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6. The Assumed Position, Circle of Equal Altitude & Intercept

6. The Assumed Position, Circle of Equal Altitude & Intercept. Presented By: Mate O. Course Outline. Navigational Astronomy Lecture 1 & 2 Mean Time / Apparent Time Lecture 3 Time Zones, Zone Description, Chronometer Time Lecture 4

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6. The Assumed Position, Circle of Equal Altitude & Intercept

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  1. 6. The Assumed Position, Circle of Equal Altitude & Intercept Presented By: Mate O

  2. Course Outline • Navigational Astronomy Lecture 1 & 2 • Mean Time / Apparent Time Lecture 3 • Time Zones, Zone Description, Chronometer Time Lecture 4 • The Earth, Celestial, And Horizon Coordinate System Lecture 5 & 6 • The Spherical Triangle Lecture 7 • The Assumed Position, Circle of Equal Altitude, & Intercept Lecture 8 • Time Diagram, Right Ascension Lecture 9 • The Nautical Almanac, Finding GHA, LHA, and Dec. Lecture 10 • Instruments For Celestial Navigation Lecture 12 • Sight Reduction of the Sun, Stars, Planets, Moon Lecture 13 - 15 • Plotting and Advancing / Retarding the Assumed Position Lecture 16 • Calculating Time of Meridian Passage (LAN) Lecture 17 • Calculating Latitude at Meridian Passage Lecture 18 • Calculating Time of Sunrise/ Sunset/ Twilight Lecture 19 • Star Shooting Schedule / Pub. 249 Lecture 20 • Azimuth and Amplitudes Lecture 21 – 24 • Polaris – Azimuth and Latitude By Lecture 25 • Star – Finder – Stars, Planets, Selecting the 3 best Stars Lecture 26 • The Complete Day’s Work Lecture 27 & 28

  3. VI: Sight Reduction Sight Reduction • We Will Learn Tabular Sight Reduction, Using the Assumed Position Method & the Pub. 229 - Sight Reduction Tables for Marine Navigation • There Are Many Other Methods of Sight Reduction and the Nautical Almanac Contains Directions for Solving Sights Using Its Own Concise Sight Reduction Tables, or Calculators.

  4. The Pub. 229 – Assumed Position Method VI: Sight Reduction The 229 – AssumedPosition Method • Consists of Six Steps: • Correct the Sextant Altitude (Hs) to Obtain (Ho) Observed Altitude • Determine the Body’s GHA and Declination (Dec.) • Select an Assumed Position (AP) and Find the Body’s Local Hour Angle (LHA) • Compute Tabular Altitude (Hct) and Azimuth for the AP • Compare the Computed (Hc) and Observed (Ho) Altitudes to Obtain an Intercept • Plot the Line of Position

  5. VI: Sight Reduction Assumed Position Method Theory • Sight Reduction Involves Determining a Circular Line of Position (LOP) Based on an Observers Distance From a Celestial Body’s Geographic Position (GP) • On This Circle, All Points Would See the Altitude Equal. This Is Referred to As a Circle of Equal Altitude • The Radius of This Circle of Equal Altitude (or Distance From the GP of the Body to the Circle) Is Equal to Your Zenith Distance in Degrees (1 Degree = 60 Miles) • Your Zenith Distance Is Equal to Your Zenith (90°) – the Altitude of the Body (Ho) ZD = 90° - Ho

  6. VI: Sight Reduction The Assumed Position • Depending on a Body’s Altitude, It’s GP Could Be Thousands of Miles From the Observer’s Position. The Size of a Chart Required to Plot Such a Large Distance Would Be Impractical. • To Eliminate This Problem, the Navigator Does Not Plot This Position Directly. (In Fact He Does Not Plot the GP at All). An Assumed Position (AP) Is Chosen Near, but Usually Not Coincident With His DR Position • The Navigator Chooses the AP’s Latitude and Longitude to Correspond to the Entering Arguments of LHA and Lat. Used in Pub. 229 • From Pub. 229, the Navigator Computes What the Body’s Altitude Would Have Been Had It Been Measured From the AP. This Yields the Computed Altitude (Hc) • He Then Compares This Computed Value (Hc) With the Observed Altitude (Ho) Obtained at His Actual Position

