LESSON 17: Altitude-Intercept Method

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LESSON 17Altitude-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 plotting a
  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 the
  pole, and rotated about the pole, it inscribes a
  circle.
• This scenario is depicted on the next slide...

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Circle of Equal Altitude

• Now, lets make two changes to our situation
• 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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Circle of Equal Altitude

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

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Circle of Equal Altitude

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

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Circle of Equal Altitude

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

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Circle of Equal Altitude

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

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Circle of Equal Altitude

• If we know the altitude of two or more stars, we
  can cross the LOPs and arrive at a celestial
  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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Circle of Equal Altitude

• Consider a problem with this idea
• For Ho60o, 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 this
  circle this is the basis of the
  Altitude-Intercept Method.

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Altitude-Intercept Method

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

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Altitude-Intercept Method

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

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Altitude-Intercept Method

• 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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Altitude-Intercept Method

• 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 our AP and the time of
  observation.

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Altitude-Intercept Method

• 3. Observe the stars altitude using a marine
  sextant, and determine the observed altitude
  (Ho).
• 4. The difference between Hc and Ho, combined
  with Zn (which we can calculate using the
  Nautical Almanac and Pub 229) is used to plot a
  celestial LOP.

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Altitude-Intercept Method

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

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Altitude-Intercept Method

• If HogtHc, we move toward the star (along Zn) to
  plot our celestial LOP.
• Ho Mo To
• If HcgtHo, we move away from the star, along the
  reciprocal bearing of Zn, to plot our celestial
  LOP.
• Computed Greater Away
• Coast Guard Academy

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Altitude-Intercept Method

• A picture clearly illustrates the idea...

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Example

• Now lets try an example to illustrate the
  concept
• A star is observed, and we determine that Ho is
  45o 00.0
• Based on our AP at the time of observation, Hc is
  44o 45.5

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Example

• First, we calculate the intercept distance, a,
  using a Ho-Hc
• The result is
• Ho 45o 00.0
• -Hc 44o 45.5
• a 14.5

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Example

• So our intercept distance is 14.5 nm, and since
  HogtHc, we must move toward the 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 of Venus, and
  came up with
• a 14.8 nm towards
• Zn091.5o T
• The plotted LOP is shown on the next slide...

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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 the chart.