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 ().
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 47 30. 052 30., chronoeter showed 11 h 15 52 s, 2 20 s slow. he sun was observed bearing 135 C, variation 20. Calculate the deviation of the copass: Approx. LM 17 08 00 00 Chronoeter 17 11 15 52 th h s th h s Long. () 3 30 00 rror 2 20 h s s Approx. U 17 11 30 00 U 17 11 18 12 th h s th h s Long. () 3 30 00 h s LM 7 48 12 h s th h s GHA at 17 11 00 00 345 07.6 Declination 10 41.7 s Increents (18 12 ) 4 33.0 d = 0.9 0.3 th h s GHA at 17 11 18 12 349 40.6 Declination 10 42.0 Longitude () 52 30.0 LHA 297 10.6
AVIGAIO Using ABC tables A 0.56 Aziuth : 076.8 B 0.21 rue bearing: 103.2 C 0.35 Using other forula AZ tan sinlha tandec.coslat. coslhasinlat. sin297 10.6 tan10 42 cos47 30 cos297 10.6 sin47 30 = tan = = 76.8 = 103.2 rue Bearing 103.2 Copass rror 31.8 Copass Bearing 135.0 C Variation 20 Copass rror 31.8 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. tar Peacock was observed bearing 250 C, variation 28. Find the copass error and deviation: Approx. LM 19 04 30 Chronoeter 19 11 15 20 th h th h s Long. () 5 21 12 00 00 h h s th h th h s Approx. U 18 23 09 U 18 23 15 20
AVIGAIO s GHA at 18 23 00 00 282 07.3 Declination 56 42.4 s Increents (15 20 ) 3 50.6 s GHA at 18 23 15 20 285 57.9 HA 53 24.2 GHA 339 22.1 Longitude () 80 15.0 419 37.1 360 00.0 LHA 59 37.1 Using ABC forula tanlat. tan32 30 A = = = 0.37 tanlha tan59 37.1 A 0.37 B 1.77 tandec. tan56 54.2 C 1.40 B = = = 1.77 sinlha sin59 37.1 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 1.7 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 55 42 s has error 3 15 s slow. Find copass deviation:
AVIGAIO Approx. LM 26 1 20 Chronoeter 10 55 42 th h h s Long. () 2 21 rror 3 15 h s Approx. U 25 22 59 Chronoeter 10 58 57 th h h s 12 00 00 h s U 25 22 58 57 th h s ϒ th h s GHA at 25 22 00 00 4 39.5 Declination 61 42.0 s Increents (58 57 ) 14 46.7 ϒ th h s GHA at 25 22 58 57 19 26.2 HA 193 56.1 GHA 213 22.3 Longitude () 35 15.0 LHA 248 37.3 Find aziuth by using forula: sinlha AZ = tan tandec.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. tan61 42.0 C 2.26 B = = = 1.99 sinlha sin248 37.3 1 1 Aziuth = tan = tan C coslat. 2.26 cos34 45 = 28.3 = 028.3 rue Bearing 028.3 Copass rror 2.3 Copass Bearing 026 C Variation 4 Copass rror 2.3 Deviation 1.7
AVIGAIO xaple 4 At approxiately 19:40 on 26 th October 2008, the chronoeter showed 1 h 42 25 s ; chronoeter error is nil. DR position 14 18, 88 18 ; observed Venus bore 246 copass, variation 2. Find copass deviation: Approx. LM 18 19 40 Chronoeter 1 42 25 th h h s h Long. () 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 23.0 23 17.1 v = 0.8 0.6 GHA 353 22.4 Long.() 88 18 441 40.4 360 LHA 81 40.4 tanlat. tan14 18 A = = = 0.04 tanlha tan81 40.4 A 0.04 B 0.44 tandec. tan23 17.1 C 0.48 B = = = 0.44 sinlha sin81 40.4 1 1 AZ = tan tan C coslat = 0.48 cos14 18 = 65.1 = 245.1
AVIGAIO rue bearing 245.1 Copass error 0.9 Copass bearing 246.0 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.
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 50 18 04 11 Declination 20 57.5 LM 52 18 04 02 d = 0.4 0.2 Difference 9 Declination 20 57.3 Latitude Correction 2 LM 50 30 18 04 09 h Longitude in ie 1 21 U 18 05 30 (table I) (20 15 ) sindec. sin20 57.3 coslat. cos50 30.0 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 14.2 xaple 6 On 17 th April 2008, in position 48 45, 158 05, the sun rose bearing 067 by copass, variation 24. Find copass error and copass deviation: LM 45 17 06 37 Declination 10 28.5 LM 50 17 06 44 d = 0.9 + 0.2 Difference 7 Declination 10 28.7 Latitude Correction + 5 LM 48 45 17 06 42 h Longitude in ie 10 32 U 16 20 10 (table I) (158 05 ) sindeclination sin10 28.7 coslatitude cos48 45.0 1 1 Aplitude = sin = sin = 16 rue Bearing 074 Copass rror 7 Copass Bearing 067 C Variation 24 Copass rror 7 Deviation 17
AVIGAIO xaple 7 On 25 th October 2008, in position 30 45, 160 15, the sun set bearing 250 by copass, variation 14. Find deviation for the ship s head: LM unrise 30 25 18 17 LM unrise 35 25 18 24 d = 0.9 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 Declination n 12 15.0 + 0.6 12 15.6 sindec. sin12 15.6 coslat. cos30 45.0 1 1 Aplitude = sin = sin = 14.3 rue Bearing 255.7 Copass rror 5.7 Copass Bearing 250.0 C Variation 14.0 Copass rror 5.7 Deviation 8.3