ASTRO~NAVIGATION PILOTING &.. !--- --"'l~_f DEAD RECKONING

Transcription

1 ASTRO~NAVIGATION PILOTING!--- --"'l~_f &.. DEAD RECKONING

2 Semidiameter (S.O,) of the Sun and Horizontal Parallax (H.P.) of Venus and Mars. For Sextant Altitude corrections S.D. January 16:3 July 15.8 February 16.2 August 15.8 March 16.1 September 15.9 April 16.0 October November 16.2 M'Y June 15.8 December 16.3 H. p Mars 1978 Jan. 1 _Mar. 10 0~2 10S0T" 1 - Ap,. 0 0:1 Mar. 20 Dec Apr.7 - May Jan. 1 Dac May 26 - Jul 'Jul. 3 - Jul Jan. 1 Apr Aug. 1 -Sep Apr Dec Dec:..!!- Sap, 13 -Nov, Jan. 1 ~ Nov Dec, Jan, 1 Feb,2 0.1 Dec Feb,3 _Jun Jan. 1 IJun. 16 Dec Jan. 1 May May 23 - Jul Jan. 1 Dec Jul Sep Jan. 1 Mar Sep.3 - Oct Mar.5 - Aug Oct Nov. 1'3 0.3 Aug. 28 Dec Nov. 14 Dec Jan. 1 Dec Jan ! Jan. 2 - Dec SIMPLE merious t::::)1c3it~l H P Venus Jan. 1 Jul.23 0: Jan. 1 Dec, 13 0:1 Jul.24 _Sep.l0 0.2 Dec Dec Sep. 11 -Oct Jan. 1 _ Feb Oct. 4 _Oct Feb. 5 _ Feb Oct Nov, 29 0.' Mar. 1 _ Mar Nov Dec Mar. 18_Apr. 21 O. Dec Dec Apr. 22-May Jan. 1 Jan May 8 - May Jan.7 - Feb \May 30-Jul Feb. 28 _. Dec Jul Dec Jan. 1 - Mar Jan. 1 Jul Mar. 2 - Apr Jul. 21 -Sep Apr May Sep.9 -Oct May 15 - May Oct. 2 -Oct May 31 _ Jul. 1 0.' Oct. 17-Nov.26 O. Jul. 2 _Jut Nov. 27- Dec Jul. 18 _ Aug Dec. 13- Dec Aug.l0-Sep Jan. 1 Jan Sep.30 - Dec Jan.5 _ Feb Jan. 1 Nov Feb. 26 Dec. 31, 0.1 Nov Dec Jan. 1 Feb, Dec Dec Feb. 28 -A?r Dec. 31 a.' APr. 20 -May Jan. 1 feb. 10 a.' May 12 -May Feb Feb MlilY 29 -Jun. 28 a.' Feb Mar Jun. 29 -Jul IMar. 1-May9 0.2 Jul. 16 -Aug May 10 Dec Aug. 7 -Sep Jiln.1 - May Sep.28 -Dec May 14 _ Jul Jan. 1 Sep Jul. 2 - Jul Sep. 29 -Nov Jul. 24 _ Aug Nov. 20 -Dee Aug.9 _Sep.l1 0.' Dec. 13 -Dec Sap. 12 _ Sep Dec. 29 -Dec ' Sep.29 _ Oct Oct.:;1:2 _ Dec. 13,0.2 Dec. 14 _ Dec. 31: 0.1 TABLE 1 BY TAMAYA DIGITAL NAVIGATION COMPUTER NC n

3 Contents Introduction PART ONE: CHAPTER I CHAPTER II CHAPTER III CHAPTER IV CHAPTER V CHAPTER VI CHAPTER VII PART TWO: CHAPTER I CHAPTER II CHAPTER III ASTRO-NAVIGATION BY NC-77 Fundamentals of Astra-Navigation 4 Taking Sight with a Sextant Finding the Geographical Position of Heavenly Bodies (Greenwich Hour Angle and Declination) 10 Computation <lnd Plotting for Fix 15 Sextant Altitude Corrections 24 Identification of Unknown Star Fix by Noon Sight and Other Sextant Applications BASIC NAVIGATION COMPUTATIONS FOR DEAD RECKONING AND PILOTING BY NC-77 Mercator Sailing and Great Circle Sailing Plane Sailing and Navigation through Current and Wind 42 Tide and Stream {Tidal Current} 46 CHAPTE R IV Speed, Time, Distance,. 48 CHAPTER V Time and Arc 49 APPENDIX EXPLANATION OF NC 77 DIGITAL NAVIGATION COMPUTER,..,. 50 Introduction With TAMAYA NC-77 DIGITAL NAVIGATION COMPUTER we can digitally solve most navigational problems with scientific accuracy and incredible speed in a very easy way. However, it is a fallacy to believe that computers will do everything for us. Safety at sea always depends on our sound judgement, whatever tools we may use to facilitate our work. For this reason, this textbook not only explains how to use NC-77 Computer but also refers to the principles and fundamentals of navigation. In PART ONE determining our position by Astro-Navigation is expounded fully from the principle to the actual steps of computation. In PART TWO Basic Navigation Computations for Dead Reckoning and Piloting are explained with examples and illustrations. The text is very easy, and no special knowledge of computer programming or mathematics is required. In the course of learning in this textbook, if any question arises about the meaning of keys and dialogue symbols of NC~77 we can refer to the Appendix where full explanation is given with illustra~ tions. For further study on navigation, it is recommended to read such classical textbooks as..american Practical Navigator" by Bowditch or "Dutton's Navigation and Piloting" by Dunlop and Shufeldt, with NC-77 computer at hand. Comprehension of these textbooks is greatly advanced because with NC-77 we can save a lot of time otherwise spent unnecessarily on acquiring techniques on mechanical computations. Consequently. we can concentrate on understanding of more important fundamentals and principles of navigation. 2 3

