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SYSTEMATIC NAVIGATION

1. 14 u ee 14 e 14 8161 181 u E eee ee 15 zm Nn Me 28 S MEMOD AN 5 en saq ee eee eye ere 28 5 2 METHOD B POLYNOMIAL COEFFICIENTS cte 29 CSTAR RET O 30 06 1 METHOD A ALMANAQC er ene 30 6 2 METHOD B POLYNOMIAL COEFFICIENTS 30 Da mM LU UM RPM IE LEM IMEEM LEE E UD LE 31 J d NL No D x sus 33 EN Ei 33 J SIT AP 34 7 3 360 SUN PLANETS MOON AND STAR CHART cccsssccsssccsscccsscccsscccsccccsccessceccscesscscssccessceecscecscsesscecsscessssessccessscessceescess 36 By IN PAL 22 i oa HO 37 Bl u uuu ul uyu SZ A mc MM 37 8 2 METHOD INPUT POLYNO
2. F Sight 1 Moon 260 13 21 2 17 Away Z Sight 2 Sirius 143 15 08 2 42 Towards lt gt Sight 3 Mars 91 54 05 3 73 Towards O Transferred DR Positions 32 1 N 14 38 W x Calculated Course See bibliography for Basic Astro Navigation by Conrad Dixon Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 10 3 3 Overview of Systematic Navigation This is a map of the application It identifies the main inputs choices and flow of information to demonstrate the flexibility between automatic calculation user choice and manual input No 1 10 11 12 Dialog Box Copyright Information Options sight No and Method Stars Subroutine 1 Altitude Bearing for Identification 2 Star Number to calculate bearing and star charts 3 Input Star Number directhy Calc Calculated SHA Sidereal Hour Angle Comment Language A English B German Confirms application directory Sumnmarises information required HALT here for manual input Keep Dead Reckoning DR Position Calculate Greenwich Hour Angle SHA and Declination DEC automatically if no user can choose method Latitude and longitude position fone time and date Course and speed if applicable Temp C and pressure Mb used in sight reduction Sight No 1 3 maximum Z
3. Sflnav50 doc 39 07 37 60 29 47 20 02 21 55 69 55 55 53 232 03 46 54 4757 4017 39 40 32 00 26 0 24 B 20 31 155 01 1023 44 148 458 206 21 117 73 2 55 21 20 193 77 132 55 317 29 250 28 103 96 4097 341 07 0 89 284 13 199 95 220 45 316 32 Sun Bars B Jupiter B Saturn Moon 53 Deneb 23 Vega 51 Altair 54 Enif 47 Eltanin 45 57 Markab 1 Alpheratz e 3 Schedar 4D Kochab 58 Polaris 41 Alphecca 50 Hunki 44 Sabik 34 Alkaid Manual v5 0 31 March 2011 36 8 Moon 8 1 Method A Aries Select Method A and no inputs are required The model uses a complex set of algorithms to derive the GHA DEC and HP which are outside the scope of this manual See the second page of the Aries schedule for the workings Example Moon s GHA DEC and HP on 27 September 1996 at GMT 05 47 22 This is an extract from the Inputs sheet Sight 1 Sight 2 Which Sight 3 Moon 3 Moon Method A Calculated B Polynomial Actual Sight Time 5 47 22 05 47 GMT 5 417 22 05 47 GMT Time Diff Miles 0 00 hrs 0 00 mis 0 00 hrs 0 00 mis Revised DR Position vos oo W ors ow DR Star Altitude k 0 00 0 26 00 0 DR Star Bearing 0 00 0 52 00
4. Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 55 Annual and Basic Decimal Data Sight 4 Sight 2 Sight 3 Year P Sun Ephemeris Q Sun Ephemeris R Aries Correction gt Radians Days From 01 01 0 01 74532983 oF 2057 Days from 01 01 1996 Days from 01 2 1996 Original Latitude Original Longitude Decimal Latitude Decimal Longitude Original Latitude Decimal Miles 40 50 dys 9 50 dys 32 7500 N 15 5000 W 0 0000 N 0 000 mis 40 29 dys 9 29 dys 32 0402 N 14 6561 W 32 0402 N 14 6561 W 0 0000 N 40 29 dys 9 29 dys 32 0520 N 14 6701 W 32 0520 N 14 6701 W 0 0000 N 0 0000 40 41 dys 9 41 dys 32 4524 N 15 1462 W 32 4524 N 15 1462 W 0 0000 N 0 0000 E Original Longitude Decimal Miles 0 000 mis 0 0000 E 0 0000 E This displays the Zone or Local Mean Time to GMT conversion table and the calculation of sight times Lookup Table for Zone Time GMT 0 7 50 22 50 37 50 82 50 67 50 62 50 97 50 1 2 3 2 6 7 Transferred DR Positions DR Position Time Date 15 500 11 00 00 1 00 0 500 12 00 00 9 2 96 35104 458 0 042 0 042 9 2 96 35104 500 9 2 96 35104 500 35104 281 35104 291 This is the Positions schedule on 9 February 1996 at GMT 12 0 0 from the DR position 32 N 45 15 W 30 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0
5. gL SAS 81 01 seag EL asnabjayag 91 JEpayss FL ejede z qeua 25 JZ LZ sue og 88 These are the two types of star charts available These use the example above for 9 February 1996 at GMT 12 00 00 at position 32 N 45 15 W 30 This second plot is sorted as directed in bearing order to show visible stars Star SHA Expected Altitude Azimuth Bearing Page 35 Manual v5 0 31 March 2011 Sflnav50 doc Systematic Navigation www sysmaps com 7 3 360 Sun Planets Moon and Star Chart There is an option to plot the visible bodies based on altitude on the DegreesCharts sheet You can plot up to twenty stars and if a star or planet is not visible N A will be displayed Altitude Star Name Mag Bearing Ho 1 z 3 4 5 6 1 53 2 49 3 51 4 54 5 47 6 46 T 57 1 9 3 10 40 11 58 12 41 13 50 14 44 15 34 16 17 18 19 20 Positions Min 20 Max 80 DR 11 0 ZT 32 Sun Venus Mars Jupiter Saturn Moon N A 53 Deneb 49 Vega 51 Altair 54 Enif 4 Eltanin 45 Rasalhague 57 Markab 1 Alpheratz 3 Schedar 40 Kochab 56 Polaris 41 Alphecca 50 Nunki 44 Sabik 34 Alkaid 45 N 15 30 W Systematic Navigation www sysmaps com 1 3 0 1 0 9 2 5 2 4 2 1 2 6 2 2 2 5 22 2 1 2 3 2 1 2 6 1 9
6. INDEX ARM across the 0 to 120 graduated scale The Greenwich Hour Angle and Declination of the body need to be computed These are equivalent to the latitude and longitude of the body in the heavens Either tables or the Almanac can be used or this application provides an automatic method needing no input from you The normal method of plotting position lines is to use the intercept and azimuth The intercept is the difference between the observed altitude and the calculated altitude represented as a distance in nautical miles If the observed altitude is greater than the calculated altitude the position line lies between the observer and the body The position line is plotted at right angles to the azimuth of the body at the distance of the intercept from the estimated position towards the body When the observed altitude is less than the calculated altitude the opposite is true The body lies away from the observer at an angle of 180 plus the azimuth Further sights of the same body can be added to provide several position lines or alternatively different bodies along a course line More observations increase the probability of position through the intersection of several lines The observer can than compute a new assumed position based on the sights as a latitude longitude position and a distance and bearing from the assumed position Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2
7. 47 Eltanin 45 Rasalhague 40 Vega 40 Kochab 27 Dubhe 39 Zubenelgenubi 23 Denebola 33 Spica 44 Sabik 50 Polaris 42 Antares 53 Deneb 22 Gienah 51 Altair N A 151111 petrirs22 x x 111107 EU IdGI I I L g 1 rot 1 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 68 19 5 Moon Star 18 Sirius and Mars on 11 September 2014 On September 11 2014 at GMT 06 30 0 the DR position is assumed to be 32 N 1 15 W 38 Three sights have been taken along a course of 315 T at a speed of 12 knots The temperature is 9 8 C and the atmospheric pressure 1010 Mb The height of the eye above the horizon is 6 0 metres Sextant index error is assumed to 077 Moon Star Mars Time of Sight GMT 5 54 52 6 05 21 6 15 235 Difference to DR Time 0 35 h 0 24 h 0 14 h Observed Angle Hs 30 26 6 32 42 9 47 10 4 Adjusted Altitude Ho 31 21 82 32 37 04 478 22 Declination 8 46 45 N 16 43 82 S 21 36 81 N GHA 12 52 1 342 47 9 327 28 1 LHA 58 19 94 328 14 01 312 52 54 Azimuth Bearing 260 13 21 143 15 08 91 54 05 Intercept Distance 2 17 Miles 2 42 Miles 3 73 Miles Direction Away Towards Towards The calculated position after several iterations is 32 N 0 02 14 W 34 46 a distance 3 154 miles and a bea
8. 71 TL DARI IP 2 22220021 20100006 M MAE IE E EE 71 2220 LLIKA Y 73 20 3 STARTING THE APPLICATION 73 a IL ee ee MM ee ee ee eee eee 74 205 VERSION AND FILE INEORMATION 75 21 LICENCE TERMS AND CONDITIONS sinesinde hanina anns EKA T 76 22 BIBLIOGRAPHY Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 3 1 Introduction Systematic Navigation is a Windows and Excel based solution for astro and offshore navigation The object of this manual is to help you get the most out of the application This manual provides background on the use of Systematic Navigation and the methods used in its formulation It also provides in a convenient form all the data you need for astronomical navigation and sight planning Systematic Navigation solves all the problems of calculating hour angles declination and sight reduction and then plots sight lines and statistical fixes for up to three sights It is totally automated and removes the need for a pocket calculator almanac or sight tables and provides e Position fixes from two or three sextant sights without an Almanac e Automatic calculation of hour angles declination and sight reduction e Chart plots and full results print outs of all angles and position lines e Stars Charts for all 59 stars giving SHA elevation and bearing e Star Identification from angle and bearing e Sch
9. GHA aries is added to the SHA 291 0733 to produce the GHA for the star as 325 0732 The model uses the Declination you input since this variable changes very slowly The almanacs contain a list of the 57 navigational stars plus the polar stars Polaris 58 and Octantis 59 There is usually a list showing the star together with the integer SHA and GHA and then the minutes to be applied for each month 6 2 Method B Polynomial Coefficients The model contains the data for 1991 2015 on five year tables Using the example above the system looks up the coefficients and calculates the GHA and DEC Star GHA and DEC 40 31 42 94 Check Sum L Calculated GHA and DEC 30 0283000 0 9999605 0 0028000 0 0052000 0 0000700 31 0258605 64 2503 325 0712 16 4990000 0 0000058 0 0009000 0 0005000 0 0000000 16 4986058 34 226 34 226 16 4991 The algorithms are similar to the Sun Calculate L 0 9856474 D d GMT 24 D Number of days from 0 0 0 on 1 1 91 or 1 1 96 4 15 the day of the month For information be derived from 98 9513 L 15 GMT in decimal hours The expressions for the GHA and DEC are GHA aj L a sin L cos 15 GMT in decimal hours DEC ap a L a sin L a cos No semi diameter is required for stars Example from Macmillan amp Silk Cut Nautical Almanac Astro Supplement 1996
