and the navigational stars. Now our circles look like this...


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Now, weneed torelate this

concept tothenavigation

triangle:


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Thus, if we know the altitude of aparticular star, and its location relative tothe earth (which we can determine from

the NauticalAlmanac),we know that ourposition must lie somewhere on this circleof equal altitude.

Therefore, the circle of equal altitude is aline of position (LOP).


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Here is a more realistic scenario, where

our assumed position does not lie exactly

on the circle of equal altitude...


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If we know the altitude of two or more stars, wecan cross the LOPs and arrive at acelestial fix.

Note that these circles cross at two points;

however, these points are usually several

hundred miles apart, and we can therefore rule

one out. If not, a third star can be used to

resolve the ambiguity.


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Consider a problem with this idea:

For Ho=60o, the radius of the circle of equal

altitude is 1800 miles! To plot this with any

degree of accuracy would require a chart larger

than this room.

Instead, we only plot a small portion of thiscircle; this is the basis of theAltitude-Intercept

Method.


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If we are near the GP, a portion of the

circle would plot as an arc...


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Now, if the distance to the GP is very

large, the arc becomes a straight line...


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Dont forget, we are still essentially drawing a

circle.

But were no longer using the radius(determined from the stars altitude) so how do

we know where, or for that matter, at what

angle, to draw the line?


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1. First, assume a position based on the ships

DR plot, and we modify the numbers slightly (for

ease of calculation).

2. Select navigational stars to shoot, and

calculate what the altitude should be (Hc,

computed altitude), given ourAPand the timeof observation.


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3. Observe the stars altitude using a marinesextant, and determine the observed altitude

(Ho).

4. The difference between Hc and Ho,combined with Zn (which we can calculate using

the Nautical Almanacand Pub 229) is used to

plot a celestial LOP.


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The difference between Hc and Hois

known as the intercept distance (a).


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If Ho>Hc, we move towardthe star (alongZn) to plot our celestial LOP.

Ho Mo To

If Hc>Ho, we move awayfrom the star,along the reciprocal bearing of Zn, to plotour celestial LOP.

Computed Greater Away

Coast Guard Academy


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A picture clearly illustrates the idea...


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Example

Now lets try an example to illustrate theconcept:

A star is observed, and we determine thatHo is 45o00.0

Based on our AP at the time of

observation, Hc is 44o45.5


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Example

First, we calculate the intercept distance,a, using a= Ho-Hc

The result is:Ho 45o00.0

-Hc 44o45.5

a 14.5


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Computed Altitude Formula

sin hc = sin L sin d + cos L cos d cos LHA

Where: hc = Computed Altitude

L = Latitude

d = declinationLHA = Local hour angle

Note: For both same and contrary name cases, the sine and

cosine functions of latitude are positive. In the contrary name

case, declination is considered as a negativeangle.


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Example

So our intercept distance is 14.5 nm, andsince Ho>Hc, we must move towardthe

star to plot our LOP.

Lets examine again the angular

relationships, and show how the LOP is

plotted...


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Example


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Plotting the Celestial LOP

Lets assume we made an observation ofVenus, and came up with

a = 14.8 nm towards Zn=091.5oT

The plotted LOP is shown on the next

slide...


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Finding Azimuth Formula

Solution by ABC

A =Tan Lat x Cot Ha A = Tan Lat / Tan Ha

B = Tan Dec x Cosec Ha B = Tan Dec / Sin Ha

C = A + B

Cot Z = C x Cos Lat.

NOTE: A is named opposite to Lat except when

Hour angle is between 90oand 270o.B is always named the same as declination.


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How to Solve and Plot the Line of


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How to Solve and Plot the Line ofPosition

Arguments Needed:

1) Assumed Latitude = 20oN

2) Assumed Longitude= 067oW

3) LHA or t = 56oE = 304o

4) Declination = 12o

24.3S

Ho = 26o31.4

Hc = 26o04.9

Int = 26.5 towards

Zn = 115.6oT

Where: Assumed latitudeis taken asthe nearest whole degree of latitude tothe DR and the assumed longitudeis

selected so that the local hour angle isa whole degree.



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GHA = 11o32.1

Assumed longitude = 67o32.1 W

LHA or t =304oor 56oE

Arguments to plot (LOP)

1) Assumed latitude = 20oN

2) Assumed longitude = 67o32.1W

3) Intercept = 26.5 towards4) Azimuth = 115.6o



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Note: To remember in West longitude, the minute of your

Longitude is equal to the minutes of your GHA. (See example).

In East longitude, do not copy the minutes of your GHA, but

instead add a number to make it into 1oand carry it to your

GHA degrees adding to your longitude.

Example: GHA = 11o32.1

Assumed long. = 67o27.9 East


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Plotting the Celestial LOP

Note that celestial plotting is usually done

on a plotting sheet, and once a fix is

established, the latitude and longitude are

used to transfer it to thechart.

(g) altitude-intercept method 1

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