4 PART ONE CHAPTER_I Fundamentals of Astra-Navigation 1. PRINCIPLE OF ASTRO NAVIGATION When we know the distance from two points, the positions of which are already known, we can determine our ship's position. Suppose the distance from our ship is 6 miles to Lighthouse A and 8 miles to Lighthouse 8. Draw a circle with a radius of 6 miles and A as center. This is called a Position Circle because our ship must be somewhere on it. Now, draw another position circle with a radius of 8 miles and B as center. ObViously, the intersection of the two position circles is our ship's position. See Fig. 1. o ~~ ~ Lighthouse B Lighthouse A o 6 mhos \J! ASTRO-NAVIGATION BY NC-77 8mil~ The next thing we must know is the distance from our ship to the GP. It can be determined by measuring the altitude of the heavenly bod~ above the horizon. For instance, if we observed a ~tar at the altitude of 40 degrees we can figure out the distance to Its GP as 3,000 miles by computation. [The distance from our ship to the. GP of a he.ave.nly body = (90' - altitude) x 60 mile.s]. See Fig. 3, and supplementary note on page 33. Fig.3 Distance. from ship to GP of star ~ - / 5;' ~ 90/ Gp '-._ miles- I Now, if we drew a position circle with a radius of 3,000 miles and the ~P as center, our ship must be somewhere on it. See Fig.4. By drawmg anot~er position circle with another heavenly body wh~~e GP an~ ~Istance are known we can determine our ship's position at their Intersection. Fig. 1 Finding Ship's Position by Measuring Distance Position Circle In Astra-Navigation, the same principle, position circle method, is used to determine the ship's position. Therefore, we must always have at least two known points, and instead of lighthouses we use heavenly bodies; the Su n, Moon, planets and stars. The.n, how do we know the. position of any of these he.ave.nly bodies? We will express their position in terms of their Geograph~ ical Position (GP). GP is the point where a line, drawn from center of the heavenly body to the center of the earth, would touch the earth's surface. In other words, if a star fell down directly toward the center of the earth, the spot that it would hit on the earth's surface is its GP, and at this point we would see the star directly overhead. * Fig. 4 Position Circle ~i~ce i~ is not feasible, in practice, to draw a 3,000 miles radius POsl.tlon ~Ircl.e on a chart, only a necessary part of it is drawn as a stra.lg.ht line 10 the manner explained in Chapter IV. This is called POSition Line or Une of Position. See Fig. 5. The principle of modern Astro-Navigation is just this simple. -, A' \, Zimuth of the sighted body from our ship \ _Position Circle,,, \,,,,,, Position Line Fig.2 GP of a heavenly body Position Circle and Position Line 4-5

5 2. BASIC STEPS AND TOOLS FOR ASTRO NAVIGATION It takes some steps and tools to determine our ship's position by Astro-Naviga ion as summarized in Fig. 6. Fig TAKING SIGHT WITH A SEXTANT. Measure the altitude of the heavenly body (Sun, Moon, planet or star) above the hori zon at your position. Record the exact Greenwich Mean Time (GMT) of the sight. I! I' I! II, ' / i! /11 l I Sextant Quartz Watch 2. FINOING GEOGRAPH ICAL POSITION (GP) OF THE SIGHTEO BODY: The GP is the point on the earth directly beneath the heavenly body, and it is expressed by Greenwich Hour Angle (GHA) and Declination (DEC), They are computed by Ne-n or found in the Nautical Almanac. DEC N20 0 GHA Greenwicr Line ~~~~~DR Lat 30 N DR Long 60 0 \ NC 77 Computer TOOLS, or Nautical Almanac 3. COMPUTATION BY NC-77 AND PLOTTING: Compute the Azimuth C=-) and Altitude (R) of the same body by Ne-n using the factors found in Steps (1) and {21, and the DR posi tion. (A ship's position determined by applying the cource and distance travelled from some known position, e,g., the departing port, is called Dead Reckoning Position.) Compare the computed Altitude (R l with the ac:wally observed True Altitude (Ral. From the above factors we can plot a line of position (LOP) on the chart or plotting sheet. Plot two LOP's to determine our ship's position at their intersection (FIX), or compute it digitally by Nc-n...,... ".' (~ '....><> 1 u' '-"'~ -',' Y C'0 92~~ _ "... &'1-. \0 DR0 ", 0 ":" Plotting Instruments NC 77 Computer 6» 7

6 CHAPTER II Taking Sight with a Sextant 1. SEXTANT Taking a sight means to measure the vertical angle or altitude between a heavenly body and the horizon in order to ascertain ~he ship's position at sea. The sextant is used as a tool to accomplish this aim. All marine sextants have two mirros arranged as shown in Fig. 7 and work on the same principle. The index mirror reflects the image of the body to the horizon mirror. The horizon mirror is so constracted that one can see the horizon at the same time he sees the reflected image of the whole body. Thus, the altitude of the body is measured by adjusting the angle of the index mirror until the reflected image contacts the horizon (Fig. 8). In a high quality sextant the altitude can be read by degrees, minutes and 1/10 minute. One minute of the sextant reading is equivalent to one nautical mile. M SUN Horizon Reflected image of the Sun Index Mirror w -' o z ~ :r Horizon mirror ~ Z ~t X w ~ Fig UUARTZ WATCH!/ Horizon-' In Astra-Navigation it is necessary to read hours, minutes, and seconds of time, so the digital quartz watch having the seconds display is very convenient for such reading of accurate time. Four seconds of time is equivalent to one minute of longitude (one nautical mile at latitude 0 ). When a sight is taken, record the altitude of the body measured by the sextant and the exact Greenwich Mean Time (GMT) of the sight. Greenwich Mean Time is the time at longirude 0. Local Mean Time (LMT) will depart 1 hour from GMT for every 15 of longitude. Therefore, Zone Time in New York, based on LMT at?5 W long., is 5 hours before GMT, and Zone Time in San Francisco based on LMT at W long. is 8 hours before GMT. If we go eastward, Tokyo based on LMT at 135 E long. is 9 hours after GMT. With this principle in mind, LMT can be easily converted to GMT. Sextant arc and reading Fig = D