10. Sflnav50 doc Manual v5 0 31 March 2011 Page 64 19 3 Sun Moon and Star on 19 June 1991 This example appears on page xxii of Compact Data 1991 On 19 6 91 at GMT 21 00 the DR position of a ship 15 32 45 N 15 30 W and it has followed a course of 325 T at a constant speed of 12 knots for several hours Altitude 6 0 metres 6 0 metres 6 0 metres 21 25 398 46 32 700 29 27 132 18 15 24 GMT 20 30 45 GMT 20 42 23 GMT 1 Sun 2 Moon 3 Vega 49 Using a further sight of Dubhe 27 the fix gained by Compact Data is 32 39 1 N 15 34 2 W and this compares well with the answer below given that the Moon is calculated using Method A with Aries coefficients DR Position Calculated Position Position Error DR Latitude 32 45 00 32 35 92 Confidence DR Longitude 15 30 007 15 W 29 33 Ellipse 95 00 DR Zone Date 19 Jun 91 Wednesday Zone GMT 20 00 00 21 00 GMT Distance Bearing Latitude 3 08 mls Course Speed 3425 00 T 12 00 kn 9 10 mls 176 27 T Longitude 4 95 mls Temperature amp Pressure 5 80 C 1010 00 mb Bearing 331 42 T Sight 4 Sight 2 Sight 3 Which Sight 1 Sum 3 Moon 2 Star Calc Almanac Polynomial B Polynomial A Calculated B Polynomial Star Humber 0 0 49 Vega Actual Sight Time 17 15 24 18 15 GMT 19 30 45 20 30 GMT 19 42 23 20 42 GMT Time Diff Miles 2 44 hrs 32 92 mls 0 29 hrs 5 85 mls 0 17 hrs 3 52 mls Revised DR Position 32 9 N 15 6 9 W 32 31 1 N 19 2
11. dis the day in the month and GMT the universal time in hours Using the example in the previous section 22 21 7236 24 32 2 0 715786 Using x GHA GMT in hours and DEC in degrees are derived from this expression ao ai x x a4 x This can be rewritten for use with pocket calculators x aj x aj x t ao You can convert the GHA in hours to degrees by adding GMT and multiplying the result by 15 to convert from hours to degrees The semi diameter is calculated using the expression S ao a x Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 29 6 Stars 6 1 Method A Almanac The system displays a box requesting the Sidereal Hour Angle and Declination for the day of the sight Daily hourly corrections are dimmed since these are only needed for the Planets The user therefore need only input two numbers for this method It can be used to check any sight using the Compact Data where the result appears to be inaccurate Example The GHA and DEC of Aldebaran 10 on 3 February 1996 at GMT 17 23 17 To derive the star s GHA the system calculates the GHA of Aries as GHA caries 360 985647 B B is the number of decimal days from day 0 of the year to the time of sight R is the Aries coefficient constant for the year and gained from a look up table on the Aries schedule In this example Aries 18 33 9998
12. ies Used 700 of 40000 Mouse Position ay 25430 m gt Standard mmm r1 He T 50 7806H Crown and rece rights 2010 0 ace End User Licence Agreement SW NN 22 11 S 560 M 92010 NAVTEQ Europa Tech Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 6 2 Installation 2 1 Description The system requires an IBM compatible computer with minimum 5 0 Mb spare hard disk capacity and sufficient RAM The software required is Windows and Microsoft Excel 2003 or later The above will be on one disk in a compressed form or downloaded from the Internet Install the application on a hard disk as shown below The text files below can be opened with any text editor and are un formatted A full pack of files for Systematic Navigation could include the following in addition to the Excel file Description File Name Approximate Size Excel Application File SFLNavXX xls 1 778 000 Icon File SFLNav20 ico 766 Basic Execution File MSBasic com 31 744 Astro Navigation in Basic AstNav40 bas 10 496 Registration and Read Me Icon Help ico 766 Read Me Text File ReadMe txt 6 978 2 2 Installation 1 Start Windows 2 Insert the Systematic Navigation disk into the CD or an alternative drive 3 In the Windows File Manager choose Run from the File Menu 4 Windows d
13. 2 5616 1 0056 0 0052 1 1953 3 8168 0 0434 5 7793 2 1718 0 0121 209 9832 0 635 0 0083 215 4544 1 2178 0 9549 Sum 450 6024 4 7040 0 9349 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 38 2 Right Ascension and Declination 0 0 0 0017 0 004111239 D 02 78758272 D 0415501 11 0 067 738077 0 448742487 0 291672971 0 204216212 3 140428067 3 013266627 4 6656260D71 219 58049 320 3230365 3 Remove Multiples and Calculate GHA DEC HP and SD Result Remove Multiples Radians Constant Constant Radians X Y z RA Degrees 1807 RA Remove Multiples 5 483902172 L GHA Aries Remove Multiples GHA Systematic Navigation www sysmaps com 0 0 0 0 0025 0 0097534 D 01740502 D 01220332 0 0661575 0 220464 D 1837223 0932696 2 50018251 1 236543 65 4095251 1348221 4 8337848 0 0025 0 00541288 0 00690593 0 00180132 0 0496343 0 0595451 D 025735T 0 878282485 HP 366 0509052 0 17896507 0 99636379 6 050905219 0 178965507 0 99636379 0 105608219 0 00312353 0 01738983 23 44 0 409105177 0 884423782 0 095470143 0 044797247 0 095712149 5 483802172 5 403802172 2b 34021 453 1411767 93 14117669 Bf 55727451 Sflnav50 doc Manual v5 0 31 March 2011 Page 39 9 Planets 9 1 Method A Input GHA and DEC The GHA and DEC box requests the Greenwich Hour Angle and Dec
14. 360 B Integer B U X 180 Q If necessary remove multiples of 360 to place the result in the range 0 to 360 3 Semi diameter The model uses a standard semi diameter for the Sun of 16 0 266667 Example from page 278 of The Nautical Almanac 1996 GHA 149 7604 DEC 11 3892 S Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 28 5 2 Method B Polynomial Coefficients The procedure is automatic as above Note that the information box on the calculation is not displayed if the user has selected the calculation to automatic B For years other than 1991 2015 the model will request the polynomial coefficients from for the relevant month from Compact Data This is the same example as above and the answers are very similar The coefficients are selected from the tables for the month and year The semi diameter is also calculated at 16 11 Sun GHA and DEC 12 1661800 2 8211000 a 0 1757000 12 4213000 0 0443100 0 2145000 0 0241800 0 5750000 0 0000700 0 0070000 Check Sum 12 2734600 14 4459000 Days X 0 7158 Calculated 12 2604 11 3895 GHA and DEC 509 7600 11 3895 GHA Removing multiples of 360 149 7600 0 26670 a 0 00240 Sum 0 26910 Semi diameter in degrees 0 2684 Semi diameter in Minutes 16 11 The calculations in the model using the coefficients are Time variable x d GMT 24 32
15. F p p G A C B An improved estimate of the fix is given by Longitude L A E B D G cos Latitude Bj C E G Departure longitude dL Ly Departure latitude dB By The model substitutes the DR position with the calculated fix in order to converge on a solution i e Ly Lex The model computes the distance between the assumed position and the improved estimated position in nautical miles from d 60 SORT Ly Lw Bi Baw Example from page 18 and 19 of Compact Data 1996 derives the same answers Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 47 The model iterates the result until it converges on an improved estimate The number of recalculations is set to 5 and you can always recalculate the model by pressing F9 or the Calculate button The system also estimates the error in position 15 the number of observations The standard deviation of the estimated position in nautical miles is given by Standard deviation o 60 SQRT S n 2 S F D dB E dL cos Bp The standard deviations for longitude and latitude og are given by oj o SQRT A G SORT C G The model assumes a probability of 0 95 and computes the size of a confidence ellipse which means that there is a 95 probability of the revised estimated position lying within the ellipse The estimated posit
16. SYSTEMATIC NAVIGATION EXCEL APPLICATION FOR ASTRO NAVIGATION USER MANUAL V5 0 31 2011 Systematic Navigation www sysmaps com Sflnav50 doc Systematic Finance plc Orchard House Green Lane Guildford Surrey GU1 212 Telephone 44 0 1483 532929 Telefax 44 0 1483 538358 E mail info system co uk Internet www sysmaps com 31 March 2011 SFLNav50 doc Version 31 December 2010 Manual v5 0 31 March 2011 Page 1 Contents 1 INERODUC CTI N 4 1 1 SYSTEMATIC MAPS WWW SYSMAPS COM 5 PE MONS A 7 2L JIJBSCRIPTION eee E MEM MM 7 222 ir 201120 EE EE 7 2 3 PULL DOWN MENUS u 2 L uz Sa lQ wide ds ca ised wand 8 10 O E uu 9 uuu E i ME MEE MEE 9 EAE TEMATIC NAVIGATION uuu 10 3 3 OVERVIEW OF SYSTEMATIC NAVIGATION u uu ed edis 11 13 4 USING SYSTEMATIC NAVIGATION
17. 0 Star Number 56 Polaris Input Star No 10 Aldebaran 0 0 DR Bearing 49 42 59 0 24 14 36 57r 029 109 44 49 0 oo Observed Angle 50 27 82 af 2 10 0 0 00 Index Error Minutes 0 00 0 00 0 00 On Off the Arc F Off Arc F Off Arc F Off Arc Height of User s Eye 2 00 mtr 0 00 mtr 6 00 mtr Enter 1 L Lower L Lower L Lower Calc HP SD 0 00 0 Calc HP SD 0 00 0 Planet Corr 0 00 0 Corrected Altitude 502451 3r 1 38 vo Calc Declination D N 0 00 Calc DEC O N 0 00 Input DEC O N 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 Star Declination 0447 North Star DEC 16 30 08 North N K DEC vo North Calc GHA 0 00 Calc GHA 0 00 Input GHA 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 Star LHA 338 37 21 JF 52 21 Star LHA 307 455 308 19 55 N K LHA ro Uu The model calculates Aries and then GHA and p polar distance using polynomial coefficients L 0 9856474 D d GMT 24 GHA ap L a sin L cos 15 GMT in decimal hours p ao a L a sin L as cos L It calculates the LHA GHA longitude in hours Ho Observed Altitude Latitude Ho p cos LHA 0 0087 p sin LHA p sin LHA tan Ho Azimuth of Polaris 58 0 p sin LHA cos Ho Azimuth of Octantis 59 180 p sin LHA cos Ho Example from Macmillan amp Silk Cut Nautical Almanac Astro
