Azimuth and Amplitude

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Britney Fields
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1 AVIGAIO Aziuth and Aplitude Aziuth Procedure for obtaining the aziuth and copass error he aziuth of a heavenly body is the angle at the observer s zenith contained between the observer s eridian and the vertical circle passing through the body. Basically, aziuth is the bearing of the heavenly body with respect to the observer. he aziuth can be calculated either atheatically, or by using the Aziuth ables. he aziuth is used to observe the copass error by taking the bearing of the heavenly body and coparing it with the result of the aziuth calculation. 1. Ascertain the U to conduct the aziuth; if necessary, convert tie to LM. his will ake later calculation easier, and also provide the approxiate bearing of the body in advance. 2. Fro the autical Alanac, extract the GHA and the declination of the body. For the star, HA of the star and GHA for the first point of Aries are needed. hen calculate LHA. 3. ith DR position, calculate the aziuth by ABC table, or by using ABC forula as follows: tanlat. A = tanlha tandec. B = sinlha A is naed opposite to latitude unless LHA is between 90 and 270 B is naed sae as declination C= A± B C is naed as A or B, whichever is greater Aziuth = tan C coslat. Aziuth is expressed in quadrantal notation and in the for: 1 1 or Aziuth or or : sae as C or : if LHA < 180 if LHA > 180 Aziuth also can be found by following forula: sinlha AZ = tan tandec.coslat. coslhasinlat. (outh value is entered as negative value) If denoinator is negative, aziuth will be naed outh ().

he aziuth can be calculated either atheatically, or by using the Aziuth ables.

2 AVIGAIO If denoinator is positive, aziuth will be naed orth (). If LHA is between 0 and 180, aziuth will be naed est (). If LHA is between 180 and 360, aziuth will be naed ast (). 4. Convert aziuth fro quadrantal notation for to three-figure notation for, then copare the aziuth with the copass reading to figure out the copass error by the following rules. Copass B, Copass rror Copass LA, Copass rror A xaple 1 On 17 th April 2008, at about 0800, DR position , chronoeter showed 11 h s, 2 20 s slow. he sun was observed bearing 135 C, variation 20. Calculate the deviation of the copass: Approx. LM Chronoeter th h s th h s Long. () rror 2 20 h s s Approx. U U th h s th h s Long. () h s LM h s th h s GHA at Declination s Increents (18 12 ) d = th h s GHA at Declination Longitude () LHA

Copass B, Copass rror Copass LA, Copass rror A xaple 1 On 17 th April 2008, at about 0800, DR position 47 30. 052 30., chronoeter showed 11 h 15 52 s, 2 20 s slow.

3 AVIGAIO Using ABC tables A 0.56 Aziuth : B 0.21 rue bearing: C 0.35 Using other forula AZ tan sinlha tandec.coslat. coslhasinlat. sin tan10 42 cos47 30 cos sin47 30 = tan = = 76.8 = rue Bearing Copass rror 31.8 Copass Bearing C Variation 20 Copass rror 31.8 Deviation 11.8 xaple 2 On 19 th July 2008, at about 0430, DR position , chronoeter showed 10 h s with no error. tar Peacock was observed bearing 250 C, variation 28. Find the copass error and deviation: Approx. LM Chronoeter th h th h s Long. () h h s th h th h s Approx. U U

8 Deviation 11.8 xaple 2 On 19 th July 2008, at about 0430, DR position 32 30 080 15, chronoeter showed 10 h 15 20 s with no error.

4 AVIGAIO s GHA at Declination s Increents (15 20 ) s GHA at HA GHA Longitude () LHA Using ABC forula tanlat. tan32 30 A = = = 0.37 tanlha tan A 0.37 B 1.77 tandec. tan C 1.40 B = = = 1.77 sinlha sin Aziuth = tan tan C coslat. = 1.40 cos32 30 = = rue Bearing Copass rror 29.7 Copass Bearing C Variation 28.0 Copass rror 29.7 Deviation 1.7 xaple 3 On 26 th October 2008, at approxiately 0120 in DR position 34 45, 35 15, tar Dhube bore 026 by copass. Variation 4. Chronoeter 10 h s has error 3 15 s slow. Find copass deviation:

1 1 1 Aziuth = tan tan C coslat. = 1.40 cos32 30 = 040.3 = 220.3 rue Bearing 220.3 Copass rror 29.7 Copass Bearing 250.0 C Variation 28.0 Copass rror 29.7 Deviation 1.