7 1 CHAPTER III Finding The Geographical Position of Heavenly Bodies (Greenwich Hour Angle and Declination) Problem 2. Find the GHA and DEC of the Moon at GMT 05h 25 m 18 s on Jan. 1, We need Nautical Almanac to find GHA and DEC of the Moon, planets and stars. NC-77 greatly facilitates the procedure of deriving the required information from the Nautical Almanac. Nautical Almanac is published every year by the U.S. Naval observatory or equivalent authorities in other countries. The Geographical Position is the point on the earth directly beneath the heavenly body, and it is expressed in terms of Greenwich Hour Angle (GHA) and Declination IDEC). GHA and DEC are like longitude and latitude that are used to designate positions on the earth. In Astro-Navigationwe use the Sun, Moon, Venus, Mars, Jupiter, Saturn and selected navigational stars as reference bodies. We can obtain GHA and DEC of the Sun by NC-77 Aimanac ~ mode. For the other bodies we use NC-77 and the Nautical Almanac. Let us work on examples. Problem 1. Find the GHA and DEC of the Sun at GMT 14 h 35m 43s on Jan. 1,1978 by NC-77. Key Display Note: 8, o. Year Month Day " h O h Hour Minute Second Ho GHA d DEC H GHA to Equation of Repeat d and H Answer: GHA Sun (Dialogue Symbol : H) 38 02'.5 DEC Sun (Dialogue Symbol : d I S22 59'.9 GHA/DEC ys. We will make use of GHA Aries (Ho ) later in the star problem, and Equation of Time (1::0) in the noon sight problem. Longitude/Latitude DEC is measured like latitude f from the equ~"or to 90 north and 90 0 south. It should be noted that GHA and longitude are not expressed exactly the same. Whereas longitude is measured from the Greenwich meridian (longitude 0 line) to east and to 180 west. GHA is measured only westward up to from it. Therefore, longitude 90 east, for instance, is equivalent to GHA 270' As an example, we will find the following data in the 1978 Nautical.A:lmanac for Sunday, January 1. See Table 2 - Excerpt from Nautical Almanac. MOON STARS G.M.T. G.H.A. Dec H,P. Nome S.H.A. D" i 00I N Acamar ' " Achernor Acrux , ,4 Adhero Aldebaran N , o 42.1 o i N Aliofh N Alkoid 08 i N o Al No'ir S N Alnilam S 1 D.1 U i~i Al'phord N o A Alphecca 13, N o y 56.7 Alpheratz N Altair N o Ankaa 16 ' Antares Arcturus N Atria , Avior Bellafri;.:: N Betelgeuse N TABLE 2 (Continue to page 12) Canopus , Capello N 11

8 G.M.T. G.H.A. SUN ARIES VENUS Dec. G.H.A. G.HA 0" 0 o, 0 o, 0 100" , OL , U , ,9 N A y , , , , , , In order to find the GHA and DEC of the Moon at GMT 05h25m_ 18 5, w~ first find the data for GMT 05 h and 06h, and feed them to NC-77 In the following manner. Problem 2 Answer GHA DEC DEC Moon K.y Display Key Display GMT GHA DEC 0~ h o. CD@ 05 h 0 0 o 42',1 h O. NO 47'.4 5 h h 15 14,1 5. NO d d O. 0,421 d d h From Nautical Almanac h O. 6 h 6. (Table 2) 6 6. d d O d d h' h' O h' d' d' NO'43'.1 MARS JUPITER SATURN G.M,T I-"O=--.H=--.A-.--C:O-,,-.-f---:G:-.:cH-:A-.----,;OCC,,=--.-+'O".H'.A'.--O".::,-.-t d hoi N N U N~ N N ~ Ll I N N N N N13 12.) N ' IDA ' ' 170 N N [ Problem 3. Find the GHA and DEC of Venu, at GMT 14h45m. 52' on Jan. 1, Problem 3 GHA DEC Venus Key Display Key Display GMT GHA DEC CD@ h O. Interpolation is unnecessary 14h h 14. as DEC in this case does not: d O. change during one hour d h O. 15 h 15. From Nautical d O. (Table 2) d h' O h' d' Answer GHA 45'55'.1 DEC 523'37'.7 ~or other plants, Mars, Jupiter and Saturn, GHA and DEC are found In the same manner TABLE 2-13

9 Probelm 4. Find the GHA and DEC of Arcturus at 16h 16m39s on Jan. 1, GHA of the Star, Arcturus, is found by adding SHA of Arcturus (Sidereal Hour Angle) to the GHA Aries. Greenwich Merid"lan GHA Aries is a reference meridian for establishing celestial longitude of Stars, It is constantly changing, an.d expressed in ~erms of westward angle from the Greenwich meridian. SHA Star IS the westward distance of the particular star from this meridian. So, the rule to compute GHA star is: GHA Star = GHA Aries + SHA Star. GHA Aries is computed by NC-77 B mode, and SHA's of fifty-seven navigational stars are found in Nautical Almanac, Key '1. '2. Display ~ h He GHA Aries G He SHA Arcturus * He GHA Arcturus G He '2 SHA Arcturus is found "In Nautical Almanac. See Table 2. When GHA becomes greater than 360 we customarily subtract 360 to express it within one round o~ the earth. If qha becomes negative it is also common practice to add 360 to express it as a positive value. DEC of Arcturus is found in Nautical Almanac. (See Table 2) as N19 17:7. It does not change for the whole day. Answer: GHA 131'27:7 DEC N19'17:7 CHAPTER IV Computation and Plotting for Fix Now we are ready to compute and plot our position. As mentioned in the Principle of Astra-Navigation, it is impractical to draw a position circle with radius of hundreds or thousands miles on the chart. So, we plot only a necessary part of the position circle as a straight line, and call it a Line of Position (LOP). LOP is obtained by comparing the computed altitude and the actually observed true altitude. The former is the altitude com puted on the assumption that our 0 R is correct, and the latter is the altitude measured by sextant at the actual position. (True Alti tude is obtained by adding corrections to the direct sextant read ing. See Chapter V Sextant Altitude Corrections.) If there is a difference between the two altitudes the assumption was wrong by the amount of the difference IAltitude Intercept). So, we will correct our DR position so that there will be no difference between the two altitudes. [t is best to follow the actual steps to understand this principle. Problem 1 The DR position of a vessel is '.8N69 35'.5W at GMT 14 h 35 m 43 s on Jan. 1, The lower limb of the Sun is sighted by the sextant at this.. monent, and the true altitude (RD) after sextant altitude corrections is 28 32:6. Required: (l) Compute the Altitude and Azimuth of the Sun. (2) Compute Altitude Intercept. (3) Piot the Line of Position. 14) Obtain "FIX" by two Lines of Position. 1. COMPUTATION OF ALTITUDE (,q) AND AZIMUTH (= ) BY NC-77 A convenient NC-77 LOP COMPUTATION CARD has been prepared to assure the proper order of input data. See the enclosed card and Table 3. Enter the date, GMT, name of body, DR Lat. and DR Long. in the blanks so designated. The GHA and DEC at GMT 14 h 35 m 43 s on Jan. 1, 1978 have been obtained in Chapter III Problem (1) as 38'02'.5 and 522'59'.9. Fill in the appropriate blanks with these data. Then, follow the steps shown on page

