Part 12. Polaris Problems

The Cutterman’s Guide to Navigation Problems

Part Twelve: Polaris Problems The star Polaris can be used to solve directly for latitude, or can be used to determine a true azimuth for compass error problems.

Latitude by Polaris Problems Problem 12-‐1 (CG-‐231). The following question is taken directly from the USCG test bank and illustrates how to solve latitude by Polaris problems. On 14 March at 1845 ZT, you take a sextant observation of Polaris. Your DR position is latitude 29° 10’ N, longitude 154° 30’ W. Your sextant reads 29° 53.5’. Your chronometer reads 04h 42m 36s, and the chronometer error is 02m 24s slow. Your height of eye is 24 feet and the index error is 1.3’ off the arc. Determine the latitude by Polaris. Answer: 29° 21.3’ N

Step 1: Determine the correct chronometer time of sight. Chronometer time of observation: 04h 42m 36s Chronometer error: 02m 24s slow Correct chronometer time of observation: 04h 42m 36s + 2m 24s = 04:45:00.

Step 2: Determine the correct GMT of the sight DR Longitude: 154° 30’ W -‐ corresponds to ZD (+10). Local time of observation: 1845 ZT GMT time of observation = 1845 ZT + 10 hours = 0445 GMT (15 Mar).

Step 3: Determine the observed altitude of the body using the correction

tables in the Nautical Almanac (reproduced at the end of this Part). Sextant altitude (hs): 29° 53.5’ Index error (1.3’ off the arc): IC = + 1.3’ Height of eye (24 feet): dip = -‐ 4.8’ Apparent altitude (ha) = 29° 53.5’ + 1.3’ – 4.8’ = 29° 50.0’ Apparent altitude (stars/planets) correction: -‐1.7’ Observed altitude (ho) = 29° 50’ – 1.7’ = 29° 48.3’

Step 4: Determine the GHA of Aries for the time of sight.

GHA (Aries), whole hours: 232° 40.4’ GHA (Aries), increment: 11° 16.8’ GHA (Aries), total: 232° 40.4’ + 11° 16.8’ = 243° 57.2’

Step 5: Determine the LHA of Aries.

GHA (Aries): 243° 57.2’ DR Longitude: 154° 30 W LHA (Aries) = 243° 57.2’ – 154° 30’ W = 89° 27.2’

Step 6: Enter the Polaris Tables with LHA (Aries), DR Latitude,

and Month to determine the A0, A1, and A2 correction factors (The complete Polaris Tables are located at the end of this Part). A0 (LHA correction): 0° 31.7’ A1 (Latitude correction): 0.5’ A2 (Month correction): 0.8’

Step 7: Calculate latitude using the Polaris Formula, provided at

the bottom of the Polaris Tables. Latitude = Observed altitude – 1° + A0 + A1 + A2 Lat = 29° 48.3’ – 1° + 31.7’ + 0.5’ + 0.8’ = 29° 21.3’ N

Compass Problems Involving Polaris Problem 12-‐2 (CG-‐496). The following question is taken directly from the USCG test bank and illustrates how to solve compass problems involving Polaris. On 5 February your 2320 ZT position is latitude 52° 28’ N, longitude 23° 48’ W. You observe Polaris bearing 000.2° pgc. At the time of observation, the helmsman noted that she was heading 224° pgc and 244° psc. The variation is 20° W. What is the deviation for that heading? Answer: 1.5° W. For instructions on solving standard compass problems, refer to Part 6: Compass Problems.

Step 1: Determine the GMT of the sight. DR Longitude: 23° 48’ W -‐ corresponds to ZD (+2). Local time of observation: 2320 ZT GMT time of observation = 2320 ZT + 2 hours = 0120 GMT (6 Feb).

Step 2: Determine the GHA of Aries for the time of sight.