18. 2 Sight 3 0 6875 0 3942 38 2453 28 48837 22 5850 2 2589 2 2058 129 25 4 126 23 02 Corrected Azimuth Z 230 5766 126 3636 Angle in Degrees 230 34 6 126 23 02 Latitude Difference 0 0774 0 0388 i 465 mls 2 33 mls Towards w Towards The options are then OK to continue Re Do to re enter the Star Options or print preview Stars charts An alternative is to click the Stars Chart which print previews a plot of bearings and altitudes at the DR Time This is an overlay graph with the bearing on the left hand Y scale and the altitude on the right hand scale This can be reviewed in more detail using the magnification within Print Preview or printed for future reference This option is repeated in the End Options if missed at this stage You then have a further option to sort the stars by SHA bearing or altitude e g to check which stars should be visible Select a sort order and the system sorts the data and print previews the plot e Input Star Number You input the star number and the system does not recalculate Example from pages 18 and 19 of Compact Data 1996 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 34 3198490 B8 SHE Od 89 28 jneujeuio 4 95 EN Iv 88 1 9 q u d yaosrra ZG 18 OS siensny sne gp UME zy gp AGES FF eun salejug esoaydiy p q Uu903
19. 6 00 N F a t oat a 35 00 N 6 00 N 34 50 M 4 00 N Course 3 00872 LL U U9SQW _ __ 34 00 N 2 00 N 4 Lh d 0 00 N 33 50 N T Bearing 0 147 _ Distance 05mm emori 42 2 00 5 33 00 N Start 32 00M 4005 32 50 6 00 5 32 00 N 8 00 5 L a s ee m 4 ees eed eee pee 1 1 4 1 1 1 1 T 1 1 1 1 1 31 50 N 15 10 W 15 00 14 90 14 80 14 70 V 14 50 14 50 W 14 40 VV 10 00 5 10 00 W 8 00 600W 400W 200 000E 200E 400 6 00 800 10 00 Longitude Longitude Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 54 16 Background Data 16 1 Description There are three schedules which contain data used by other schedules These are e Aries Background data for corrections Stars look up and Moon calculations e Positions Schedule of SHA Altitude and Bearing at the DR position time and date Data Lookup table of polynomial data for the DR date This is an extract from the Aries schedule showing the annual coefficients Lookup Table for Annual Update Coefficients 75 8011 76 76 41 fb 7672 fh 502 75 7333 Th F163 This extract shows the derivation of decimal time for each observation and the revised sight position
20. 60 sin T cos Latitude Bix t V 60 cos T Leix and Bex are the estimated longitude and latitude at the time of fix and t is the time interval hours Example DR 32 N 45 32 757 15 W 30 15 50 W at GMT 12 0 0 A vessel has been on a course of 315 T at 12 knots since GMT 6 58 52 To calculate the start position Longitude 15 50 5 0188 12 60 sin 315 cos 32 75 Longitude 15 50 5 0188 0 20 0 70711 0 841039 14 6561 W Latitude 32 75 5 0188 12 60 cos 315 Longitude 32 75 5 0188 0 20 0 707107 32 0402 N The position lines for one or more observations can be plotted using the azimuth Z and the intercept p p Ho He If p is positive the position line is drawn along the azimuth If p is negative the position line is away from the assumed position by adding 180 to the azimuth Provided that there are no observation errors the observer should be close to or along the position line Two or more position lines are required to determine a fix The model uses the Method of Least Squares to determine fix from up to three observations and Z are the intercept and azimuth for the first observation etc The model calculates these values cos 21 cos Z cos 41 cos Z4 cos Z gt cos Z sir Z sin Z D pi cos Z p cos 22 E pi sin Z4 p2 sin Z
21. B Pohynomial 26 Regulus 19 38 23 20 39 GMT 0 20 hrs 5 87 mis 31 31 9 14 55 6 W 27 1 26 267 45 31 26 0 00 0 00 1 94 0 00 0 00 2r 0 66 11 59 62 North aU 27 1 30 5 267 45 34 0 60 mls 3T 31 5 N 411 Q L 1 1 1 1 1 L 1 1 F if 1 Sight 2 2 Star Pohynomial 42 Antares 19 45 47 0 14 hrs 31 33 27 28 5 9 Jb 6 6 0 00 0 00 2 02 0 00 0 00 26 4 56 20 25 22 445 47 8 151 54 97 1 32 mls 31 34 4 N 37 13 Confidence 1 22 Ellipse 95 00 Bearing Latitude 4 55 mls 182 71 T Longitude 3 25 mls Bearing 332 5 amp 8 T Sight 3 2 Star B Pohynomial 40 Kochab 20 45 GMT 20 10 34 21 10 GMT 4 74 mls 0 10 hrs 3 52 mls 14 W 3T 407 N 15 3 6 W 151 54 97 AT 27 88 358 55 51 AT 27 61 0 00 0 00 0 91 0 007 0 00 AT 26 7 South T4 10 977 Horth 331 49 67 177 36 14 2 3254 331 54 87 356 58 51 178 58 51 1 19 mis Away 14 36 WwW 31 38 97N 15 3 6 W 37 13 15 1 22 W 22 9 MLS 182 71 T 15 06 W 1502 W 1500W 14 96 W Longitude O Sight 1 Regulus 267 45 31 0 6 Away Sight 3 Kochab 358 58 51 1 19 Away DR 32 0 N 15 Q W x Calculated Course Systematic Navigation www sysmaps com 14 86 W 1494W 1492W 14 590 W Sight 2 Antares 151 54 97 1 32 Away D Transferred DR Positions
22. Company name and address Enter the name or company name and password sent to you after registration If you enter the name and code correctly and press F9 the licence type and expiry date above will be updated to Registered and a later expiry date Name Password Licence Data valid until 31 Dec 2015 IMPORTANT DO NOT DELETE OR MOVE THIS FILE THIS INFORMATION IS USED BY ALL FILES IH SYSTEMATIC NAVIGATION If you have any problems or would like more information about this product or any of our other activities please contact Systematic Finance plc as above Similarly if you have any suggestions regarding this product please let us know We will try to incorporate your improvements into the next version Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 75 21 Licence Terms and Conditions This notice is intended to be nonsense agreement between you licencee and Systematic Navigation division of Systematic Finance plc Systematic The software and associated documentation are subject to copyright law They are protected by the laws of England If you use this software you are deemed to have accepted the terms and conditions under which this software was supplied No part of the accompanying manual may be reproduced transmitted transcribed stored in a retrieval system or translated without the prior permission of the copyright holde
23. Diphda 22 B Cet 68 37450 0 9999657 0 00550 0 00030 5 Achernar 0 6 Eridani Eri 14 81380 0359997658 0 00940 0 00300 22 Arietis Ari 67 49320 0529929600 0 00530 0 00240 7 Acamar 3 1 H Eridani Eri 5467990 0235999746 0 00570 0 00440 8 Menkar 28 Ceti Cet 53 70730 0352999635 0 00430 0 00340 9 Mirfak 1 9 A Persei Per 4623940 0 9999490 0 00610 0 00590 10 Aldebaran 1 1 Tauri Tau 30 30610 0 9999599 000280 0 00510 11 Rigel 0 3 B Orionis Ori 20 653340 0 9999665 0 00190 0 00540 12 Capella 0 2 Aurigae Aur 20 15180 0 9999485 0 00270 0 00770 13 Bellatrix 17 C Orionis Ori 17 99730 0 9999627 0 00170 0 00550 14 Elnath 1 8 A Tauri Tau 1r 72780 05999561 0 00190 0 00620 15 Alnilam 1 8 Orionis Ori 15 22030 09999647 0 00140 0 00550 16 Betelgeuse 0 5 Orionis Ori 10 48800 0 9999624 0 00100 0 00560 17 Canopus 0 9 3 22390 09999035 0 00060 0 00940 18 Sirius 1 6 CMa 357 97200 09999691 0 00600 19 Adhara 1 6 E CMa 354 59260 0 9999721 0 00050 0 00650 20 Procyon 0 5 34445140 09999637 0 00130 0 00550 21 Pollux 1 2 B Gem 342 965670 0259299562 0 00170 0 00610 1 7 333 58070 09999830 0 00440 0 01000 23 Suhail 2 2 L 32224530 09999726 0 00430 0 00620 24 Miaplacidus 1 8 B Car 320 66670 0 9999873 0 00930 0 01260 25 Alphard 22 Hydrae Hya 317 37340 09999855 0 00350 0 00420 25 Regulus 1 3 Leonis Leo 307 18560 09999634 0 00420 0 00350 27
24. Page 39 The answers given are DEC N 167 30 and GHA 324 34 8 324 58 There is an addition error in the text since GHA Aries is calculated from the tables as 33 998 and SHA as 291 0733 These add up to 325 0716 3257 4 2980 not 324 580 3247 34 8 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 30 6 3 Polar Stars You can use the model to calculate latitude with the polar stars e g the latitude of the observer when Polaris 58 is observed at 50 27 82 at GMT 17 23 17 on 15 January 1997 at longitude 15 The model provides the answer Latitude 49 7170 49 N 42 57 Azimuth 1 250 PE 17 87 DR Position Calculated Position A English DR Latitude 48 H 43 00 50 N 24 79 Confidence 0 00 DR Longitude 1 E 15 00 4 E 45 35 Ellipse Date 15 Jan 97 Wednesday Distance 46 164 mls Latitude 0 00 mils Zone GMT 17 23 17 17 23 Bearing 25 90 Longitude 0 00 mls Course Speed 0 00 T 0 00 kn Bearing Sight 1 Sight 2 Which Sight Hame 2 Star 2 Star 0 N K Method B Polynomial B Polynomial A Almanac Actual Sight Time 17 23 17 17 23 GMT 17 23 17 17 23 GMT 0 00 00 00 00 GMT Time Diff Miles 0 00 hrs 0 00 mis 0 00 hrs 0 00 mis 0 00 hrs 0 00 mis Revised DR Position Ag 43 N 1 15 49 43 T 15 0 0 DR Star Altitude 7 0 00 0 0 00 0 0 00 0 DR Star Bearing h 0 00 E 0 00 E 0 0 00
25. Sight 2 Sun 124 42 51 0 09 Towards OO Transferred DR Positions x DR 32 45 N 15 30 W x Calculated Course Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 67 This is a listing of the visible planets and stars at the DR poition at 6 30 0 GMT based on a minimum of 20 and a maximum of 80 This sheet can be used to ascertain the potential bodies and show the approximate altitude and bearing Star Name Mag C Altitude Bearing 1 Sun 15 53 05 25 2 Venus 13 88 119 82 3 Mars N 35 107 390 98 4 Jupiter 41 08 182 32 5 Saturn 307 291 11 B Moon 29 098 25647 1 37 37 Arcturus 0 2 71 44 228 34 2 34 34 Alkaid 1 9 67 18 322 3 32 32 Alioth 1 7 56 76 324 1 4 AT 4 Eltanin 2 4 54 80 45 35 5 45 45 Rasalhague 2 1 51 65 113 36 6 49 49 Vega 0 1 48 5 66 63 40 40 Kochab 22 46 54 oor 8 27 27 Dubhe 2 41 54 326 00 9 38 39 Zubenelgenu 2 9 40 92 186 74 10 26 28 Denebola 2 2 40 61 260 89 11 33 33 Spica 1 2 39 19 214 58 12 44 44 Sabik 2 6 33 87 145 09 13 56 58 Polaris 2 1 33 44 0 13 14 42 42 Antares 1 2 26 01 160 37 15 53 53 Deneb 1 3 27 64 51 89 16 29 29 Gienah 2 8 24 38 22671 17 51 51 Altair 0 8 21 85 93 45 18 256 47 19 25647 20 256 4r Sun Venus Bars N A B Jupiter B Saturn Moon 37 Arcturus 34 Alkaid 32 Alioth