10 Key. f0e) lW Display Answer LH O. Computed Altitude 28 37~8 LH Azimuth ~1 T LH *1 (measured clockwise \ LH *2 ' from north1 d O. d L O. L R _ ( Rand =can be repeated Fig.9 Spherical Triangle N "1 GHA and LHA: When continuing directly to ~ mode from ~ mode do not confuse Hand LH. H stands for Greenwich Hour Angle (GHA) and LH for Local Hour Angle {LHA). LHA = GHA ± DR Longitude. Since ~ key changes the sign to ~egative this rule is automatically observed if we always add longitude. This computation may be made in either 8 or ~ mod~, but the dialogue symbol does not change from H to LH until ~ mode key is pressed. *2 Some navigators are accustomed oto expressing ~HA al~ays a.= a positive vaiue by applying 360 : LHA = : '.0. In such a case we may enter LHA '.0 instead of '.0. The end result is the same. s Mathematics for Altitude and Azimuth Computation The spherical triangle as formed on Fig. 9 is solved by the following equations to obtain computed Altitude (,q ) and Azimuth ( z: Ne-77 symbol,) A =: sin- 1 [cos h cosd"cosl + sind"sinl ] _'[ sind -sina"sinl Z = cos cosa.cosl Where d: declination A: Computed Altitude L: DR Lat. Z: Computed Azimuth h: LHA lobtained by GHA ± DR Long.) Since these equations are programmed in the NC-77~ mode A and Z are computed simply by feeding d, Land h. 2. COMPUTATION OF ALTITUOE INTERCEPT The intercept is simply the difference between the observed true altitude ( Ro ) and the computed altitude ( R ). The observed true altitude is obtained by adding corrections to the direct sextant reading. These altitude corrections, consisting of multiple factors, are easily computed by NC-77, and are explained separately in CHAPTER V Sextant Altitude Corrections (See problem 1 on page27). For ~urposes of this problem, just take 2S03t6,as the ~bs;rved true altitude, and the Intercept IRa - R ) ; ) ; -5:215.2 milesl p

11 _ NC-77 ~ or ~J+-~L~N~a~ut~ic~a~'1A~I~m~a~n:a:;,cJ +l-- --' NC-77~ 2 SUMMARY OF NC n KEY SEQUENCE FOR lop COMPUTATION For Chapter IV Problem (1) Preparation of the data: LHA DEC DR LAT (See page 10) Data Dat8 Source Key Jan. 1, 1978 Chapter 111 Problem OJ GMT 14h3Sm 43 s Chapter III Problem GHA ARIES ',2 Computed by DEC '.9 Computed by Ne ~ GHA 0 3S002'.5 Computed by DR LONG W Chapter IV Problem (1) G \8) LHA ',0 Computed by Ne Computation of Altitude and Azimuth (See page 161 Data Data Source LHA Continued from above DEC Recall Memory 1 DR LAT Chapter IV Problem (1) ComputedAltitude Computed by NC 77 True Al;muth Computed by NC Display ~ h Ho d H H "1 H "2 For., and *2 see page 16 Display LH d L R ,431 Sextant Altitude Corrections for True Altitude (See page 271 Data Data Source Key Display Sextant reading 28 20'.5 Directly from sextant '.5 d Index error 0'.5 too low Check sextant d Index error corrected alt. ] R, Hsight of eye 3m from water ht 3. Dip corrected alt. Computed by R, Refraction corrected alt. Computed by NC Rn Sun sight 0 5d O. Sun's SemJdlemeter 16'.3 Table 1 of this booklet.163 5d Lowsr limb tower 11mb was sighted l:& 5d Ro Altitude Intercept tsee page 20, Data Data Source Key Display Ro Computed by NC d R Computed by NC' 77 ( d d Note: We may use memory keys for the data used repeatedly, It is recommendable, however, to write down the data in LOP Computation Chart whenever they become available. Errors, jf there was any, can be easily traced by this way. Plot Line of Position or Compute Fix by NC-77 with data

