Transcript Altitude-Intercept Method

LESSON 17:
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
plotting a celestial LOP.
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...
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.
• Now our circles look like this...
Circle of Equal Altitude
• Now, we
need to
relate this
concept to
the
navigation
triangle:
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.)
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).
Circle of Equal Altitude
• Here is a more realistic scenario,
where our assumed position does
not lie exactly on the circle of equal
altitude...
Circle of Equal Altitude
• If we know the altitude of two or
more stars, we can cross the LOP’s
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.
Circle of Equal Altitude
• 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 this circle; this is the basis of the
Altitude-Intercept Method.
Altitude-Intercept Method
• If we are near the GP, a portion of the
circle would plot as an arc...
Altitude-Intercept Method
• Now, if the distance to the GP is very
large, the arc becomes a straight
line...
Altitude-Intercept Method
• Don’t forget, we are still essentially
drawing a circle.
• But we’re no longer using the radius
(determined from the star’s altitude)
so how do we know where, or for that
matter, at what angle, to draw the
line?
Altitude-Intercept Method
• 1. First, assume a position based on
the ship’s 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.
Altitude-Intercept Method
• 3. Observe the star’s 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.
Altitude-Intercept Method
• The difference between Hc and Ho is
known as the intercept distance (a).
Altitude-Intercept Method
• 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”
– “Coast Guard Academy”
Altitude-Intercept Method
• A picture clearly illustrates the idea...
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
• First, we calculate the intercept
distance, a, using a= Ho-Hc
• The result is
Ho
-Hc
a
45o 00.0’
44o 45.5’
14.5’
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
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
• 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.