1 The Celestial LOP Junior Navigation Chapter 7

2 Learning Objectives Understand the altitude-intercept method, and relationship between Ho, Hc and intercept. Identify the parts of the navigational triangle. Compute altitude (Hc) and azimuth (Zn) of the sun using a scientific calculator. Convert Z (azimuth angle) to Zn (azimuth).

3 Computers & Calculators Any scientific calculator Any scientific calculator With 3 or 4 memory registers helpful With 3 or 4 memory registers helpful Programmable scientific calculators helpful Programmable scientific calculators helpful Special purpose Nav. Calculators, Nav. Software, spreadsheets, etc. Special purpose Nav. Calculators, Nav. Software, spreadsheets, etc. You must know how to do all tasks for SR manually for your SF and exam. You must know how to do all tasks for SR manually for your SF and exam.

4 Sight Reduction June + G g zm Enter Lat as positive. If Lat/Dec contrary name enter Dec as negative. Convert LHA, Lat, and Dec to 5 place rounded decimal degrees. Round Zn to whole degrees

5 Sight Reduction To convert to decimals degrees, divide minutes by / 60 = Rounded to / 60 = Rounded to / 60 = Rounded to ? +

6 Sight Reduction NOW FOR THE DIFFICULT PART (cos LHA x cos Lat x cos Dec) + (sin Lat x sin Dec) = sin Hc (cos x cos x cos 23.14) + (sin x sin 23.14) ~ ~ = sin = º Enter LHA, press COS, press X Enter Lat, press COS, press X Enter Dec, press +/-, press COS, press = Press STO, press 1 Enter Lat, press SIN, press X Enter Dec, press +/-, press SIN, press = Press +, press RCL, press 1, press = This is the SIN of HC Press 2 nd, press SIN, record ANSWER

7 Sight Reduction NOW FOR THE DIFFICULT PART x ?

8 Sight Reduction NOW FOR THE DIFFICULT PART [sin Dec – (sin Lat x sin Hc)] / (cos Lat x cos Hc) = cos Z [sin – (sin x sin )] / (cos x cos ) ~ / ~ = ~ cos = Enter Dec, press +/-, press SIN, press – press (, Enter LAT, press SIN, press X Enter HC, press SIN, press ), press =, press /, press (, Enter Lat, press COS, press X Enter HC, press COS, press ), press = This is the COS of z

9 Sight Reduction NOW FOR THE DIFFICULT PART ?? Is your latitude N or S Is your LHA 180º ?

Na Ps Pn Q1Q1 Q S N Z d d1d1 dec GHA 10 Plane of the Celestial Meridian Bowditch, Article 1433

Formed by the GP, DR, & Elevated Pole Formed by the GP, DR, & Elevated Pole The sides The sides Co-latitude (Co-L) Co-latitude (Co-L) Co-declination (Co-Dec) Co-declination (Co-Dec) Co-Altitude (Co-H) Co-Altitude (Co-H) Internal angles Internal angles LHA LHA Azimuth angle (Z) Azimuth angle (Z) Parallactic angle Pn DR GP Z LHA Co-H Co-Dec Co-L 11 Navigation Triangle Observer’s Meridian p Hour Circle of Body

12 Z to Zn conversion To plot the intercept (a), must determine azimuth (Zn) Zn - the direction from your DR to the GP of the body Measured clockwise around the horizon from true north True direction of the GP Pn DR GP Z LHA Co-H Co-Dec Co-L Observer’s Meridian Hour Circle of Body p

13 Z to Zn conversion North Latitude and LHA 180º South Latitude and LHA 180º Z is N/W: Zn = 360º – Z Pn DR GP Z LHA Zn NW

Pn GP DR Z Zn LHA 14 Z to Zn conversion North Latitude and LHA 180º South Latitude and LHA 180º Z is N/W: Zn = 360º – Z Z is N/E: Zn = ZNE

Ps DR GP Z Zn LHA 15 Z to Zn conversion North Latitude and LHA 180º South Latitude and LHA 180º Z is N/W: Zn = 360º – Z Z is N/E: Zn = Z Z is S/W: Zn = 180º + Z S W