12 3. PLOTTING A LINE OF POSITION Now, we can plot the Une of Position on the chart or plotting sheet with our DR Lat. 30' 22:SN, 69' 35:5Wand Intercept-5:2, Azimuth :1. We take the intercept 5:2 from the latitude scale of the chart by marine dividers and tranfer it onto the azimuth line. 5:2 of latitude is 5.2 nautical miles on the earth's surface. The line crossing the azimuth line at right angle at this point is called Line of Position (LOP). (Fig. 101 Looking at the illustration in Fig. 11, we can figure out that when Ro (the true altitude) is greater than R (the computed altitude with the assumption that our DR position is correct), we should shift our position from the DR position towards the Sun along the Azimuth line. The opposite should be done if Ro is less than R. N 30' 4. FIX BY TWO LOP'S In the theory of Astra-Navigation as explained at the outset a ship's position can be determined only after at least two LOP's ~re obtained. The intersection of the two LOP's called "fix" is the ship's position (Fig. 6 on page 6 ). RUNNING FIX If the tt fix tt must be made only by Sun sights, we should obtain two LOP's by allowing a time interval between the two sights as the Sun changes its azimuth in a day moving from east to west at a considerable speed. In this case, the first LOP is advanced along the ship's course by the amount of the distance run between the two sights. The crossing point of the advanced LOP and the second LOP is the ship's position at the time of the second sight (Fig. 12) This is called Running Fix. N 25' L.at 30"20' ~.'l-"" '1 DR Z8N 69 35:SW >«---~ Fix Fig. 10 Plotting a Line of Position DR has been advanced 18 miles on COUrse 110 to 30"16:6N, 69" 16:0W. (Use c: c At GMT 1S h 38 m Jan. 1, 1978 At GMT 14 h 35 m 435 R Ro Fig. 12 Running Fix Ro<,q Ro>R Move from the DR away from the Sun Move from the DR towards the Sun. 20 Fig.11 Direction of Intercept b 21

13 In order to advance LOP1, first, compute the new DR position applying the course and distance. For this computation see Dead Reckoning by Mercator Sailing by NC-n on page 38. At this position plot the advanced LOP1 repeating the same procedure. Suppose we took the second Sun sight at this new DR position and computed the azimuth :1 and intercept 6.5 miles away. This result is also plotted on the chart as LOP2. The intersection of the advanced LOP1 and LOP2 is our ship's position.... Vega \ \F~ o JI.. Sirius DIGITAL FIX BY NC-n While we are able to read the plotted fix position from the chart, or plotting sheet, it may be digitally computed more precisely by NC-n as follows. Input: Data irom iig. 12 DR Lat '.6N DR Long, 6g0 16:0W Alt. Intercept (1) 5.2 miles away Azimuth (1) ~1 Alt. Intercept (2) 6.5 miles away Azimuth (2) B!l Key CO ) Display Note: In ~ mode, if 90 0 or is entered as the first azimuth the answer will become "E" as tan 90 0 or tan included in the program produces "E". However, a 90 0 or can be accepted as the second az imuth. o. ~ :t O. 1l d O. d-5.2 _ O. ~ d O. d -6.5 O. = L Repeat L and II Answer Lat :5N Long. 6g0 14:7W (FIx at GMT lsh 3S m 03s) Fig. 13 Fix by Two Stars FIX BY TWO CELESTIAL BODIES We may take sights of two different celestial bodies like the Sun and Moon, the Moon and a star, two different stars etc. If we take sights of two bodies in a very short time interval we can consider it as a simultaneous observation,and a Line of Position can be plotted from one DR position as illustrated in Fig. 13. The position "fix" has the best reliability when the two LOP's are at right angle to each other. (This is also true with running fix.) For star sights, suitable stars to make an ideal fix Can be selected from the list of fifty-seven navigational stars, Polaris and four planets in the Nautical Almanac. Before taking a sight the azimuth and altitude of the desired star may be precomputed using the approximate time of the sight to be taken. In this way the star can be found very easily b

14 CHAPTER V Sextant Altitude Corrections After taking a sight of a celestial body we must make necessary corrections to the direct sextant reading to obtain the true altitude. The corrections to be made are (1) Index correction (2) Dip correction (3) Refraction correction (4) Semldiameter correction, and (5) Parallax correction. (1) Index correction Index error is the error of the sextant itself. This error can be checked by looking at the horizon with the sextant with its reading set at 0 00:0, If the reflected image of the horizon in the horizon mirror does not form a straight line with the directly viewed horizon through the clear part, an error exists caused by the lack of parallelism of the two mirrors. Then, move the index arm slowly until the horizon line is in alignment, and see how much the reading is off the"o", This amount should be added to or subtracted from the sextant reading depending on the direction of the error (Fig Height of eye.. EARTH Fig. 15 #~ X al\rtude measured Altitude\Without Dip\ " I Horizon sea level "" Horizon viewed from above sea (3) Refraction correction Refraction is the difference between the actual altitude and apparent altitude due to the bending of the light passing through media' of varying densities (Fig. 16). Dip * Apparent Position * Actual Position EARTH Fig. 11. Fig.16 Refraction Horizon in alignment Fig.14 Index Error Horizon out of alignment Index error present (4) Semidiameter correction When measuring the altitude of the Sun or Moon by sextant it is customary to observe the upper or lower limb of the body because the center of the body cannot be easily judged. In this case the semi diameter of the disk of the body must be subtracted from or added to the measured angle (Fig. 17), (2) Dip correction Dip is the discrepancy in altitude reading due to the height of the observer's eye above sea level. If we could IT'~asure the altitude of a body with our eye at the sea water level this correction would not be neccessary (Fig. 15)

15 Center of the sun--"*-~ $emidiameter... Lower limb -~~.I.-\:\c--- L~--'--IJ Horizon SEXTANT ALTITUDE CDRRECTIONS BY NC n NC-77 has ~ (Standard Altitude Corrections) and ~ (Variable Altitude Corrections) modes for sextant altitude corrections. is used to make altitude corrections under the standard temperature and atmospheric pressure (10 C, mb, or 50' F, 29,92 in.l. ~ is used when the corrections under varying temperature and pressu re are desired. These factors affect the refraction correction. Fig. 17 Semidiameter (5) Parallax correction Parallax is the difference in the apparent position of the body viewed from the surface of the earth and the center of the earth. While the angle must be measured from the center we can view the body only from the surface, and the difference must be adjusted {Fig, 18). STANDARD ALTITUDE CORRECTIONS Problem 1. The sextant reading of the lower limb of the Sun is 28'20:5 on Jan.l, The sextant reads 0:5 too low because of the index error. The height of eye above sea level is 3 meters. Find the true altitude of the Sun. First, make the index correction. Sextant Reading. Index Correction. 28'20' '21.0 ~ mode, and make computation as fol Then, select NC-77 lows. Surface of the Earth,~.- ~...L:._,.L--' Center of the Earth., '" b Fig.18 Parallax This correction is applied to the Sun, Moon, Venus and Jupiter, In NC-77 the Sun's Parallax correction is made in combination with its semidiameter correction. On the other hand, the Moon's semi diameter correction is made together with its parallax cor rection. It is easy to make the first Index correction mentally, but the other corrections are based on rather complex equations, and it is best to solve them by NC-77 programs

