LESSON 17: Altitude-Intercept Method Learning ObjectivesLearning Objectives –Comprehend the...

LESSON 17:LESSON 17:Altitude-Intercept MethodAltitude-Intercept Method

• Learning ObjectivesLearning Objectives– Comprehend the concept of the circle of Comprehend the concept of the circle of

equal altitude as a line of position.equal altitude as a line of position.– Become familiar with the concepts of Become familiar with the concepts of

the circle of equal altitude.the circle of equal altitude.– Know the altitude-intercept method of Know the altitude-intercept method of

plotting a celestial LOP.plotting a celestial LOP.

Circle of Equal AltitudeCircle of Equal Altitude

• Imagine a pole attached to a flat Imagine a pole attached to a flat surface, with a wire suspended from surface, with a wire suspended from the pole.the pole.

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

• This scenario is depicted on the next This scenario is depicted on the next slide...slide...


• Now, let’s make two changes to our Now, let’s make two changes to our situation:situation:– make the pole infinitely tallmake the pole infinitely tall– make our surface sphericalmake our surface spherical

• Now we have something similar to Now we have something similar to the earth and the navigational stars.the earth and the navigational stars.

• Now our circles look like this...Now our circles look like this...


• Now, we Now, we need to need to relate this relate this concept to concept to the the navigation navigation triangle:triangle:


• If we know the altitude of a star (as If we know the altitude of a star (as measured using a marine sextant), measured using a marine sextant), we can draw a “circle of equal we can draw a “circle of equal altitude” of radius equal to the altitude” of radius equal to the coaltitude (the distance between the coaltitude (the distance between the GP of the star and our AP.)GP of the star and our AP.)


• Thus, if we know the altitude of a Thus, if we know the altitude of a particular star, and its location relative particular star, and its location relative to the earth (which we can determine to the earth (which we can determine from the from the Nautical AlmanacNautical Almanac), we know ), we know that our position must lie somewhere that our position must lie somewhere on this circle of equal altitude.on this circle of equal altitude.

• Therefore, the circle of equal altitude Therefore, the circle of equal altitude is a line of position (LOP).is a line of position (LOP).


• Here is a more realistic scenario, Here is a more realistic scenario, where our assumed position does where our assumed position does not lie exactly on the circle of equal not lie exactly on the circle of equal altitude...altitude...


• If we know the altitude of two or more If we know the altitude of two or more stars, we can cross the LOP’s and arrive stars, we can cross the LOP’s and arrive at a celestial fix.at a celestial fix.

• Note that these circles cross at two Note that these circles cross at two points; however, these points are points; however, these points are usually several hundred miles apart, usually several hundred miles apart, and we can therefore rule one out. If and we can therefore rule one out. If not, a third star can be used to resolve not, a third star can be used to resolve the ambiguity.the ambiguity.


• Consider a problem with this idea:Consider a problem with this idea:• For Ho=60For Ho=60oo, the radius of the circle of , the radius of the circle of

equal altitude is 1800 miles! To plot equal altitude is 1800 miles! To plot this with any degree of accuracy would this with any degree of accuracy would require a chart larger than this room.require a chart larger than this room.

• Instead, we only plot a small portion of Instead, we only plot a small portion of this circle; this is the basis of the this circle; this is the basis of the Altitude-Intercept MethodAltitude-Intercept Method..

Altitude-Intercept MethodAltitude-Intercept Method

• If we are near the GP, a portion of the If we are near the GP, a portion of the circle would plot as an arc...circle would plot as an arc...


• Now, if the distance to the GP is very Now, if the distance to the GP is very large, the arc becomes a straight large, the arc becomes a straight line...line...


• Don’t forget, we are still essentially Don’t forget, we are still essentially drawing a circle.drawing a circle.

• But we’re no longer using the radius But we’re no longer using the radius (determined from the star’s altitude) (determined from the star’s altitude) so how do we know where, or for so how do we know where, or for that matter, at what angle, to draw that matter, at what angle, to draw the line?the line?


• 1.1. First, assume a position based on First, assume a position based on the ship’s DR plotthe ship’s DR plot, and we modify the , and we modify the numbers slightly (for ease of numbers slightly (for ease of calculation).calculation).

• 2. 2. Select navigational stars to shoot, Select navigational stars to shoot, and calculate what the altitude should and calculate what the altitude should be (be (HcHc, , computed altitudecomputed altitude), given our ), given our AP and the time of observation.AP and the time of observation.


• 3. Observe the star’s altitude using a 3. Observe the star’s altitude using a marine sextant, and determine the marine sextant, and determine the observed altitude (Ho).observed altitude (Ho).

• 4. The difference between Hc and 4. The difference between Hc and Ho, combined with Zn (which we can Ho, combined with Zn (which we can calculate using the calculate using the Nautical AlmanacNautical Almanac and Pub 229) is used to plot a and Pub 229) is used to plot a celestial LOP.celestial LOP.


• The difference between Hc and Ho is The difference between Hc and Ho is known as the known as the intercept distance (a).intercept distance (a).


• If Ho>Hc, we move toward the star If Ho>Hc, we move toward the star (along Zn) to plot our celestial LOP.(along Zn) to plot our celestial LOP.– ““Ho Mo To”Ho Mo To”

• If Hc>Ho, we move away from the If Hc>Ho, we move away from the star, along the reciprocal bearing of star, along the reciprocal bearing of Zn, to plot our celestial LOP.Zn, to plot our celestial LOP.– ““Computed Greater Away”Computed Greater Away”– ““Coast Guard Academy”Coast Guard Academy”


• A picture clearly illustrates the idea...A picture clearly illustrates the idea...

ExampleExample

• Now let’s try an example to illustrate Now let’s try an example to illustrate the concept:the concept:

• A star is observed, and we determine A star is observed, and we determine that Ho is 45that Ho is 45oo 00.0’ 00.0’

• Based on our AP at the time of Based on our AP at the time of observation, Hc is 44observation, Hc is 44oo 45.5’ 45.5’

ExampleExample

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

• The result isThe result is Ho 45Ho 45oo 00.0’ 00.0’ -Hc 44-Hc 44oo 45.5’ 45.5’ a 14.5’a 14.5’

ExampleExample

• So our intercept distance is 14.5 nm, So our intercept distance is 14.5 nm, and since Ho>Hc, we must move and since Ho>Hc, we must move toward the star to plot our LOP.toward the star to plot our LOP.

• Let’s examine again the angular Let’s examine again the angular relationships, and show how the LOP relationships, and show how the LOP is plotted...is plotted...

ExampleExample

Plotting the Celestial LOPPlotting the Celestial LOP

• Let’s assume we made an Let’s assume we made an observation of Venus, and came up observation of Venus, and came up withwith– a = 14.8 nm “towards”a = 14.8 nm “towards”– Zn=091.5Zn=091.5oo T T

• The plotted LOP is shown on the The plotted LOP is shown on the next slide...next slide...

Plotting the Celestial LOPPlotting the Celestial LOP

• Note that celestial plotting is usually Note that celestial plotting is usually done on a plotting sheet, and once a done on a plotting sheet, and once a fix is established, the latitude and fix is established, the latitude and longitude are used to transfer it to longitude are used to transfer it to the chart.the chart.

LESSON 17: Altitude-Intercept Method Learning ObjectivesLearning Objectives –Comprehend the...

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