Lect 13C Altitude Intercept Method

Lesson 18: Altitude Intercept Method: 

11/15/2007 Lesson 18: Altitude Intercept Method

Lesson 18: Altitude Intercept Method: 

AGENDA: The Circle of Equal Altitude The Altitude-Intercept Method Applicable reading: Hobbs pp. 295-309. Lesson 18: Altitude Intercept Method

Circle of Equal Altitude: 

To illustrate the basic concept, consider a pole of known height erected vertically on level ground. The base of the pole establishes its GP Guy wires are stretched taut to points on the ground equidistant from the base The distance from the base of the pole (GP) can be determined by trigonometry. Circle of Equal Altitude

Slide4: 

Consider a pole of known height erected vertically on level ground. The base of the pole establishes its GP Guy wires are stretched taut to points on the ground equidistant from the base

Circle of Equal Altitude: 

Circle of Equal Altitude Now, let’s 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. We need to relate this concept to the navigation triangle:

Slide6: 

If we know the altitude of a star (as measured using a marine sextant), we can draw a circle of equal altitude...

Circle of Equal Altitude: 

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).

Slide8: 

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

Slide9: 

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

Circle of Equal Altitude: 

Circle of Equal Altitude Consider the following: 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 this circle; this is the basis of the Altitude-Intercept Method.

Slide11: 

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

Slide12: 

If the distance to the GP is very large, the arc becomes a straight line...

Altitude-Intercept Method (Complete): 

Altitude-Intercept Method (Complete) STEP 1: Assume a position based on the ship’s DR plot. You may modify the numbers slightly (for ease of calculation). STEP 2: Select navigational stars to shoot, and calculate what the altitude should be (Hc, computed altitude), given our AP and the time of observation.

Altitude-Intercept Method (Complete): 

STEP 3: Observe the star’s altitude using a marine sextant, and determine the observed altitude (Ho). STEP 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. STEP 5: The difference between Hc and Ho is known as the intercept distance (a). Altitude-Intercept Method (Complete)

Slide15: 

If Ho>Hc, we move toward the star (along Zn) to plot our celestial LOP. “Ho Mo To” If Hc>Ho, we move away from the star, along the reciprocal bearing of Zn, to plot our celestial LOP. “Computed Greater Away”

Example: 

Example Now let’s 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’

Example: 

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’

Example: 

Example So our intercept distance is 14.5 nm, and since Ho>Hc, we must move toward the star to plot our LOP. Let’s examine again the angular relationships, and show how the LOP is plotted...

Example: 

Example

Plotting the Celestial LOP: 

Plotting the Celestial LOP Let’s assume we made an observation of Venus, and came up with a = 14.8 nm “towards” Zn=091.5o T The plotted LOP is shown on the next slide...

Plotting the Celestial LOP (Short-Form): 

Plotting the Celestial LOP (Short-Form) STEP 1: Plot your DR position STEP 2: Plot a course line from your DR STEP 3: Plot an AP (a Lat, a ) STEP 4: Draw a construct line STEP 5: Draw a LOP  to construct line @ intercept distance (a).