16 Problem 1 Key Display Answer SUN(lower limb of the Sun) l R, 0 Sextant Altitude R, (Index error corrected) 28 he o. Height of eye 3 he 3. Height of eye 3.0 meters( 9.84 R, Dip corrected alt. Rn Refract. corrected alt. 16',3 (Jan. 1, 5d o Q~ 5d 0,163 Semidiameter of the Sun (lower Ro 28,326 True alt '.6 Problem 2. Problem 2 MOON CC (upper limb) Sextant Altitude (Index error corrected) 18 46'.5 Height of Eye 6.5 meter (21.3 tt) H.P. 58'.9 (Jan. 25,1978) The Moon's upper limb is sighted. Compute the true altitude with the following data. Key 6.5 QJ Display Answer At o. R, hi: O. hi: 6.5 RI" Rn 18,391 hp o. hp 0,589 H.P.Moon hp Ro True altitude 1'9".,.9 The true altitude is 28 32',6. Before entering the data make sure whether computation is made in meter or feet, checking the side selector switch. Choose upper or lower limb by Orr. or Orr. key depending on which side was sighted. The Sun's S.D. (Semidiameter) is given in the Nautical Almanac. The summarized data is given in TAB LE 1. It yaries from 15'.8 to 16'.3 in any year (15'.8-16'.0 April September and 16'.1-16'.3 October - March). So, we could safely use the average 15'.9 for the first, and 16'.2 for the second six months and be within 0'.1 of the true altitude. If S.D. or H.P. is entered with a wrong decimal point position, for instance, 16.3 instead of in the above case, the program blocks it and asks the re-entry of the correct information without having to go back to the very beginning. The Moon's H.P. (Horizontal Parallax) at every hour of the day is found in the Nautical Almanac. Problem 3.. Venus is sighted, following data. Compute the true altitude with the Problem 3 Key Display Answer VENUS Sextant Altitude (Index error ) R, O. corrected) 34 20' R, Height of Eye 6.5 he o. (21.3 ftl 6.S he 6.S H.P. 0'.3 (Sep. 15, R, Rn Q] J hp O )'P Ro True altitude '.8 H.P. (Horizontal Parallax) applies only to Venus? and Mars 0 (See TABLE 1 of this booklet for H.P. data), There is no H.P, for the other navigational planets, Jupiter and Saturn, Altitude corrections for these two planets are, therefore, made as for the stars, which have no H.P, 28 L 29

17 Problem 4. Arcturus is sighted. Compute the true altitude with the following data. Problem 4 ARCTURUS Sextant Altitude (Index error corrected) '.9 Height of Eye 6.5 meters (21.3 ft.) Since there is no H,P. for the stars, the refraction corrected altitude 8" is the true SUMMARY Key ~ 6.5 Key o;splay K"L_"'" Oi!play Key lei R, S,~,"n, Alt. (IMox R, Display.q, 0 R, ht O. ht 6.5 R : Rn Answer i~~~~;,i.~tude e"o' o.,,,oe,od) i hi: Height.,f Eyo ht SAME AS SUN ~ I ~ ~~::J "p!cdb hp r--- "~c.0._"_a_'_"_'_)"_o_"_s:o~~,,---l-'~c.'_ '_"_rn_,"_",_' -,,~.~_~,~p.ltasle1~_~: J 8, Sextant Altitude Rr 0 ip Corrected 8,.., Refraction Corrected Ho True Altitude he Height of eye Sd Sun's Semidiameter hp Horizontal Parallax of Moon, Venus or Mars Problem 5. The upper limb of the Sun is sighted. Compute the true altitude using the measured temperature and pressure. Problem 5 SUN (Upper limb) Sextant Altitude (Index error corrected) 5 20~2 Height of Eye 6.5 meters (21.3 ft.) Temperature-3 C ( F) Pressure 986mb (29.12 in.) S.D. 16'.2 Key Display (D ) R, O R, hl= O. 6.5 hl= ~ O~ : 3 r:il t -3. :@J P 0 : 986 P 9~6. Rn 5.059: "0'...,, 'sd 'i/, ()C Ro Answer Dip corrected alt, '7 Refraction corrected alt '.9 True alt ',9 The key sequence for 8 until Refraction Correction is uniform for all Sun, Moon, planets and stars. In the case of Jupiter, Saturn and Stars 8" equals the True Altitude since there is no Horizontal Parallax or Semidiameter to be taken into consideration. Accuracy: In J ~ mode programs, correction for dip = -1'.776 vheight of'eye in meters = -0'.98 Vheight of eye in feet is used based on F.W. Bessel's terrestrial refraction theory. For astronomical refraction R. Radau's mean refraction table is simulated by the program. There is no significant difference in accuracy between the various refraction theories. VARIABLE SEXTANT ALTITUDE CORRECTIONS When a low altitude body is sighted refraction becomes a relatively significant factor ~n computing the true altitude. In such a case, say, less than 10 of altitude, temperature and pressure factors should be introduced for more precise computations. ~ mode computes the True Altitude by Var' ole Sextant Altitude Corrections when the use of varying temperature and atmospheric pressure is desired, 30 31