26. 0 Star Number h 0 0 53 DR Bearing 12120477 2T2 34 52 212042 272 34 18 Observed Angle 3 29 00 3 20 00 Index Error Minutes 0 00 0 00 On Off the Arc F Off Arc F Off Arc Height of Users Eye 5 00 mtr 6 00 mtr Upper Lower Limb L Lower L Lower Moon HP SD 0 00 59 163 Calc HP S8D 0 00 0 716 3 Corrected Altitude 42524 4 25 33 o w P v O P IT gt OGa Calc Moon DEC O N 0 00 Calc DEC O N 0 00 0 0 00 0 0 00 0 0 00 0 0 00 Moon Declination gt 33449 North Moon DEC 2 34 05 North Calc Moon GHA 0 00 Calc GHA 0 00 0 0 00 0 0 00 0 0 00 0 0 00 Moon LHA Gr 39 04 er 39 584 Moon LHA 8739 44 Gr 39 44 8 2 Method B Input Polynomial Coefficients Chebyshev monthly coefficients are available in the model as in the example above Sight 2 The Moon s right ascension RA and declination DEC are derived from trigonometric expressions involving 4 p and the adopted value of the obliquity 23 44 The time variable x is calculated from x d UT24y32 where d is the day of the month and is the universal time in hours Each of the quantities 7 and HP is derived as follows Calculate 2 2x Set bnt 1 bn 0 Use the recurrence relation b yb 2 1 2 2 1 0 to calculate and by Then the required quantity in degrees is obtained from the expression by b
27. 0 00280 0 00030 26 Regulus 307 18560 0 9999634 0 00420 0 00350 12 01030 0 000014 0 00150 0 00120 27 Dubhe 293 36180 0 9999615 0 01010 0 00450 61 79800 0 000015 0 00080 0 00470 26 Denebola 202 008600 0 9999651 0 00530 0 00120 1462050 0 000015 0 00190 0 00170 29 Gienah 275 32420 0 00550 0 00050 17 49410 0 000015 0 00230 0 00140 40 Acrux 272 63680 0 01150 0 00040 63 05150 0 000015 0 00130 0 00500 31 Gacrux 271 49500 0 00960 0 00010 57 065500 0 000015 0 00140 0 00460 32 Alioth 255 74960 0 00940 0 00080 56 00640 0 000014 0 00150 0 00480 33 Spica 257 98000 0 00520 0 00130 11 11680 0 000013 0 00200 0 00060 34 Alkaid 252 36260 0 00770 0 00270 49 35580 0 000012 0 00260 0 00430 35 Hadar 248 36350 0 00290 0 00450 60 33230 0 000012 0 00050 0 00440 36 Menkent 247 62170 0 9 Fe 0 00610 0 00280 36 32540 0 000012 0 00070 0 00260 3f Arcturus 245 34670 999 0 00510 0 00250 19 22670 0 000013 0 00280 0 00200 36 Rigul Kentaurus 239 41070 0 00960 0 00580 60 79990 0 000010 0 00100 0 00410 38 J7Zubenelgenubi 236 58440 9999611 0 00460 0 00330 16 00700 0 000010 0 00140 0 00100 40 Kochab 236 47990 1 000005 0 01620 0 01150 74 19010 0 000010 0 00340 0 00460 41 Alphecca 22558310 0 9999709 0 00420 0 00450 2674250 0 000007 0 00360 0 00210 42 Antares 211 94500 0 9999571 0 00320 0 00550 2641440 0 000004 0 00010 0 00100 43 Atria 207 22840 02
28. 17 6 69 12 20 16 02 17 85 17 52 025 25 Jan 10 27 06 18 26 9 92 231 4 26 9 47 13 01 14 62 026 28 Jan 10 37 40 28 44 19 71 11 46 3 98 2 50 782 11 10 027 27 Jan 10 47 03 38 18 2922 20 47 12 20 4 66 1 87 7 10 028 20 Jan 10 54 80 46 70 37 89 25 90 20 07 11 57 3 95 2 79 023 29 Jan 10 56 69 52 54 44 79 36 08 27 07 18 13 0 54 1 59 030 30 Jan 10 55 89 54 27 43 62 41 09 32 54 23 55 14 53 5 76 031 31 Jan 10 50 07 50 92 485 38 43 04 35 81 21 45 18 55 948 032 1 Feb 10 40 37 43 76 44 20 41 50 35 45 29 48 21 31 12 51 033 2 Feb 10 29 43 34 50 37 24 37 25 34 52 29 45 22 14 70 034 3 Feb 10 18 13 24 35 26 17 30 93 30 54 27 55 22 65 16 00 035 4 Feb 10 6 92 13 99 19 67 23 51 25 16 24 44 21 44 16 48 036 5 Feb 10 3 93 3 79 10 44 15 63 19 00 20 25 19 28 16 18 037 6 Feb 10 14 29 6 04 1 38 12 48 15 48 16 44 15 28 038 7 Feb 10 24 05 15 39 7 32 0 12 5 90 10 42 13 15 13 89 039 8 10 33 07 24 12 15 54 7 59 0 54 5 29 961 12 13 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 42 This is a chart for a selected day in the year Use the combo box to select a specific day in the year i m gt i E 2 un T oo m uh t a O a a T 4 1 1 1 1 1 1 1
29. 2 17 mls Away 2 42 mls Towards wo mls Towards Calc Position 31 55 4 N 14 29 7W 31 55 14 32 37W 31 58 8 N 147 31 27W 2 This is the complete worked example from pages 60 and 61 of Compact Data 2006 The answer given is 32 7211 N 32 N 43 266 15 4707 W 15 W 28 2420 a 5 089 nm b 3 959 nm azimuth 350 using the same methods for four rather than three Observations Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 69 POSITION AT 5 30 0 ZT 14 SEP 2011 FIX 32 0 02 14 24 46 W 0 MLS 107 36 T 32 03 N 32 02 N 32 01 N 32 00 N 31 99 31 98 N 31 97 N 31 96 N 31 95 N 31 94 N 31 93 N 31 92 N 1466W 1464W 1462W 1460W 1458W 1455W 1454W 1452W 1450W 1448W tea E F O Sight 1 Moon 260 13 21 217 Away lt Sight 2 Sirius 143 15 08 2 42 Mis Towards c Sight 3 Mars 91 54 05 3 73 Towards D Transferred DR Positions x DR 32 1 N 14 38 W x Calculated Course POSITION AT 5 30 0 ZT 14 SEP 2011 FIM 32 0 02 14 24 46 W 0 MLS 107 38 T B OR 32 1 N 14 38W DR 32 1 NAF 38 W 2 00 4 00 6 00 8 00 10 00 10 000 8 000 6 000 4 000 2 000 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 70 20 Information 20 1 Read Me Notes Systematic Navigation Version 5 0 31
30. 300 5 79 8 2 59 Azimuth Bearing 290 14 09 123 42 94 356 45 86 Intercept Distance 3 60 Miles 3 51 Miles 3 26 Miles Direction Towards Towards Away The Model uses the Method of Least Squares to compute a fix at the DR Time of 31 N 55 78 15 W 2 88 This position is on a bearing of 211 07 T 4 87 miles from the DR Position The results also show the confidence ellipse using standard deviation at 95 with its angle bearing 42 48 T The length of the ellipse is 6 88 miles and its width 13 03 miles Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 61 DR Position DR Latitude DR Longitude DR Zone Date Zone GMT Course Speed Temperature amp Pressure 32 2 15 21 Jun 94 22 00 00 325 00 9 80 C 0 00 0 00 Tuesday 23 00 GMT 8 00 kn 1010 00 mb Calculated Position 34 N 15 W Distance 4 81 mls 55 r0 2 00 Bearing 211 07 T Position Error Confidence Ellipse Latitude Longitude Bearing 95 00 6 66 mls 13 03 mis 042 48 T Which Sight Calc Almanac Palynomial Star Number Actual Sight Time Time Diff Miles Revised DR Position DR Bearing Observed Angle Index Error Minutes Height of Users Eye DIP Refraction R Ro f Parallax in Altitude Semi Diameter Corrected Altitude Calc Declination Sun GHA POSITION AT 22 32 05 32 00 31 95 31 90 31 85 31 80 31 7
31. 31 March 2011 Page 56 Star DR Days GHA Aries SHA 1 Sun 11 7631 3554467 356 26 77 356 4467 3409457 5577 1480755 1 Venus 9 2154 318 2305 318 13 83 318 2305 3027305 302 43 83 0 3040 S 2 Mars 11 3980 350 9693 350 58 16 350 603 335 4693 335 28 16 14 1061 5 3 Jupiter 146797 400 1955 400 11 73 40 1955 24 6955 2447 73 23 0035 5 Saturn 96327 3244841 3242905 3244841 308 9641 308 59 05 4 5438 S 1 Moon 318 8716 127 6945 12741617 127 6045 112 1945 112 11 67 5 4231 5 1 1 Alpheratz 316 8264 316 8264 3158 49 59 357 9548 301 3264 301 19 59 29 0698 N 2 2 Ankaa 312 3544 312 3544 312 21 27 353 4828 2068544 206 5127 4233105 3 3 Schedar 308 8005 308 8005 308 48 03 3499289 2933005 2793 18 03 56 5188 4 4 Diphda 308 0258 306 0255 308 1 55 34915427 29025258 21323155 1801095 5 5 Achernar 294 46568 2044858 204 29 15 335 6142 276 9850 276 59 15 5726225 B 287 1327 287 1322 Zur 7 93 328 2606 271 6522 271 3793 234435N T 7 Acamar 25143440 2743440 274 20 647 315 4724 25006440 258 5064 40 3265 5 G 8 Menkar 23a 273 3511 AF 21 07 3144795 257 8511 25r 51 07 4 0716 N 9 9 Mirfak 267 8560 267 8560 26751 36 308 5844 25235807 257 21 36 49 8489 N 10 10 24009433 2409434 249 55 6 201 0716 23444537 234266 16 4990N 11 11 Rigel 240 2798 240 2798 240 16 79 201 4081 2247798 224 45 79 8 2109 S 12 12 Capella 230 7645 23937646 239 458 200 8930 2242646 2274 1587 459939N 13 13 B
32. DR 32 0 15 0 W m Calculated Course Systematic Navigation www sysmaps com Longitude Sight 2 Moon 123 46 47 3 51 Towards Transferred DR Positions Sflnav50 doc Manual v5 0 31 March 2011 Page 62 19 2 Regulus Antares and Kochab on 4 July 1994 This example is taken from the The Nautical Almanac 1994 80 7 Required calculate the position of a ship on 4 July 1994 at GMT 21 0 0 which has been travelling on a constant course of 325 for several hours at a speed of 20 knots Three observations have been taken Sight No Number Star GMT Universal Time Adjusted Altitude Sight 1 26 Regulus GMT 20 39 23 27 0109 Sight 2 42 Antares GMT 20 45 47 26 0764 Sight 3 40 Kochab GMT 21 10 34 47 4449 The time is GMT 21 0 0 and the estimated position DR is 32 N 15 W No Hour Angle Declination and corrections to the Observed Angle are needed with Systematic Navigation and the intermediate results using the same format as The Nautical Almanac 1994 HMSO are Star Regulus Antares Star Number 26 42 Time of Observation 20 39 23 UT 20 45 47 UT 21 10 34 UT Adjusted Altitude Ho 27 0109 26 0764 47 4449 Greenwich Hour Angle 80 4516 346 7984 17 6023 Local Hour Angle 65 5084 331 8312 2 5424 Time Difference to DR 0 3436 hours 0 2369 hours 0 1761 hours Revised Latitude 31 5250 N 31 5730 N 31 6480 N Revised Longitude 14 9320 W 14 9
33. Declination 38 46 99 N 5 43 04 N 12 39 53 S GHA 323 3 758 39 17 12 324 54 23 LHA 308 30 9 56 41 5 308 45 01 Azimuth Bearing 65 45 64 257 27 11 126 42 51 Intercept Distance 0 34 Miles 0 39 Miles 0 09 Miles Direction Towards Towards Towards The calculated position after several iterations is 32 N 44 06 15 W 30 45 a distance 1 02 miles and a bearing of 202 71 degrees from the DR position POSITION AT 11 00 ZT 15 FEB 2006 FIX 32 44 06 15 30 45 W 1 02 MLS 202 71 T B DR 3245 N15 30 W 2 00 4 00 6 00 8 00 10 00 10 000 8 000 6 000 4 000 2 000 20 This is the complete worked example from pages 60 and 61 of Compact Data 2006 The answer given is 32 7211 N 32 N 43 266 15 4707 W 15 W 28 2420 a 5 089 nm b 3 959 nm azimuth 350 using the same methods for four rather than three observations Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 66 DR Position Calculated Position Position Error DR Latitude 32 N 4500 32 M 44 06 Confidence DR Longitude 19 W 30 007 15 1 30 45 Ellipse 95 00 DR Zone Date 15 Feb 06 Wednesday Zone GMT 11 00 00 12 00 GMT Distance Bearing Latitude 0 82 mls Course Speed 315 00 T 12 00 kn 1 02 mls 202 71 T Longitude 1 76 mls Temperature amp Pressure 9 30 C 1010 00 mb Bearing 355 49 T Sight 1 Sight 2 Sight 3 Which Sight Hame 2 Star 4 Moon 1
34. Hs D Ro 0 0187 tan H 7 31y h 4 4 f 0 28 Pressure Temp 27 3 Refraction R Ro f Oblateness of Earth OB Parallax Parallax Altitude lt semi Diameter 5 Corr Altitude 5 Sight 4 37 4167 0 0000 40 0718 37 3449 0 0217 1 0000 0 0217 0 0014 0 9386 0 7462 Systematic Navigation www sysmaps com sight 2 16 00 hrs DEC 0 000003 0 0048000 0 0019000 0 00000 Polar Stars or 0 00000 C Alt Azimuth Sight 2 28 4833 28 4115 0 0306 0 0000 0 0000 Sflnav50 doc sight 3 Sight 3 sight 3 GHA DEC 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000 0 0000 0 0000 0 00000 0 Manual v5 0 31 March 2011 22 The third page of workings derive the intercept and azimuth from the computed angle and the fix position using the method of least squares It also calculates the standard deviation and the estimated position error 0 Sight Reduction Altitude Sight 1 Sight 2 Sight 3 Computed Altitude Angle in Degrees Azimuth Angle Angle in Degrees Corrected Azimuth 27 Angle in Degrees Latitude Difference Latitude as Miles Towards Away Towards E Computed Position Position Sight 1 Azimuth 1 Take out Excess 360 Uu WU Take out Excess 360 True Azimuth Bearing Z 232 132 T 125 384 T Plot Position Direction 037 8