GHA (Aries), whole hours: 151° 04.9’ GHA (Aries), increment: 5° 00.8’ GHA (Aries), total: 151° 04.9’ + 5° 00.8’ = 156° 05.7’

Step 3: Determine the LHA of Aries. GHA (Aries): 156° 05.7’ DR Longitude: 23° 48’ W LHA (Aries) = 156° 05.7’ – 23° 48’ W = 132° 17.7’

Step 4: Enter the Polaris Tables with LHA (Aries), DR

Latitude, and Month to determine the azimuth to Polaris (the full Polaris Tables are located at the end of this Part). Azimuth (interpolated) = 358.7°

Step 5: Determine the gyro compass error (using the

acronym G-‐E-‐T). G (Gyro): 000.2° pgc E (Error): TBD T (True): 358.7° per azimuth tables

Gyro error = 1.5° W

Step 6: Determine the deviation (using a standard compass problem format). G: 224° pgc (Given) E: 1.5° W (Determine in step 5) T: 222.5° (Calculated) V: 20° W (Given) M: 242.5° (Calculated) D: 1.5° W (Calculated) C: 244° per steering compass (Given)

Additional Problems and Answers All of the following questions labeled “CG” were taken directly from the 2013 USCG test bank and illustrate the concepts in this Part. Note – not all problems have been worked and are subject to occasional errors in the database. For more problems and answers, see the USCG database of questions (database information located in the preface). Problem CG-‐170. On 10 June your 2010 zone time DR position is latitude 41° 10.0’ N, longitude 61° 15.0’ W. At that time you observe Polaris with a sextant altitude (hs) of 40° 35.8’. The chronometer time of observation is 00h 08m 18s, and the chronometer error is 01m 45s slow. The index error is 2.0’ on the arc, and the height of eye is 40 feet. What is your latitude by Polaris?

a) 41° 10.6’ N b) 41° 15.0’ N-‐ correct c) 41° 18.3’ N d) 41° 21.2’ N

Problem CG-‐177. On 11 February your 1832 zone time DR position is longitude 110° 52.6’ W. At that time you observe Polaris with a sextant altitude (hs) of 26° 19.8’. The chronometer time of sight is 01h 34m 56s and the chronometer error is 02m 16s fast. The index error is 2.7’ off the arc, and the height of eye is 60.2 feet. What is your latitude by Polaris?

a) 25° 27.2’ N-‐ correct b) 25° 34.2’ N c) 26° 27.2’ N d) 26° 34.2’ N

Problem CG-‐214. On 13 October at 1847 ZT, your vessel’s DR position is latitude 42° 17.4’ N, longitude 138° 46.2’ W. AT approximately this time you obtain a sextant altitude (hs) of Polaris reading 42° 16.8’, with an index error of 3.2’ on the arc. Your chronometer reads 03h 45m 20s and is 01m 32s slow. What is your latitude by Polaris, given a height of eye of 44 feet?


Problem CG-‐231. On 14 March at 1845 ZT, you take a sextant observation of Polaris. Your DR position is latitude 29° 10’ N, longitude 154° 30’ W. Your sextant reads 29° 53.5’. Your chronometer reads 04h 42m 36s, and the chronometer error is 02m 24s slow. Your height of eye is 24 feet and the index error is 1.3’ off the arc. Determine the latitude by Polaris.

a) 29° 11.7’ N b) 29° 15.5’ N c) 29° 18.0’ N d) 29° 21.3’ N-‐ correct

Problem CG-‐240. On 15 February at 0610 ZT in DR position latitude 56° 53.0’ N, longitude 157° 02.9’ E, you observe Polaris at a sextant altitude (hs) of 56° 10.4’. The index error is 2.5’ on the arc and the height of eye is 18 meters. What is the latitude?