18 CHAPTER VI Identification of Unknown Star If we know the altitude and bearing of a star, and want to find out what star it is, NC 77 is used in the following manner. *1 Add if longitude is west. *2 See Chapter III for how to find GHA ARIES by NC-n ~ mode. *3 If the answer becomes negative, add to get SHA. If the answer is greater than 360 0, subtract Problem 1. Required: At GMT19h32m16son Jan. 1,1978 an unknown star is observed at altitude 62 36'.3 and approximate azimuth not. The ship's DR position is 12 40'N 'E. Identity of the star Key ~ Il"J Il"J Display LH O. LH 72. d d, L L R O O Approximate declination Approximate local hour angle Note On Fig. 3 on page 5. The more theoretical presentation, at the expense of difficulty in comprehension of the relations among the star, ship and GP, is illustrated as supplement to Fig. 3. Then compute the following in ARC mode. Local hour angle of star (LHA). Subtract DR longitude of ship. Greenwich hour angle of star (GHA). Subtract GHA Aries for 19h32m16s (GHA) Jan. I, 1978 Sidereal hour angle of star (SHA). 332'20' OE * '.6 * *3 Horizon Entering Star table on Pages of the Nautical Almanac with SHA 145'49'.0 and DEC 19'28'.6N, the star with the closest values is found to be C( Bootls (SHA 146'20'.2 DEC N19 17'.7), another name of which is Arcturus, star No. 37. In the event that a reasonably close match of the computed SHA and DEC values. cannot be found in the Star table, it is possible that the body observed was actually a planet, and the SHA values of the four navigational planets at the bottom of the STARS table of the daily pages also should be checked

19 CHAPTER VII Fix by Noon Sight and Other Sextant Applications 1. FIX BY NOON SIGHT We can find our latitude and longitude at the same time if we measure the Sun's highest altitude of the day and record the time. Longitude: The Sun travels from east to west at an equatorial speed of 15 miles per minute. It crosses the Greenwich meridian at GMT 12 o'clock. At this moment on the Greenwich line the Sun has reached its highest altitude of the day, and we observe the Sun due South or North. This is called Meridian Passage. If we were not on the Greenwich line (longitude 0 ) we would observe the Sun reach its highest altitude at a different time. For instance, jf we observed the Sun's meridian passage at GMT 14 o'clock, we can judge from the Sun's speed that our longitude is two hours (or 30' of Arc) west of the Greenwich line. This is the basic principle of finding longitude by Sun's Meridian Passage, however, an adjustment, with Equation of Time, must be introduced to obtain our exact longitude because the earth's rotation is not truly at a constant speed. Since for convenience we use a fictitious constant Mean Sun as the basis for measurement of time the True Sun is not necessarily at the highest altitude at noon by the Mean Sun. Equa tion of time is the difference in time between the True Sun and the Mean Sun. It is computed by NC-n ~ mode or found in the Nautical Almanac. Latitude: After measuring the highest true altitude of the Sun by sextant our latitude can be determined by the following rules. (1) If DR latitude and declination have contrary names. Lat. = (90 - Alt.) - dec. (2) If DR latitude and declination have the same name (North or South) a) When Lat. > dec. Lat. = dec. + (90' - Alt.) b) When Lat. < dec. Lat. = dec. - (90' - Alt.) Problem 1. The Sun's meridian passage (the highest altitude) was observed as 34 19'.7 at GMT 21 h42 m 38s Declination of the Sun is S22 58'.4 and we are in north latitude. Equation of time is 3 m 42 s. Step by step Computation Longitude: Latitude: Noon Latitude and Longitude Computation by NC-77 If it is difficult to remember the rules, the same computation can be automatically made by NC n ~ (Meridian Passage) mode as follows. Problem 1 21 h42 m 38 s j 144'44:0 In this case Lat '19' N GMT of Meridian Passage 21h42m38s Noon Altitude.Bearing South '.7 Declination of the Sun S22 58'.4 Equation of Time for Jan. 1, 1978 GMT21 h42m38s -3m42s 1 GMT of Meridian Passage Greenwich Noon Difference in time Equation of time for Jan. 1, 1978 at GMT 21 h42m38s computed by NC n ~ mode '1 Total difference in time Time to Arc conversion (use NC n) Longitude of our ship : :0W (90'-Alt.) - dec. Noon Altitude Declination of the Sun Latitude of our ship Key Display 0 ) h O h Ro O @ 2 Ro d O @ d 1:.0 O J:..:J L II -144,440 Repeat L and II Answer: Lat '.9N Long '.OW '1 Equation of Time is (True Sun - Mean Sun). Eqn. of T. computed by NC-n is accompanied by (-) minus Sign when Mean Sun is faster than True Sun. In this case make input with the (-) minus sign here. *2 Here, indicate if the Sun was due North or South at noon

20 Noon longitude by Nc-n Longitude alone can be obtained quickly by NC-n in the course of computing Equation of Time by ~ mode. In the above example before the Equation of Time (-3m42s). NC-n ~ mode computes the GHA of Sun at Jan. 1, 1978, GMT21h 42m38s as 144'44'.1 W (H-144,441), which is the longitude of the ship. If GHA of Sun exceeds 180', the ship is in east iongitude. For instance, if GHA of Sun is 200', the ship's position is 160' E (360' - 200' = 160'). One tenths of a mininute (0'.1) difference between the longitude computed by NC-n ~ mode and I mode (144'44'.OW vs. 144'44'.1W) in the example is accounted for by rounding to one decimal place in ~ computation. Note: Time of meridian passage can best be determined by plotting on cross~section paper a series of observed altitudes versus times (GMT) of observation, commencing several minutes before estimated local apparent noon (based on the DR longitude) and continuing until several minutes after meridian passage. From a curve faired through the plotted points, the time of maximum altitude can be established. DEC Sun and Eqn. of Time are derived by NC 77 ~ mode or taken from the Nautical Almanac. 2. APPLICATION OF MARINE SEXTANT IN MEASURING DISTANCE Problem 2 Key Display Answer Sextant Altitude 0 35'.2 CO ) R. O. (corrected for index errorl R, Height of Eye 15 " O. (49.2ft. ) 15 he 15. Height of the mountain h> O. meters (3281ft.l 1000 he d n.m. Select meters or feet by the selector switch before entering the data. The answer is always given in nautical miles. Note that a: (dip corrected angle) is automatically computed, if we enter sextant altitude and height of eye. Needless to say, any index error, (the error of sextant itself) must be corrected before entering RI. Equation: o where o H h a j tana H-h ( ) 2 +-=-c:':::::c:c- 0, tan a distance to object in nautical miles height of object beyond horizon in feet height of the observer's eye in feet above see level dip corrected sextant vertical angle (Dip is - 0'.98V h in feet ) The marine sextant may be used to measure the vertical angle subtended by the height of an object. Distance to the object is then computed by the equation shown in Fig. 19 on page 37 which is programmed in the ) mode. Problem 2. The altitude of a mountain top was measured by sextant. Compute the distance to it with the following data. \ 36 I Fig. 19 Distance to Object 37