Ps DR GP Z LHAZn16 Z to Zn conversion North Latitude and LHA 180º South Latitude and LHA 180º Z is N/W: Zn = 360º – Z Z is N/E: Zn = Z Z is S/W: Zn = 180º + Z Z is S/E: Zn = 180º – Z S E

17 Sight Reduction NOW FOR THE DIFFICULT PART ? Zn = 360º – 154.7º = 205.3º a.025º (180º – z) b.155º (=z) c.205º (360º – z) d.335º (180º + z) a b c d DR

18 Compute Hc & Zn Chris, Bob, Jeff, & Wil Dave, John, Terry, & Kris Dean, Dale, Karen, & Nancy Body Sun LL Sun UL UT DR Lat 45 º 00.2 ’ N GHA 29 º 02.4 ’ 30 º 23.6 ’ 85 º 47.9 ’ LHA 296 º 15.9 ’ 297 º 37.1 ’ 353 º 01.4 ’ Dec 23 º 25.5 ’ N 23 º 25.3 ’ N Ho 34 º 33.6 ’ 35 º 32.6 ’ 67 º 38.4 ’ Intercept Azimuth ??? READY FOR YOUR ANSWERS?

Sight Reduction Chris & Bob, Jeff & Wil

20 Compute Hc & Zn Chris & Bob Jeff & Wil Dave & John Terry & Kris Dean & Dale Karen & Nancy Body Sun LL Sun UL UT DR Lat 45 º 00.2 ’ N GHA 29 º 02.4 ’ 30 º 23.6 ’ 85 º 47.9 ’ LHA 296 º 15.9 ’ 297 º 37.1 ’ 353 º 01.4 ’ Dec 23 º 25.5 ’ N 23 º 25.3 ’ N Ho 34 º 33.6 ’ 35 º 32.6 ’ 67 º 38.4 ’ Intercept Azimuth 4.0 A 090 º ??

Sight Reduction Dave & John, Terry & Kris

22 Compute Hc & Zn Chris & Bob Jeff & Wil Dave & John Terry & Kris Dean & Dale Karen & Nancy Body Sun LL Sun UL UT DR Lat 45 º 00.2 ’ N GHA 29 º 02.4 ’ 30 º 23.6 ’ 85 º 47.9 ’ LHA 296 º 15.9 ’ 297 º 37.1 ’ 353 º 01.4 ’ Dec 23 º 25.5 ’ N 23 º 25.3 ’ N Ho 34 º 33.6 ’ 35 º 32.6 ’ 67 º 38.4 ’ Intercept Azimuth 4.0 A 090 º 2.4 A 091 º ?

Sight Reduction Dean & Dale, Karen & Nancy

24 Compute Hc & Zn Chris & Bob Jeff & Wil Dave & John Terry & Kris Dean & Dale Karen & Nancy Body Sun LL Sun UL UT DR Lat 45 º 00.2 ’ N GHA 29 º 02.4 ’ 30 º 23.6 ’ 85 º 47.9 ’ LHA 296 º 15.9 ’ 297 º 37.1 ’ 353 º 01.4 ’ Dec 23 º 25.5 ’ N 23 º 25.3 ’ N Ho 34 º 33.6 ’ 35 º 32.6 ’ 67 º 38.4 ’ Intercept Azimuth 4.0 A 090 º 2.4 A 091 º 2.5 A 163 º Next Week Bring your plotting tools Next Week Bring your plotting tools

25 Circles of Position (COP) One COP based on Observed Altitude One COP based on Observed Altitude passes through DR (radius is 90° – Ho) passes through DR (radius is 90° – Ho) Other COP based on Computed Altitude Other COP based on Computed Altitude passes through location where sight was taken (radius is 90° – Hc) passes through location where sight was taken (radius is 90° – Hc) Difference between Hc and Ho equals intercept (a) in nautical miles Difference between Hc and Ho equals intercept (a) in nautical miles GP a DR