  7. VI: Sight Reduction Intercept • The Difference Between the Computed Altitude (Hc) and the Observed Altitude (Ho) Is Equal to the Distance Between the Two Circles of Equal Altitude, This Distance Is Called the Intercept. • If the Ho Is Greater Than Hc Then the Circle of Equal Altitude Is Toward (or Closer) to the G.P. If the Hc Is Greater Than Ho Then the Circle of Equal Altitude is Away (or Farther) From the G.P. • Knowing the Location of the Assumed Position and the Direction or Azimuth of the G.P. We Can Draw a Line of Position Perpendicular to This Zn (Azimuth Line) Which Is Drawn Through the AP. Its Location Referenced Towards or Away From the A.P. (Which Is on the Circle of Equal Altitude for Hc)

  8. VI: Sight Reduction Intercept • The Analogy Of Observing A Flag Pole Is Often Used To Describe The Circle Of Equal Altitude Principle • An Observer Who Sees The Flagpole At A Certain Altitude Will Be On A Circle With A An Equal Distance Around The Pole • If Another Observer Sees The Top Of The Flag Pole At A Higher Altitude Then He Is On A Circle That Is Closer To The Flag Pole • If Another Observer Sees The Top Of The Flag Pole At A Lower Altitude His Circle Of Equal Altitude Must Be Further From The Pole

  9. VI: Sight Reduction Intercept • Just Like The Flag Pole, The Same Applies To The Altitude Of A Body. • If The Observed Altitude (Ho) Is Greater Than Calculated Altitude At The Assumed Position (Hc) Then The Observer Is Towards The GP. • If Observed Altitude (Ho) Is Less Than Calculated Altitude At The Assumed Position (Hc) Then The Observer Is Away From The GP. • Memory Aids HoMoTo = Ho is More You are Towards CGA (Coast Guard Away) = Computed Greater Away

  10. VI: Sight Reduction Circle of Equal Altitude • The Assumed Position Will Normally Not Be On The Observed Altitude Circle.

  11. VI: Sight Reduction Circle of Equal Altitude • Circle Of Equal Altitude On Earth • The Radius Of The Circle Of Equal Altitude (Distance To The GP) Is Equal To The Zenith Distance

  12. VI: Sight Reduction Circle of Equal Altitude Pn • Combining Two Or More Circles Of Equal Altitude Result In A Fix • The Observer Is At The Intersection Of The 3 Circles Of Equal Altitude Ps

  13. VI: Sight Reduction Intercept • The Line of Position Is Plotted As a Straight Line, Even Though It Is Part of a Large Circle of Equal Altitude. (The Reason: Since the Radius of the Circle of Equal Altitude Is So Large That a Small Section of This Circle Closely Approximates a Straight Line). Enlarged To Show Detail AP 22° N 22° N Intercept Towards GP of Body GP of Sun Sun LL0830 ZN (or Aimuth of the Body)

  14. VI: Sight Reduction Selecting an Assumed Position • Three Entering Arguments Must Be Found In Order to Use Pub. 229: • Assumed Latitude (in Whole Degrees) = L • Declination (Dec.) • Local Hour Angle (in Whole Degrees) = LHA • Latitude and LHA Are Functions of the Assumed Position • Because We Need to Enter Pub. 229 With Whole Degrees of Lat. and LHA, the Navigator Selects the Whole Degree of Latitude Which Is Closest to His DR Position, and Longitude Which When Applied to GHA Will Make LHA a Whole Degree

  15. Closest λ To DR Position Which Makes LHA a Whole Degree Closest λ To DR Position Remember to Make 60’ Another Degree VI: Sight Reduction Selecting an Assumed Position Example:DR Position at Time of Observation: #1 L 22° 46’ N λ 045° 36’ W #2 L 27° 36’ N λ 125° 59’ E Assumed Lat: 23° N Assumed Lat: 28° N GHA Body 348° 15’ - W λ Assumed 045° 15’ LHA Body 303° 00’ GHA Body 202° 47’ + E λ Assumed 126° 13’ LHA Body 329° 00’

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