21 PART TWO: BASIC NAVIGATION COMPUTATIONS FOR OEAO RECKONING ANO PILOTING BY Ne-77 CHAPTER I Mercator Sailing and Great Ciicle Sailing Note on Accuracy: The principle of (Q J J'computation is Mercator Sailing. The oblate spheroid characteristics of earth (flattened at the poles and bulged at the equator) is taken into consideration in the pro gramming. The most up-to-date WGS-72, World Geodetic System 1972 spheroid (Eccentricity = is being used to guarantee the utmost accuracy. When the course is exactly or the program automatically switches to Parallel Sailing. In this case the earth is considered as a sphere. 1. Dead Reckoning by Mercator Sailing 3. Great Circle Sailing Problem 1 Dead Reckoning mode computes the latitude and longi,ude of the point of arrival. Departure Point Lat ',6N Departure Point Long. 11So36'.2W Course ' Distance miles 2. Course and Distance by Mercator Sailing Problem 2 Course and Distance mode computes the course and distance from the depar:ture point to the arrival point. Departure Point Lat '.4N Departure Point LO~g" 12So08'.2W Arrival Point Lat :28 Arrival Point Long '.OW lw I l1b.3621ej I I I I I Display I I. O. L :: O , O. c d O. d '_ Aepeat Land.'f Key CD ] lW I 'I I&l I (g) I I I Display o. L I: 0, L O. t II O ,30 c 203,405 d Repeat c and d Answer D. R. Lat '.2N D.R. Long ',6W Answer Course made good 203'"'40'.5 Distance n.m. Great Circle Sailing mode computes the great circle distance between two points and also the initial course from the departure point. The program continues to compute the latitude and longitude of the vertex, and the latitude at any selected longitude on the great circle track. Problem 3 Key Display Answer Departure Point L, O. Great circle distance 37 50'.aN 37.50slW n.m. Oeparture point Long. I If O. Initial great circle course '.5W [g.l '.9 " " (San Francisco) ~ L o. Vertex Lat '.ON Arrival point Lat L Vertex Long. 16S03S'.8W 34 52'.ON I O. Latitude at " Arrival Point Long ) SoW 45 48'.7N '.oE I d W 46 46'.7N (Yokohama) I c I L,... 48,190 I : I '" o. " 14S@ /I' -145 I L' [@ 11' O. 150 (gj ' " I L' ,.. I " o. Continue Note: In computing the great circle distance the earth is considered as a sphere. The vertex is computed between the departure and the arrival point. If there is no vertex to be found between them the next vertex on the same great circle track beyond the arrival point is computed

22 Mercator Sailing and Great Circle Sailing: The course obtained by Mercator Sailing is a rhumb Hne, appearing as a straight line on the Mercator chart. It makes the same angle with all meridians it crosses, and maintains constant true direction. The Great Circle track is the shortest distance between any two points on the earth. On the Mercator chart a great circle appears as a sine curve extending equal distances each side of the equator. The comparison of rhumb line and great circle track is shown in the illustration. 0' Vertex: '.0' 1l0' '60',,' I~O' 110' 100' ISO' '00' llo',lo' I I),,, ", Great circle track \ / ~"- L ,8 ~ milesi-t---t--.. "." :: 1/ YOKOHAMA 7hum~ Lin,..I. SAN FryANC'I SCO, miles ~I.. I I I I I I \ MERCATOR CHART Every great circle lies half in the northern hemisphere and half in the southern hemisphere. Any two points apart on a great circle h~ve the same latitude numerically, but contrary names, and are 180 apart in longitude. The point of greatest latitude is called the vertex., " Composite Sailing: When the great circle would carry a vessel to a higher latitude than desired, a modification of great circle sailing called c~mposite sailing, may be used to good advantage. The composite track consists of a great circle from the point of departure and tangent to the limiting parallel, a course Ilne along the parallel, and a great circle tangent to the limiting parallel and through the destination. If such a course is desired, it can be computed by NC-n With the equations and key sequence shown inthe example below. Problem: Between San Francisco, 37 50',8N, ',5W and Yokohama 34 52'.ON, '.OE, find the composite track with the maximum limiting latitude of 45 N. Equations: tan L DLoV1 = COS-I (t L 1 an max Key sequence: DLovl; Answer: DLov, ; 1 I tan L, DLoV2 = costan L max OD GJ45 0m~ OD GBm~ Vl: The longitude at which the limiting parallel is reached is 39 00',9 west of the departure point, which is 'AW, V2: The longitude at which the limiting parallel should be ieft is 45 50'.0 east of the arrival point, which is ',OW, Point to point planning: Since a great circle is continuously changing direction as one proceeds along it, no attempt is customarily made to follow it exactly. Rather, a number of points are selected along the great circle, and rhumb lines are followed from point to point, taking advantage of the fact that for short distances a great circle and a rhumb line almost coincide. These points are selected every 50 of longitude for convenience (the number of points to use is a matter of personal preference), and the corresponding latitudes are computed by NC-n as in problem 3, Composite Sailing 40 41