26 Intercept: Toward or Away? When Ho is greater than Hc, Observer is closer to the GP than DR The intercept is measured from the DR toward (T) the GP When Hc is greater than Ho, Observer is further from the GP than DR The intercept is measured from the DR away (A) from the GP To GP LOP DR Intercept Toward LOP Intercept Away

27 Find the Intercept Given: Hc is 39° 52.6´ and Ho is 40° 02.4´ Find the value of the intercept and determine if it is toward or away. Ho40°02.4´ Hc39°52.6´ a 9.8´ = 9.8 nm Ho is greater than Hc. The intercept a is Toward (T)

28 Find the Intercept Given: Hc is 50° 10.2´ and Ho is 49° 46.7´ Find the value of the intercept and determine if it is toward or away. Hc50°10.2´ Ho49°46.7´ a 23.5´ = 23.5 nm Hc is greater than Ho. The intercept a is Away (A)

29 Calculating Zn Given: DR L = 28°36.4´ N DR Lo = 80°50.4´ W, GHA sun = 110°08.5´, Z = 119.9° Provide the correct labels for Z and calculate Zn. GHA sun 110°08.5´ Lo W – 80°50.4´W LHA 29°18.1´ LHA < 180°, Body west of observer DR Lat is N Z = N 119.9° W Zn = 360° – Z 360.0° Z – 119.9° Zn 240.1° rounded to 240°

30 Calculating Zn Given: DR L = 9°56.5´ S DR Lo = 89°18.5´ E, GHA sun = 232°44.8´, Z = 95.0° Provide the correct labels for Z and calculate Zn. GHA sun 232°44.8´ Lo E + 89°18.5´E LHA 322°03.3´ LHA > 180°, Body east of observer DR Lat is S Z = S 095.0° E Zn = 180° – Z 180.0° Z – 95.0° Zn 85.0° rounded to 85°

31 Evaluating Sights “Practice makes perfect” Observations for JN Sight Folder from a DR – estimated position (EP) from a GPS Fix – intercept is ‘sight error’, (SErr) Sight folder intercepts Not more than 5.0 nm

32 Sight Folder USPS Sight Certification Form Two copies, one retained by SEO, other returned to candidate with completed sight folder

33 Sight Folder USPS Sight Certification Form USPS Sight Log Sheets Minimum of three qualified sights on UL of sun and three qualified sights on LL of sun, taken between 2 and 6 hours.

34 Sight Folder USPS Sight Certification Form USPS Sight Log Sheets USPS Sight Reduction Form 96 One for each of two sights listed on Sight Log selected to be reduced.

35 Sight Folder USPS Sight Certification Form USPS Sight Log Sheets USPS Sight Reduction Form 96 USPS Constant Latitude Scale Small Area Plotting Sheet (CLS SAPS) NEXT WEEK

36 1. Find the intercept and its direction (T or A) for the following: Hc = 40° 54.4'; Ho = 41° 28.2' a = ________ Hc = 51° 29.3'; Ho = 50° 59.7' a = ________ 33.8 nm T 29.6 nm A Quiz

37 2. Co-Dec is measured: a. along the hour circle of a body from the equator to the GP of the body. b. along the hour circle of a body from the GP of the body to the elevated pole. c. along the observer's meridian from his DR position to the elevated pole. d. along the observer's meridian from the equator to his DR position. Quiz

38 3. The distance between the GP of a body and an observer's position is: a. co-altitude. b. altitude. c. azimuth. d. intercept Quiz

39 4. Co-Dec is always less than 90°. a. True b. False Quiz

40 5. Azimuth is always measured from true north in a clockwise direction to the GP of a body. a. True b. False Quiz

41 6. A celestial LOP is always plotted perpendicular to the azimuth. a. True b. False Quiz

42 7. If your DR is at L 23° 45.8‘ S, Lo 138° 49.5‘ E, your elevated pole is the North Pole. a. True b. False Quiz

43 The Celestial LOP End of Junior Navigation Chapter 7