35. Method Add lower limb and subtract upper limb 9 Calculate the Observed Altitude Ho The model uses the Observed Altitude in sight reduction and compares it against the Computed Altitude Hc to derive the intercept and azimuth This is an extract from the Inputs sheet showing workings for the Moon on 9 February 1996 observed at an altitude of 37 28 02 37 41677 Corrected Altitude Decimals Altitude Sight 1 Observed Hs 37 4167 Index Error 1 0 0000 DIP Height D20 0283 SqrtH 0 0718 Apparent Altitude H2Hs LD 37 3449 Ro 0 0167Aan H 7 31 Wih 4 4 0 0217 f20 28 Pressure Temp 27 3 1 0000 Refraction R Ro f 0 0217 Oblateness of Earth OB 0 0014 Parallax 0 9386 Parallax Altitude PA HP cosH 0 7482 Semi Diameter 5 0 2558 Corr Altitude 5 38 3238 Example from page 19 of Compact Data 1996 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 44 11 2 Observed Angle This example from The Nautical Almanac 1996 assumes height of 5 4 metres temperature of 3 0 C pressure of 982 Mb The date is 22 October 1996 at GMT 10 0 0 Altitude Observed Hs Index Error I DIP Height 0 0293 Sqrt H Apparent Altitude H Hs I D Ro 0 0167 tan H 7 31 h 4 4 f 0 28 Pressure Temp 273 Refraction R Ro f Oblatenes
36. OF Iqnuabjauaqnz srunejua niy snunjorg 26 yuayua p JE GE PEAY pe eads olg ce xnioet LE suog 62 82 94430 ze sninBay gz 82 snpioe detji pz ee 22 Lc 2 EL snug 81 sndoue z asnab ajag 91 WEIL SL qeu FL neeg EL ejede LL 01 APEMH 6 jeXuaW g PUES 2 wep 9 G epudig p 5 eeu 2 zjeiaud e OF PARETET zE 92 Gz uueg zy sinc pier PE 82 eed wok a 4 sninjarg eos ydiy Lp er qeuait 62 ME eads g Ww n gp GE 3 495 pr I euns eec xniaet LE Ge suog OF ap siensng sne gp run OS meme sem ines LS P xu EE snpioejdel pz JO 22 3148190 BG 7G SS G sndoue 9G peu Z Ju 3 pS IPP epudiq p qel 2G g 20190 N 15 30 Expected Altitude C Azimuth Bearing in in N o T N 5 e 5 N T L ec t e Y e e e z gt e lt j
37. Sight Charts Stars Charts Positions RiseSet Aries Data Version Background notes on installation and operation of the Application Graphical overview of the Application Registration document together with details on how to register the Application Enter details of up to three sights View summary results and chart plot View large scale chart plot View star charts in SHA altitude or bearing order View hour angles and declination for position date and time in Inputs View sun and moon rise and set for position date and time Inputs Background calculations Data for the date and time in Inputs Version information and entries for registration codes Systematic Navigation Data valid until 31 Dec 2015 Automated Data Entry Reset to Top of Page Page Calculate Now F9 Select Option Great Cirde Version 5 0 31 Mar 2011 Custom Toolbars Excel Toolbars Main Option Schedule Description Menu ReadMe Registration Inputs Results Sight Charts Position Plot Stars Charts DegreesCharis Positions Rise Set Moon Rise Set Moon Calculation Altitude Table Altitude Table Great Circle Aries Background notes on installation and operation of the Application Graphical overview of the Application Registration document together with details on how to register the Application Enter details of up to three sights View summary results and chart plot View large scale chart plot View direction of fix from current posit
38. Sun Calc Almanac Pohynomial B Polynomial A Calculated B Polynomial Star Humber 49 Vega 0 0 Actual Sight Time 5 28 52 06 28 GMT 5 33 52 06 33 GMT 8 53 45 09 53 GMT Time Diff Miles 5 31 hrs 65 23 mls 5 26 hrs 55 23 mis 2 06 hrs 25 25 mls Revised DR Position 31 57 2 14 34 8 W 31 57 9 14 35 6 W 32 26 2 N 15 9 2 W DR Bearing 47 59 55 B5 45 64 29 2594 257 27 11 24 8 59 124 42 51 bserved Angle 48 52 26 25 996 23 58 902 Index Error Minutes 0 00 0 00 0 00 Height of Users Eye DIP 4 317 0 007 4 317 Refraction R Ro f 0 907 1 74 223 Parallax in Altitude 0 00 47 53 0 13 Semi Diameter 0 00 14 73 16 18 Corrected Altitude 47 60 29 25 33 24 3 65 Calc Declination 36 46 99 North 5 43 04 Horth 17 39 53 South Star GHA LHA 323 3 75 308 26 97 T3 17 12 50 41 5 3245423 309 45 01 65 45 64 0 34 mls 31 57 4 N 65 45 64 Towards 14 34 aw 21 11 0 39 mls 31 57 9 257 21 11 Towards 14 36 1 W 124 42 51 0 09 mls POSITION AT 11 0 0 ZT 15 FEB 2006 FIX 32 4 06 15 20 45 W 1 02 MLS 202 71 T 32 60 32 TU N 32 50 N 32 50 N 32 30 M 32 20 N 32 10 N 32 00 N 31 90 N 15 60 W Longitude 7 4 a 14 60 W 1 124 42 51 Towards 15 9 1 DR 6 33 52 GMT Sight 1 Vega 65 45 64 0 34 Towards 4 Sight 2 Moon 257 27 11 0 39 Towards lt gt
39. a new file The system will prompt you for a name but the default is Year Month Day xls 1 e 96Feb09 xls This way you can keep a full record of the inputs intermediate calculations and results Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 25 14 You have the choice of chart plots or a combined results and chart plot Examples of the Results sheet are in the worked examples These are example chart plots from the SightCharts schedule for 9 February 1996 at GMT 12 0 0 from an assumed position of 32 N 45 15 W 30 POSITION 11 0 0 ZT 9 FEB 1996 32 36 57 15 32 23 W 0 MLS 196 92 T 32 80 N 32 70 32 60 N 3250N 1 3240 N DR395345 GMT _ 32 30 N 32 20 N 32 10 N 32 00 N 31 90 N 1560W 1550W 1540W 1530W 1520W 1510W 15 00W 1490W 1480W 1470W 1460W Longitude OG Sight 1 Moon 230 346 4 65 Mis Towards lt Sight 2 Deneb 52 7 92 6 32 Away c Sight 3 Sun 126 23 02 2 33 Towards O Transferred DR Positions x DR 32 45 15 W x Calculated Course 1 1 1 There 15 also a plot of Sun Moon and Planets on SightCharts schedule SUN MOON AND PLANETS 92221996 DR 11 0 ZT 32 45 H 15 30 W io B ieu Jupiter 190 0 Bearing Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 M
40. accepted regarding the use or accuracy of the programs and associated data We will make every effort to correct such software errors that are found and reported to us Crown Copyright and or database rights Reproduced by permission of the Controller of Her Majesty s Stationery Office and the UK Hydrographic Office www ukho gov uk Date Reference V5 0 31 March 201 1 Expiry Date 31 December 2011 Systematic Navigation 18 a division of Systematic Finance plc Orchard House Green Lane Guildford Surrey UK GUI 2LZ Telephone Number 44 0 1483 532929 Telefax Number 44 0 1483 538358 E mail info system co uk Web www system co uk www sysmaps com Registered Number 2443802 VAT No GB 572 5542 32 Registered Office Orchard House Green Lane Guildford GU1 2LZ Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 4 1 1 Systematic Maps www sysmaps com See also Systematic Maps at www sysmaps com for free on line mapping provided by government and collaborative organisations This site offers more explanation of the astro navigation program together with a number of different maps UK Ordnance Survey topographical maps Cloudmade open source world wide maps French IGN topographical maps OpenStreetMap and German BKG topographical maps with Bing MuliMap Google Yahoo relief and other layers Google maps with search and StreetView window Bing MultiMap e Navteq with lo
41. agy2 See bibliography for Astro Navigation by Pocket Computer by Mike Harris Algorithms are on page 69 Example from Compact Data 1996 Page 7 Answer given as GHA 87 6592 DEC 2 5688 HP 0 996 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 37 The Moon s RA and DEC are calculated from and 7 as follows Set X cos fj Y cos cos f sin A sin e sin p and Z sin e cos sin A cos e sin p where e 23 44 Then tan Y X and DEC sin Z If X 0 add 180 to RA If X gt 0 and Y 0 add 360 to RA To obtain the Greenwich hour angle of the Moon GHA calculate Le 0 9856474 D d UT 24 where UTh is the universal time in hours 4 is the day of the month and D 18 the number of days elapsed as per the table anuary 0 at 0 UT to the beginning of the month on day 0 at 0 UT Alternatively it may be calculated using the formula in section 4 2 Then GHA Aries 99 3133 15UT and GHA GHA Aries RA This is a detail from the complex Chebyshev calculations showing the RA GHA and DEC 1 Calculation of Factors UT 5 7894 Lookup R 96 9513 Base Year for D 1996 244 d 2f x 0 651286339 y 1 405153356 L 267 34821 Data Line No 69 N HP 13 13 0 0 0 0 0 0 0 0 0 0017 0 0026 0 0 0065 0 0061 0 0 0204 0 0063 0 0 0065 0 0025 0 0 0884 0 0659 0 0 1099 0 1153 0 0025 0 0129 0 0599 0 0019 0 3676 0 9706 0 0038
42. miles Away Azimuth Bearing 37 15 5 217 15 5 123 7 23 303 7 23 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 59 The position fix with two observations is 50 N 46 1 W 18 using the Basic program This provides acceptable accuracy against the Excel results below 50 N 47 39 W 18 22 DR Position Calculated Position Position Error DR Longitude DR Zone Date Zune GMT Course Speed Temperature amp Pressure 50 1 8 96 23 35 24 000 00 9 80 C sight 1 45 00 18 00 sunday 23 35 GMT 0 00 kn 1010 00 mb 50 N 1 W Distance 1 40 mls sight 2 47 39 18 22 Bearing 354 12 T Confidence Latitude Lon sight 3 95 00 4 16 ms 6 19 mis 334 43 T Which Sight Hame Calc amp lmanac Polynomial Star Number Actual Sight Time Time Diff Miles Revised DR Position DR Bearing Observed Angle Index Error Minutes Height of User s Eye DIP Refraction R Ro f Parallax in Altitude Semi Diameter Corrected Altitude Calc Declination Star GHA LHA POSITION AT 23 50 60 N 50 78 N 20 79 20 78 N 20 78 N 50 77 N L a t i t u d e 50 77 N 20 76 N 20 76 N 1 34 W I I I r I I I r I 1 33 W 2 Star B Polynomial 27 Dubhe 23 20 52 0 14 hrs 50 46 N 39 20 31 0 007 0 00 1 21 0 00 0