5 AVIGAIO Approx. LM Chronoeter th h h s Long. () 2 21 rror 3 15 h s Approx. U Chronoeter th h h s h s U th h s ϒ th h s GHA at Declination s Increents (58 57 ) ϒ th h s GHA at HA GHA Longitude () LHA Find aziuth by using forula: sinlha AZ = tan tandec.coslat. coslhasinlat. sin = tan tan cos34 45 cos sin34 45 = 28.2 = Find aziuth by using ABC forula: tanlat. tan34 45 A = = = 0.27 tanlha tan A 0.27 B 1.99 tandec. tan C 2.26 B = = = 1.99 sinlha sin Aziuth = tan = tan C coslat cos34 45 = 28.3 = rue Bearing Copass rror 2.3 Copass Bearing 026 C Variation 4 Copass rror 2.3 Deviation 1.7

coslat. coslhasinlat. sin248 37.3 = tan tan61 42.0 cos34 45 cos248 37.3 sin34 45 = 28.2 = 028.2 Find aziuth by using ABC forula: tanlat. tan34 45 A = = = 0.27 tanlha tan248 37.3 A 0.27 B 1.99 tandec.

6 AVIGAIO xaple 4 At approxiately 19:40 on 26 th October 2008, the chronoeter showed 1 h s ; chronoeter error is nil. DR position 14 18, ; observed Venus bore 246 copass, variation 2. Find copass deviation: Approx. LM Chronoeter th h h s h Long. () 5 53 rror nil Approx. U Chronoeter th h h s h s U th h s GHA Declination Increents d = GHA v = GHA Long.() LHA tanlat. tan14 18 A = = = 0.04 tanlha tan A 0.04 B 0.44 tandec. tan C 0.48 B = = = 0.44 sinlha sin AZ = tan tan C coslat = 0.48 cos14 18 = 65.1 = 245.1

() 5 53 rror nil Approx. U 18 13 47 Chronoeter 1 42 25 th h h s 12 00 00 h s U 18 13 42 25 th h s GHA 342 46.7 Declination 23 16.7 Increents 10 36.3 d = 0.6 0.4 GHA 353 23.

7 AVIGAIO rue bearing Copass error 0.9 Copass bearing C Variation 2 Copass error 0.9 Deviation 1.1 Aplitude he aplitude of a heavenly body is the arc of horizon contained between the position of the body when rising or setting and the ast or est point of the horizon. Alternatively, it is the angle between the bearing of the body when rising or setting and the ast or est direction. In the above diagra, α is the aplitude of body X, which is setting and has north declination, so the aplitude is naed as α. β is the aplitude of body Y, which is rising and has south declination, so it is naed β. Basically, the aplitude of a heavenly body is naed ast if rising, and est if setting, followed by orth or outh depending on the declination of the body at tie of observing. sindeclination Aplitude = coslatitude he aplitude is a siple and quick ethod for checking copass error. he bearing of a heavenly body when rising or setting is calculated in advance, which is the true bearing. At the oent it is at the horizon, the bearing is taken with the copass. Copare the true bearing and copass bearing to establish the copass error.

Alternatively, it is the angle between the bearing of the body when rising or setting and the ast or est direction.

8 AVIGAIO xaple 5 On 18 th July 2008, in position 50 30, 20 15, the sun rose bearing 080 by copass, variation 10. Find copass error and copass deviation: LM Declination LM d = Difference 9 Declination Latitude Correction 2 LM h Longitude in ie 1 21 U (table I) (20 15 ) sindec. sin coslat. cos Aplitude = sin = sin = 34.2 rue Bearing Copass rror 24.2 Copass Bearing C Variation 10.0 Copass rror 24.2 Deviation 14.2 xaple 6 On 17 th April 2008, in position 48 45, , the sun rose bearing 067 by copass, variation 24. Find copass error and copass deviation: LM Declination LM d = Difference 7 Declination Latitude Correction + 5 LM h Longitude in ie U (table I) ( ) sindeclination sin coslatitude cos Aplitude = sin = sin = 16 rue Bearing 074 Copass rror 7 Copass Bearing 067 C Variation 24 Copass rror 7 Deviation 17

0 1 1 Aplitude = sin = sin = 34.2 rue Bearing 055.7 Copass rror 24.2 Copass Bearing 080.0 C Variation 10.0 Copass rror 24.2 Deviation 14.

9 AVIGAIO xaple 7 On 25 th October 2008, in position 30 45, , the sun set bearing 250 by copass, variation 14. Find deviation for the ship s head: LM unrise LM unrise d = 0.9 Difference 7 Declinatio Latitude Correction + 1 LM unrise (table I) h Longitude in ie ( ) U unrise Declination n sindec. sin coslat. cos Aplitude = sin = sin = 14.3 rue Bearing Copass rror 5.7 Copass Bearing C Variation 14.0 Copass rror 5.7 Deviation 8.3

9 Difference 7 Declinatio Latitude Correction + 1 LM unrise 30 45 25 18 18 (table I) h Longitude in ie 10 41 (160 15 ) U unrise 25 07 37

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