Problem CG-‐241. On 15 July at 0447 ZT, your vessel’s DR position is latitude 22° 42’ N, longitude 126° 36’ E. At approximately that time, you obtain a sextant altitude (hs) of Polaris reading 23° 46.2’ with an index error of 1.6’ off the arc. Your chronometer reads 08h 48m 28s and is 1m 16s fast. What is your latitude by Polaris, given a height of eye of 33 feet?

a) 22° 44.1’ N b) 22° 46.2’ N c) 22° 50.2’ N d) 22° 54.1’ N-‐ correct

Problem CG-‐344. On 22 August your 1852 zone time DR position is longitude 155° 54’ E. At that time you observe Polaris with a sextant altitude (hs) of 27° 36.9’. The chronometer time of observation is 08h 54m 06s and the chronometer error is 02m 20s fast. The index error is 3.6’ off the arc and the height of eye is 61.5 feet. What is your latitude by Polaris?

a) 27° 05.5’ N b) 27° 31.0’ N c) 28° 05.9’ N-‐ correct d) 28° 09.5’ N

Problem CG-‐517. On 7 March at 1838 ZT in DR position latitude 34° 26.9’ N, longitude 58° 16.2’ W, you observe Polaris for latitude. The sextant altitude (hs) is 35° 08.4’. The index error is 2.5’ off the arc. The height of eye is 54 feet. What is the latitude at the time of sight?

a) 34° 29.8’ N b) 34° 33.4’ N-‐ correct c) 34° 34.8’ N d) 34° 36.8’ N

Problem CG-‐451. On 28 October at 1754 ZT, your vessel’s DR position is latitude 28° 30’ N, longitude 63° 24’ W. At this time you obtain a sextant altitude (hs) of Polaris reading 28° 42.6’ with an index error of 2.4’ on the arc. Your chronometer reads 09h 50m 00s and is 4m 41s slow. What is your latitude by Polaris given a height of eye of 28 feet (8.5 meters)?

a) 28° 25.2’ N b) 28° 30.6’ N c) 28° 34.9’ N-‐ correct d) 28° 41.3’ N

Problem CG-‐178. On 11 January your 0450 ZT position is latitude 38° 42’ N, longitude 14° 16’ W. You observe Polaris bearing 358.5° pgc. At the time of observation the helmsman noted he was heading 160° pgc and 173° psc. The variation is 9° W. What is the deviation for that heading?

a) 1° E b) 1° W c) 3° W-‐ correct d) 13° W

Problem CG-‐306. On 19 November, your 0146 ZT position is latitude 33° 48’ N, longitude 25° 22’ E. You observe Polaris bearing 359.8° pgc. At the time of observation, the helmsman noted that he was heading 224° pgc and 222.5° psc. The variation is 2° E. What is the deviation for that heading?

a) 2.0° E b) 0.5° E c) 1.0° W-‐ correct d) 1.5° W

Problem CG-‐387. On 23 July, your 2100 ZT position is latitude 36° 43.0’ N, longitude 16° 09.8’ W, when you observe an azimuth of Polaris to determine compass error. Polaris bears 359.0° per gyrocompass. At the time of the observation, the helmsman noted that he was heading 319° per gyrocompass and 331° per standard compass. Variation is 12.0° W. Which of the following statements is TRUE?

a) The gyro error is 0.7° E b) The gyro error is 1.7° W c) The deviation is 1.7° E-‐ correct d) The compass error is 13.7° W

Problem CG-‐469. On 3 October your 2122 ZT position is latitude 26° 32’ N, longitude 84° 26’ W. You observe Polaris bearing 359.8° pgc. At the time of observation, the

helmsman noted that he was heading 106° pgc and 107° psc. The variation is 0°. What is the deviation for that heading?

a) 1° E b) 0° -‐ correct c) 1° W d) 2° W

Problem CG-‐470. On 3 October your 0330 zone time (ZD +5) DR position is latitude 47° 41’ N, longitude 86° 49’ W. At that time you observe Polaris bearing 357.5° pgc. The chronometer time of observation is 08h 32m 04s and the chronometer is 0m 27s slow. The variation is 5.5° W. What is the gyro error?

a) 7.5° E b) 5.0° E c) 3.5° E d) 2.0° E-‐ correct

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Part 12. Polaris Problems