43. tabs at the bottom of the screen The status bar at the bottom of the screen will display messages from time to time to keep you informed In manual mode you can enter all figures and labels in a blue bold typeface on the Inputs schedule You easily can switch between the Excel and the Custom toolbars Use the pull down menu to switch to Excel or use the button Welcome sheet to switch from one to another The system will prompt you when you exit the application Either save the file with or without a back up quit without saving or halt to stop the process A further prompt asks you if you want to re set the schedules to their respective top of the page Answer yes or no It is a good idea to save the file every time you exit Systematic Navigation If you ever experience any problems with the application re copy your back up disk Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 8 3 Overview 3 1 General Principles Out of sight of land there are no landmarks for checking assumed or dead reckoning positions Similarly stand alone GPS or GPS units in mobiles can exhibit problems or run out of battery power Astro navigation 18 one method of deriving positions using observations of the Sun Moon Stars and Planets The basic steps in astro navigation are e Taking a sight with a marine sextant from an assumed position and noting the exact time e Applying cor
44. the object above the horizon This angle can then be compared to your corrected sextant angle to produce a position line and a measure of distance along this line With several sights the model plots a fix through the statistical intersection of these position lines The following sight reduction formulae are used 1 Computed Altitude Hc Hc Asin sin Latitude sin Declination cos Latitude cos Declination cos LHA 2 Azimuth or True Bearing Z Z Acos sin Declination sin Computed Altitude sin Latitude cos He cos Latitude If the Local Hour Angle is less than 180 then the Azimuth is 360 less the product of the above expression This is an extract from the Inputs sheet showing the workings for the example in the previous section D Sight Reduction Altitude Sight 1 Sight 2 Computed Altitude Hc Angle in Degrees Azimuth Angle Angle in Degrees Corrected Azimuth 27 Angle in Degrees Latitude Difference Latitude as Miles Towards Away Towards Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 46 13 Calculated Position 13 1 Method An estimate can be made of the position at the adopted time of fix The position at the time of the observations can then be easily calculated provided that the course and speed has been constant Using speed V in knots and the track T the algorithms are Longitude Lx t V
45. 0 00 55 3 15 3 Calc HP SD 0 00 0 0 00 16 Corrected Altitude 381943 20 22 06 22 37 43 MM M PPP M M Calc Moon DEC D N 0 00 Calc DEC H 0 00 Calc DEC D N 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 Moon Declination 42485 South Star DEC 45 16 03 North Sun DEC 14 50 27 South Calc Moon GHA 0 00 Calc GHA O E 0 00 Calc GHA 0 0 00 0 0 00 0 0 00 0 0 00 0 000 0 0 00 0 0 00 Moon GHA LHA 52 12 077 3271 Star LHA 294 185954 27953873 Sun LHA 324 53 11 308 44 34 from the DR position 3 The screen shows a best fit calculated position with the latitude and longitude and the distance and true bearing The model uses the least squares method from Compact Data et al to produce a most probable position within a confidence ellipse of 95 To produce an accurate fix three sights are normally required with some angle between them to provide a good cut A summary of the position lines for other sights is included If any sights are inaccurate such that the intercept is greater than 500 miles the system will not compute a fix and will display an error message Similarly the system will not compute a fix with only one sight although it will derive the latitude longitude position of the observation from a single azimuth and intercept Press OK to continue to print view and Re Do options The following show the background calc
46. 0 00100 Horizontal Parallax 0 0010 HP Minutes 0 06 The answers are very similar to the Almanac results above The calculations using the coefficients are the same as for the Sun Time variable x d GMT 24 32 d is the day in the month and GMT the universal time in hours GHA GMT in hours and DEC in degrees are derived from this expression ao ai x a4 x The horizontal parallax is calculated using the expression HP ag x Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 41 10 Annual Altitude Table 10 1 Method Select Sun Stars Moon erc and press the button to repopulate the table This has to recalculate many times and will take about three minutes The resulting table shows the altitude by day for the selected object Table Calculation This routine recalculates each hour within the day and all days in the year such that the number of loops exceed 9 000 The time required is een three and five minutes Do you want to continue 01 00 UT 02 00 UT 03 00 UT 04 00 UT 05 00 UT 06 00 UT 07 00 UT 08 00 UT 00 00 01 00 02 00 03 00 04 00 05 00 06 00 118111 13 09 4 92 3 80 1271 21 44 29 59 36 63 41 83 001 1 Jan 10 62 93 51 49 56 35 48 08 40 50 31 60 22 68 14 03 002 2 Jan 10 56 21 56 91 57 69 52 97 45 94 37 65 26 60 19 81 003 3 Jan 10 45 03 51 27 53 57 52 32 47 67 41 14
47. 00 JF 27 19 61 45 72 262 19 36 1 32 W 1 31 W 23 20 GMT 0 00 mis T 187 W 37 15 5 North 281 1 38 15 5 Away T 18 57W 35 24 ZT 6 DEC 1996 FIX 50 47 3 2 Star B Polynomial 20 Procyon 23 25 55 0 09 hrs 0 45 N 30 12 91 30 13 0 00 0 00 171 0 00 0 00 30 14 29 5 13 85 314 41 05 Fix 50 47 49 N 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 223 20 Sight 1 Dubhe 37 15 5 0 52 Away x DR 50 46 N T 18 W Transferred Position Systematic Navigation www sysmaps com sight 3 Hamal 242 15 88 2 28 Away 3 4 51 94 1 30 W 1 29 W Longitude 1 18 22 W f DR 27 50 evi MV 1 26 W 23 25 GMT 0 00 mis T 18 W 123 7 53 North 313 23 05 7 23 Away 1 20 17W 0 10177710777 1 27 W B Polynomial 3 cee perce woo 7 ee te uber 1 26 2 Star 6 23 35 24 0 00 hrs 50 46 N 49 30 43 4g 29 0 00 0 00 0 85 0 00 0 00 49 28 15 23 25 93 40 5 52 1 25 W 23 35 GMT 0 00 mis T 18 W 242 15 99 North 40 47 52 62 15 99 Away 1 14 57W Sight 2 Procyon 123 7 23 1 52 Away O Transferred DR Positions X Sflnav50 doc Manua
48. 011 Page 9 3 2 Systematic Navigation The methodology described above requires the Almanac and concise mathematics plus plotting instruments to prove a position These methods are prone to error and time consuming Systematic Navigation is an Excel workbook with groups of separate sheets or schedules It contains all the base data required and reduces sights and fixes positions for up to three sextant sights of the Sun 59 navigational Stars the Moon or the planets of Venus Mars Jupiter and Saturn Data is available from 1991 and is updates in five yearly intervals as new data becomes available It dispenses with all the manual calculation of corrected altitudes hour angles and declination from the Almanac and the plotting of position lines on a chart Systematic Navigation is not intended as a complete introduction manual of astro navigation This manual does however contain full explanations of the methods used and lists the algorithms T Hipparchus 057 Example fix POSITION 5 30 0 ZT 14 SEP 2071 FIX 32 0 02 14 34 46 W 3 15 MLS 107 36 T 1 1 1 1 1 1 1 1 J2oll222 22 22222 Lb 2 2 2 2 2 J 2 2 22 2 L 2 2 2 2 2 2 J 2 L 2 2 2 J 2 2 2 L 2 2 2 1 1 1 1 1 S DR E302T 324 N 4438 eMe Fies 321 0027 844 34 DR3 6 15 23 GMT
49. 015 United Kingdom Hydrographic Office ISBN 978 0 7077 41048 887331 8 Harris M 1989 Astro Navigation by Pocket Computer Adlard Coles ISBN 0 229 11846 1 Dixon Conrad 1968 Basic Astro Navigation Adlard Coles ISBN 0 229 11740 6 Stein Walter and Kumm Werner 1989 Astronomische Navigation Delius Klasing Verlag Klasing amp Co GmbH ISBN 3 87412 095 3 Molt J rgen and Hempe Klaus 1986 Sterne im Computer perComp Verlag GmbH ISBN 3 891 71007 0 B hm Winfried 1988 Handbuch der Navigation BusseSeewald ISBN 3 512 00845 3 Astronomical almanac on line at http asa usno navy mil Celestial Ce estial Navigation for the iPhone at http navimatics com Movable Type for navigational formulas at www movable type co uk scripts latlong htm Alastair L Day Guildford 31 December 2010 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 77
50. 089 0 00200 0 00010 9 Mirfak 48 23930 05999490 0 00610 0 00590 49283190 00000078 0 00120 0 00290 10 Aldebaran 30 30810 0 9999599 0 00260 0 00510 16 49350 0 0000033 0 00090 0 00040 11 Rigel 2063340 0359999655 0 00190 0 00540 821010 0 0000009 0 00290 0 00060 12 Capella 20 15160 04999485 0 00270 0 00770 45 99120 0 0000005 0 00200 0 00110 13 Bellatrix 17 99730 0 9999627 0 00170 0 00550 6 34350 00000002 0 00170 0 00020 14 Elnath 17 72780 609999561 0 00190 0 00620 26 60190 0 00040 0 00050 15 Alnilam 15 22030 09999647 0 00140 0 00550 1 20580 0 000001 0 00230 0 00040 16 Betelgeuse 10 46600 0 9999624 0 00100 0 00550 7 40720 0 000002 0 00150 0 00020 17 Canopus 3 22390 0 9999836 0 00060 0 00940 5268960 0 000004 0 00550 0 00040 18 Sirius 357 97200 0 9999691 0 00600 15 70280 0 000006 0 00350 0 00030 19 Adhara 354 59260 0 9999721 0 00050 0 00650 28 955880 0 000006 0 00450 20 Procyon 344 45140 0 999963 0 00130 0 00550 524880 0 000009 0 00180 0 00050 21 Pollux 342 96670 0 9999582 0 00170 0 00610 28004860 0 000009 0 00040 0 00110 22 Avior 333 58070 09999830 0 00440 0 01000 59 480560 0 000010 0 00520 0 00210 23 Suhail 32224530 09999726 0 00430 0 00620 43 39880 0 000012 0 00450 0 00220 24 Miaplacidus 32068870 0 9999873 0 00930 0 01250 69 68080 0 000013 0 00470 0 00330 25 Alphard 317 37340 0 9999655 0 00350 0 00420 8 62020 0 000013
51. 15 6226 115 37 35 57 08905 32 32 Alioth 4854044 125 4044 125 2426 165 5328 109 9044 109 5426 55 9763 33 335 4776203 1176203 11r 37 22 158 7487 102 1203 102722 11 14135 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 57 17 Data Schedules 17 1 Description There are several schedules of polynomial coefficients which are looked up by the Data schedule These are for Sun Star Planet 1 Sun 2 Star 4 Venus 5 Mars 6 Jupiter 7 Saturn This data is for the period 1991 2015 If the model is used outside these dates it will prompt you for Almanac or revised polynomial data This is an extract from the Stars schedule showing the Stars for 2006 2015 GHA DEC Star 2 1 az 1 Alpheratz 7 17970 05999628 0 00590 0 00070 29042080 0 0000148 0 00230 0 00240 2 Ankaa 69820 0 0 99099676 000710 0 00020 42355270 0 0000143 0 00140 0 00410 3 Schedar 89 156240 0959999572 0 00950 0 00030 56 49030 0 0000145 0 00120 0 00450 4 Diphda 66 37450 0 009965 0 00550 0 00050 18 03370 0 0000143 0 00210 0 00220 5 14 81360 09999768 0 00040 0 00300 57 27990 O 0000127 0 00230 0 00480 6 57 49320 09999600 0 00530 0 00240 23 42250 0 0000115 0 00130 0 00170 f 5467990 09999746 0 00570 0 00440 40 33820 0 0000092 0 00360 0 00330 Menkar 53 70730 09199635 0 00430 0 00340 4 05700 0 0000
