1. Lesson 17a: The Navigation Triangle
“Getting Acquainted Lecture”
Instructor Bio:
Commissioned May, 1993; NROTC Unit, IIT
Reported to Hue City (CG-66) homeported in Mayport, FL for a 42 mos tour
24 mos - Engineering Dept (Auxiliaries Officer & Damage Control Assistant)
18 mos - Operations Dept (Air Warfare Officer/BW Flag Liaison Officer)
Command Employment (while aboard Hue City)
1995 Med Deployment 95-2 with USS Theodore Roosevelt
1996 Baltops ‘96 (Scandinavian countries)
1997 Med Deployment 97-2 with USS John F. Kennedy
Midshipmen Cruises (emphasize student contribution to course)
CV (CV 63) - Secrest
Tico’s (LKE, VLG) -Waterston, Pope, Sullivan
Burkes (DDG 61) - Kuckel
OH Perry (FFG 61) - Phillips
LHA/LHD (LSD 44) - Fink, Sutherland
AOE (AOE-8) - Hertel
Review Syllabus:
Course objectives
Course resources (webpage, Textbook, Workbook)
Case studies - provide vivid and intriguing examples of the the fundamental principles taught in this course.
12/29/201812/29/2018

2. Lesson 17a: The Navigation Triangle
AGENDA:
The Celestial/Astronomical Triangle
The Navigation Triangle
Applicable reading: Hobbs pp

3. The Celestial Triangle
The celestial, horizon, and terrestrial coordinate systems are combined on the celestial sphere to form the astronomical or celestial triangle.

4. The Celestial Triangle

5. The Celestial Triangle
The three vertices of the celestial triangle are:
Celestial pole nearest the observer (referred to as the elevated pole)
Observer’s zenith
Position of the celestial body

6. The Celestial Triangle
The three sides of the triangle are of paramount importance; these are used in determining position. The length of each side is:
colatitude = 90 - latitude
polar dist. = 90 +/- declination
coaltitude = 90 - altitude

7. The Celestial Triangle
Two of the interior angles are also of concern:
Meridian angle (t)
Azimuth angle (Z)
Meridian angle (t) is simply a more convenient way of expressing LHA
if LHA<180, t=LHA (west)
if LHA>180, t=360-LHA (east)

8. The Celestial Triangle
Likewise, azimuth angle (Z) is simply a more convenient way of expressing true azimuth (Zn).
The third angle is known as the parallactic angle and is not of use in our discussion.

9. The Celestial Triangle

10. The Navigation Triangle
When the celestial triangle is projected downward onto the earth’s surface, it becomes the navigation triangle.
The solution of this triangle is the basis of celestial navigation.
Each of the three coordinate systems forms one side of the triangle.

11. The Navigation Triangle

12. The Navigation Triangle
Now the vertices of our triangle are
Our assumed position (AP)
The geographic position (GP) of the celestial body
The elevated pole (Pn or Ps)

13. The Navigation Triangle
The sides of the triangle are
colatitude
coaltitude
polar distance
A quick hint- the polar distance may be greater than 90 degrees, if the GP and the elevated pole are on opposite sides of the equator, but coaltitude and colatitude are always less than 90 degrees.

14. The Navigation Triangle
The angles are the same, namely
Meridian angle (t)
measured 0 to 180 degrees, east or west
suffix E or W is used to indicate direction
Azimuth angle (Z)
measured 0 to 180 degrees
prefix N or S is used to indicate elevated pole
suffix E or W used to indicate on which side of the observer’s meridian the GP lies.

15. The Navigation Triangle
Let’s consider the scenario shown on the following slide...

16. EXAMPLE
Given:
LHA = 040o
Zn = 290 oT
Find: t Z

17. Solution Since the LHA<180o, LHA and t are equivalent, thus:
t = 40oW
To determine Z, it is usually helpful to draw a diagram, as shown on the next slide….

18. Z is the angle between the elevated pole and the GP, as seen by the observer.
Since Ps is the elevated pole and the GP is west of the observer, we must subtract 180 degrees.
Therefore,
Z = S 110o W

19. LHA, t, Zn, and Z
If you think about, there are only four possible combinations possible, when you combine
GP either east or west of the observer
Elevated pole either north or south
It is simple enough to come up with an equation for converting between Zn and Z for each case, or you can draw a picture as we just did.

20. Homework Chapter 16 Section 1: 3 - 8 Section 2: 3 - 5 Section 3: 3 - 6