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

Lesson 17a: The Navigation Triangle AGENDA: The Celestial/Astronomical Triangle The Navigation Triangle Applicable reading: Hobbs pp. 289-300.

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

The Celestial Triangle

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

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

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)

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.

The Celestial Triangle

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.

The Navigation Triangle

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)

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.

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.

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

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

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….

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

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.

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