52. 2011 Page 27 5 Sun 5 1 Method A Aries Select and the routine will move to the Observed Angle and thereafter the system displays a box informing you that the GHA and Declination are automatically calculated Press OK to continue and the system displays the option box to denote the end of the required inputs for the sight Example The GHA and DEC of the Sun on October 22 1996 at GMT 21 43 25 Sun GHA and DEC Calculations Sun DEC U 288 723 V 209 770 DEC E 0 199 Declination in Degrees 11 3920 0 483 Add to 180 468 723 Calculated Sun GHA 509 760 Sun GHA 149 7600 removing multiples of 3607 The above uses two annual update quantities P and Q which are located on a look up table on the Aries schedule These are the mean anomaly on day 0 of the year and the earth s longitude at perihelion The values for 1996 are 3 9212 and 77 1260 respectively A further variable B is the decimal time from day 0 of the year to the GMT sight time where hours of the day are also expressed as decimals Example 22 October 1996 at GMT 21 43 25 22 October 1996 0 January 1996 296 days GMT 21 43 25 21 723611 24 0 905150 B 296 days 0 905150 hours 296 905150 The algorithms used by the model are 1 DEC U 0 9856 B V U 1 916 sin U 0 02 sin 2 U Q DEC Asn 0 3978 sin V 2 GHA X Atn 0 9175 tan V If sign sin X lt gt sign sin V then U U 180 GHA
53. 33 07 24 30 004 4 Jan 10 41 08 45 85 47 39 45 93 41 57 35 06 27 18 005 5 Jan 10 22 41 2D 88 35 850 39 70 40 63 30 05 34 67 286 70 006 6 Jan 10 10 42 18 42 25 32 30 60 33 72 34 28 32 16 21 10 007 T Jan 10 1 31 TU 14 52 20 94 25 54 26 00 26 03 25 64 008 amp Jan 10 12 66 4 00 4 05 11 15 16 31 20 92 22 03 22 45 009 9 1 10 23 53 14 68 6 23 1 50 8 18 13 46 15 99 18 47 010 10 Jan 10 33 82 24 88 18 11 7 87 0 42 592 10 83 13 99 011 11 Jan 10 43 33 34 40 25 48 18 81 8 73 1 49 4 60 9 24 012 42 Jan 10 51 69 43 09 34 11 25 18 18 58 8 81 1 51 442 013 13 Jan 10 58 18 50 47 41 79 32 78 23 85 15 29 7 35 0 32 014 14 Jan 10 81 88 55 88 48 05 39 32 30 30 21 35 12 78 4 85 015 15 Jan 10 61 20 58 34 52 28 44 40 35 65 26 60 17 64 9 04 016 16 Jan 10 57 02 57 33 53 84 47 54 39 60 30 84 21 78 12 79 017 17 Jan 10 50 34 53 18 52 46 48 37 41 84 33 83 25 06 15 99 018 18 Jan 10 42 24 45 83 48 47 46 79 42 16 35 41 27 33 18 54 019 19 Jan 10 33 32 39 12 42 56 43 07 40 55 35 46 28 51 20 38 020 20 Jan 10 23 94 30 55 35 34 37 67 37 19 33 99 28 53 21 43 021 21 Jan 10 14 15 21 43 27 24 31 04 32 40 31 13 27 40 21 68 022 22 Jan 10 4 13 11 90 18 52 23 53 26 47 27 04 25 18 21 10 023 23 1 10 6 13 2 06 9 35 15 35 19 67 21 94 21 85 19 70 024 24 Jan 10 18 56 8 03 0
54. 45 30 W 4 00 8 00 8 00 10 00 10 000 8 000 8 000 4 000 2 000 Sflnav50 doc Manual v5 0 31 March 2011 Page 49 Systematic Navigation www sysmaps com DR Position Calculated Position Position Error DR Latitude DR Longitude DR Zone Date Zone GMT Course Speed Temperature amp Pressure 32 N 15 W B Feb 96 11 00 00 315 00 T 9 60 45 00 30 00 Friday 12 00 GMT 12 00 kn 1010 00 mb 32 N 15 W Distance 6 66 mis 35 59 ALT Bearing 196 55 T Confidence Ellipse Latitude Longitude Bearing 2 11 mis 3 26 mls 333 25 T Which Sight Calc Almanac Polynomial Star Number Actual Sight Time Time Diff Miles Revised DR Position DR Alt Bearing bserved Angle Index Error Minutes Height of User s Eye DIP Retraction R Ro T Parallax in Altitude Semi Diameter Corrected Altitude Calc Moon DEC Moon GHA LHA 3 Moon A Calculated 49 58 58 52 5 01 hrs 31 56 20 31 25 002 0 00 4 31 122 4 15 35 38 19 43 F 24 85 ae 12 07 230 36 38 0 89 mls 31 56 5 N 06 56 GMT 50 23 mls 14 41 6 W 230 36 36 south 3r 30 45 50 36 38 Away 14 40 87W Sight 2 2 Star B Poltynomial 53 Deneb 6 03 52 455 hrs 31 56 7 N 268 23 75 26 26 906 0 00 4 317 1 84 0 00 0 00 ao 22 85 45 16 03 294 16 94 2 4 62 0 69 mis 31 5
55. 5 2 07 03 GMT 59 23 mis 14 42 47 W 52 4 62 North oro 36 5 Sight 3 1 Sun Calculated 0 8 53 45 2 06 hrs a2 20 7 N 22 37 41 22 26 002 0 00 4 317 2 40 0 13 16 00 22 312437 14 50 27 324 53 11 1287 19 23 mils POSITION AT 11 00 ZT 9 FEB 1996 FIM 32 36 59 15 32 47 W 6 66 MLS 196 55 T 32 80 N 32 70 N 32 60 N 32 50 N 32 40 N 32 30 N 32 10 N 32 00 N 31 90 N 31 80 N m mR T Q4 HQ mm emm emm 09 53 GMT 25 25 mis 119 W 128 19 23 South 309 42 14 126 19 23 Towards 15 10 9 W 15 60 W 15 50 W 15 40 W 15 30 W 15 20 W 1 Sight 1 Moon 230 36 36 0 89 Away gt Sight 3 Sun 126 19 23 0 02 Towards x DR 32 45 N 15 W x Calculated Course Systematic Navigation www sysmaps com 15 10 W Longitude 15 00 W 14 90 W 14 80 W 14 70 W 14 50 W Sight 2 Deneb 52 4 62 0 88 Away D Transferred DR Positions gt Sflnav50 doc Manual v5 0 31 March 2011 Page 50 14 Sun and Moon Rise and Set 14 1 Description The model calculates Sun rise and set for the dead reckoning date and position Set the application to manual and access the RiseSet schedule after entering assumed position data on the Inputs schedule Press F9 to recalculate the application as this schedule can require more iterations to converge on the resul
56. 5 3 W 32 33 15 26 9 W DR Bearing 21 33 65 264 51 89 47 25 2 204 2 47 29 24 01 60 27 27 Observed Angle 21 25 4 46 32 7 29 27 13 Index Error Minutes 0 00 0 00 0 00 Height of User s Eye DIP 4 317 0 007 0 007 Refraction R Ro f 253 0 87 1 76 Parallax Altitude 0 13 39 02 0 00 Sem Diameter 15 77 15 45 0 00 Corrected Altitude 21 34 477 AP 28 177 2U 2537 Calc Declination fo 25 53 North 11 58 South oo 45 45 North Sun LHA OF 32 15 TE 25 24 jT 33 21 18 7 87 298 59 36 2833294 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 65 19 4 Vega Moon and Sun on 15 February 2006 This example applies the theory from the previous sections to bring together the calculation of GHA LHA Declination with sight reduction and statistical fixes This example is taken from Compact Data On February 15 2006 at GMT 11 0 0 the DR position is assumed to be 32 N 45 15 W 30 Three sights have been taken along a course of 315 T at a speed of 12 knots The temperature is 9 8 C and the atmospheric pressure 1010 Mb The height of the eye above the horizon is 6 0 metres Sextant index error is assumed to 07 Star Vega 49 Time of Sight GMT 6 28 52 6 33 52 9 53 45 Difference to DR Time 5 32 h 5 26 h 2 06 h Observed Angle Hs 48 5 2 28 26 23 58 9 Adjusted Altitude Ho 47 60 29 26 33 24 8 68
57. 5 N 31 70 N 31 65 N 31 60 N 31 55 N 31 50 N L a t i t u d e F F t Sight 1 1 Sun B Polynomial 49 18 00 00 4 00 hrs 31 33 8 12 474 11 57 0 00 0 00 4 55 0 14 15 76 12 6 35 y 26 29 104 33 7 290 14 29 3 60 mls 31 35 N 0 ZT DR 22 D ZT 320 N 15 19 00 GMT 14 36 47 W 290 14 29 North oo 55 34 290 14 29 Towards 14 42 2 Sight 2 3 Moon Polynomial 0 18 23 00 3 37 hrs 31 38 3 N 12 41 1 11 34 0 00 0 00 460 59 00 16 41 12 44 6 20 17 64 314 50 11 123 46 47 3 51 mils 31 34 4 N 21 JUNH 1984 FIX 31 55 78 N 15 2 Tem T Wu 1 7 eee eee eet ears olia 19 23 GMT 26 93 mls 14 40 45 123 45 47 south 300 9 66 123 46 47 Towards 14 37 1 W on W 4 8 Sight 3 2 Star B Polynomial 40 Kochab 21 23 20 0 36 hrs 31 56 N 47 335 34 47 31 0 00 0 00 0 91 0 00 0 00 4r 30 09 10 93 23 1 61 FMLS 241 07 T e e j j 22 13 GMT 4 89 mis 14 56 7 W 355 44 69 North 8 4 91 176 44 69 Away 14 56 5 W 15 10 W 15 05 W 15 00 W 14 85 W 14 90W 14 85 W 1480W 14 75 14 70W 1465 1460W 14 55 W O Sight 1 Sun 290 14 29 3 6 Towards Sight 3 Kochab 356 44 69 3 26 Away x
58. 58 58 18 ASTRO NAVIGATION IN BASIC 59 18 1 ASTINAVAU BAS 59 IE SPAN I E E D D 1 59 11 20 Re one 59 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 2 19 WORKED EXAMPLES S s 61 19 1 SUN MOON ANDA STAR ON 21 JUNE 61 19 2 REGULUS ANTARES AND KOCHAB ON 4 JULY 1994 sss see 63 19 3 SUN MOON AND STAR ON 19 JUNE 199 uu A 65 19 4 VEGA MOON AND SUN ON 15 FEBRUARY 2006 dea aee rer n ep ask ka p o eia 66 19 5 MOON STAR 18 SIRIUS AND MARS ON 11 SEPTEMBER 2014 69 20 TAFORMA TON m
59. 7 T 036 38 T Distance 2 4 99 mls 1 87 ms Bearing Miles 3 5 4 9889 W 1 874 E Latitude Longitude 0 095 W 0 036 Revised Fix Position 14 765 W 15 111 W Minutes 9 581 5 6998 6 5322 F Fix Method of Least Squares G Estimated Position Error Sights 3 Sta iation 1 2563 mis No of Sights 0 9793 mis Deviation Latitude 1 2587 mis 2 X 1 357 0 11173 Atan 2 Ellipse Azimuth 333 244 0 01859 Probability P 0 95 Scale 2 4477 1 85695 ALK 3 2613 mis 2 1159 mis Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 23 Systematic Navigation Calculated Fix Position Distance from DR Calculated Position Fix 32 38 58 N 15 32 23 W 6 69 186 83 T DR Position DR 32 45 N 15 30 W Date Time 9 2 1996 11 0 0 ZT Course Speed 315 T 12kn Sight 1 Moon Bearing Azimuth 230 34 6 Intercept 4 64 mls Towards Sight 2 Deneb Bearing Azimuth 52 7 92 Intercept 6 32 mls Away Sight 3 5un Bearing Azimuth OK to Continue Intercept 12 The system displays an options box repeating the Calculated Position and requesting the next action View input sheet and halt for manual input View results and chart plot View chart plot and sights charts Update and sort stars charts by SHA altitude or bearing View stars charts View Sun Moon Planets and Stars positions View Sun and Moon rise and set and Sun transits View background d
60. 790 W 15 0590 W Azimuth Z 267 7551 151 9161 358 9752 Calculated Altitude 27 0210 26 0983 47 4647 Distance p 0 0100 0 0220 0 0198 Intercept I 0 60 miles 1 32 miles 1 19 miles Direction Away Away Away The Almanac calculates a final estimated position of 31 6193 N 15 0204 W 31 N 37 158 15 W 1 224 The fix using the model is 37 13 15 W 1 22 at a distance from the DR position of 22 90 miles on a bearing of 182 71 The system print out is on the next page 9 Example from pages 282 and 283 Position calculated as 31 6193 31 37 158 15 0204 W 15 W 1 224 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 63 DR Position DR Latitude DR Longitude DR Zone Date Zone GMT Course Speed Temperature amp Pressure 32 N 0 00 i 15 W 0 00 4 10 94 Monday 20 00 00 21 00 GMT 325 00 T 20 00 kn 9 80 C 1010 00 mb 31 H 15 W Distance 22 30 mls Calculated Position Position Error Which Sight Name Calc Almanac Polynomial Star Number Actual Sight Time Time Diff Miles Revised DR Position DR Bearing bserved Angle Index Error Minutes Height of Users Eye DIP Refraction R Ro f Parallax in Altitude Semi Diameter Corrected Altitude Calc Declination Star LHA 32 10 N x 32 00 N 31 90 N 31 80 N 31 70 N 31 60 N 31 50 31 40 N 15 08 W Sight 1 2 Star
61. 99255 0 00690 0 01440 89 01390 0 000003 0 00350 0 00220 44 Sabik 201 69360 0 9999601 0 00210 0 00550 15 71590 0 000001 0 00090 0 00020 45 Shaula 195 90870 0 9999529 0 00190 0 00690 37 09930 0 0000003 0 00120 0 00060 45 Rasalhague 195 53060 0 9999676 0 00150 0 00560 125684 0 0000002 0 00330 0 00070 47 Eltanin 190 06260 0 9999852 0 00160 0 00890 51408580 0 0000018 0 00540 0 00100 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 58 18 Astro Navigation in Basic 18 1 Basic File AstNav40 bas The disk may contain an original program named AstNav40 Bas written in Microsoft Basic MsBasic Com should also be present as an alternative to the Excel Astro Navigation version This dates back to the original version in 1990 Use normal Basic commands to load and run the program It will prompt to retain the DR position Guildford and also for annual coefficients as below N Year R Aries 1996 3 9212 77 1260 98 9529 1997 3 1930 77 1087 99 6982 1998 3 4505 77 0916 98 4579 1999 3 7078 77 0744 99 2177 2000 3 9523 77 0605 98 9817 A full list until 2015 is to be found on the Aries schedule of Systematic Navigation or under Background Data earlier in this manual This programme could be downloaded on to a pocket computer such as a Sharp PC1248 to be used in conjunction with the sight planning within Systematic Navigation 18 2 Procedure 1 Th
62. Dubhe 2 0 Ursae Majoris 293 36180 0 9999615 0 01010 0 00460 28 Denebola 22 B Leonis Leo 28200880 09999851 0 00530 0 00120 29 Gienah 28 C Corvi 2 5 32420 0 9999635 0 00550 0 00050 30 1 1 Crucis Cru 272 6365580 09999559 0 01150 0 00040 31 Gacrux 1 6 Crucis Cru 271 49500 09999500 0 00960 0 00010 32 Alioth 1 7 Ursae Majoris UMa 265 74960 09999724 0 00940 0 00080 33 Spica 1 2 Virginis Vir 25 98000 0359929629 0 00520 0 00130 34 19 G Ursae Majoris UMa 25238260 0439999745 0 00770 0 00270 35 Hadar 0 9 B Centauri Cen 248 36350 09999477 0 00990 0 00450 35 Menkent 2 3 Centauri Cen 247 62170 0905786 0 00610 0 00280 37 Arcturus 0 2 Bootis Boo 24534670 0599966867 0 00510 0 00250 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 33 Identification Mag c tter Constellation Abreviation GHA 211 az 0 00590 7 2 Star Finder The model allows you three methods of identifying and using stars The model prompts you in the dialog boxes or you can select stars as one of the options on the End Results box Often you have a star sight and need to identify it or alternatively you can check a computed altitude and bearing before using the observation The options are e Star Identification A box requests the altitude and bearing of a star Press Re Do to return to the previous screen or to continue
63. Enter an altitude and bearing and the system calculates the star number and name from list Enter the star number and to continue or Re Do to re enter the altitude and bearing The model then moves to request the Observed Angle Example Deneb 53 at a bearing of 52 E and an altitude of 28 5 at 327 45 15 W 30 on 9 February 1996 at GMT 07 03 52 The system performs the mathematics backwards and derives the DEC as 45 3817 N and the 278 6130 The GHA is therefore 294 2691 Star Identification Sight 1 Sight 2 0 0000 52 000 0 000 LHA 28 500 LHA 0 0000 GHA 0 9556 GHA 0 0000 Aries 000 DEC Rads 0 7921 Aries 0 0000 N Aries 0 0000 Declination 453817 M Aries SHA 0 0000 E SHA Integer Integer Match Match Star Star The system calculates GHA Aries as 244 6356 and derives the Sidereal Hour Angle as 49 6335 It then compares this to the list of SHA s and finds number 53 Deneb to be the best match e Star Finder You are prompted to enter the star number on the Star Identification box The identification is dimmed Press to continue or Re Do to return to the Options box The altitude and bearing of the star is calculated using the sight reductions calculations below The system calculates the altitude at 26 3608 and the bearing at 52 218 for Deneb 53 at the sight time and position D Sight Reduction Altitude Sight 4 Sight
64. Longitude Q0E 000 Bearing nia Distance n a Bearing 1 Distance Speed 1 Destination 2 Bearing and Distance 10 00 35 50 N Finish 35 00N 8 00N m k im 35 00 N 6 00 N 44 50 N 400N 34 00 N 2 00 N EN 0 00 N 33 50 Bearing 352 207 c Distance 1581 Z nm _ _ _ 33 00 N 2 00 5 14 50W 4005 NUR ONERE UEM QN MM 2211 6 003 32 00 N 6 003 eee be m m k 31 50 N 15 10 W 15 00 14 90 14 80 W 14 70 14 60 W 14 50 VW 14 40 W Longitude 10 00 5 10 00 W 8 00V SDD VV 400W 200W 000E 200E 400E 600 800 1000 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 53 The units are kilometres statute miles or nautical miles The model calculates the item left blank Enter data to the cells in blue and leave blank the unknown item The model will calculate either item and leave the known item blank Inputs Results Date Time Units Nautical Miles Degrees Minutes 1 Destination Starting Latitude Starting Longitude Destination Latitude Destination Longitude 2 Bearing Distance Bearing 352 22 T Distance 484 74 nm Bearing Distance Speed 2 Bearing and Distance 10 00 35 50
65. MIAL COEFFICIENTS 37 VEM S NND S X 40 91 MBIHODJX INPUTOGELA AND yr uuu ubt a E 40 9 2 METHOD B POLYNOMIAL COEFFICIENTS 4 10 ANNUAL ALTITUDE TABLE vo tnt eei u u a THEY m ui AOT EEXU FI QN On PE SUE 42 ANON PEDE 42 111 CORRECTEDALTIFUDE 44 IN M TOD RR E E 44 LS Or ID 10 T u u atc M UR MM 45 I2 SICHT REDUCTION Q u uu AA D dI 46 I 51 41 15 u u u 46 0 ALCULA POSITION u u u unu u us 47 47 48 14 SUN AND MOON RISE AND SE I 51 I4 T Ru E MM M E M E E 5 A EXAMPLES e ee uu uu asus MM M E 52 I gt GREAT CIRCULE E 53 16 BACK GROUND DATA vinaria 55 LOTO Chh Ju uuu E ee 55 I PAS PEDULI Saa
66. Mar 2011 Registered Copy CONTENTS Introduction Explanation of Systematic Navigation Installation Starting the Application Systematic Navigation Trial Copy Licence Agreement Unless registered this is an Evaluation version which is valid for a 21 day evaluation period for a single position The software is not free and after 21 days you should register it and keep your conscience clear Introduction Systematic Mavigation comprises a complete application in Microsoft Excel for astro navigation without tables or almanac has been full revised and updated for the period 1991 2015 and should be of interest to navigators astonomers and students particularly those studying for the yachtmaster examinations Y ou will find a registration document under Information for our products with all Trial Copy packages may mE copies and pass on the software to others provided that you make no charge This is however aluation copy and if you use it then you must register it after the 21 day evaluation period Please see the registration document with this application and register your copy to fund development of the next version Registration entitles you to a comprehensive user manual with several worked examples and more explanation of the methodology all future up dates to the applications and free support as a Registered user The model accepts up to three sextant sights taken from one position or along a
67. Supplement 1997 Page 39 Answer given as 49 N 42 for the latitude and 0 for the azimuth Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 31 POSITION 17 23 17 ZT 15 1997 FIX 50 24 79 1 45 35 E 0ML 8 25 9 T 50 50 N 50 40 50 30 50 20 N 50 10 N 1 1 1 1 T 1 T 4 1 4 20 00 49 90 48 80 N 48 70 N 49 80 N 0 00 E 0 20 E 0 40 E 0 60 E 0 60 E 1 00 E 1 20 E 1 40 E 1 50 E Longitude O Sight 1 Polaris 0 24 14 41 92 Mls Towards lt Sight 2 Aldebaran 109 4449 4 35 Mis Towards C Sight 2 Aldebaran 109 44 49 4 35 Towards O Transferred DR Positions x DR 49 43 N 1 15 E x x Transferred Position 17 23 27 49 43 N 1 1 Aldebaran 17 23 ZT Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 32 7 Star Charts 7 1 Star Numbers Systematic Navigation like The Nautical Almanac uses this list to identify stars by number The example above uses star Aldebaran 10 which has an SHA of 291 1996 This table assumed a date of 1996 1 Alpheratz 22 97 17970 09999628 0 00070 2 Ankaa 2 4 5269820 0 9999676 0 00710 0 00020 3 Schedar 2 5 89 16240 0239299572 0 00950 0 00030 4
68. arch 2011 Page 26 Positions Min 20 Max 80 DR 11 0 ZT 32 45 15 30 W Sun 4 Venus Bl Jupiter wee eh E saturn 224 Stars dee ede ee de ee 3 ee 270 00 POSITION 11 0 0 ZT 9 FEB 1996 FIM 32 36 57 15 32 23 W 0 ML S 196 82 T DR 3245 N 15 30 W ELLE pec a s SSS SSP pm eque 2 00 4 00 6 00 8 00 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 L 4 1 1 1 1 1 1 1 1 1 1 1 1 10 00 10 000 8 000 6 000 4 000 2 000 6 000 8 10 000 The following sections provide an explanation of each body by method with the inputs required and the options available at each stage If Automatic Calculation is left selected see Section 4 2 Systematic Navigation will compute ephemeris without recourse to you for any data inputs The following sections assume that you have chosen to select the manual method of derivation of GHA and DEC Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March
69. ata and Aries corrections 9 View polynomial coefficients for the date of the sights 10 Re Run some or all of the sights 11 Halt for manual input 12 Quit Astro Navigation and return to Windows with an option to save files pe lo If you press Halt then the system displays the Welcome sheet Use the tabs at the bottom to activate any of the other sheets You can review all data on the Inputs sheet Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 24 Systematic Navigation Options Position calculated as Fix 32 38 58 N 15 32 237 W Distance from DR Position 5 69 Mis 196 93 T Option 9 View Inputs and Halt for manual input View Results and Chart Plot 3 View Chart Plot and Sight Charts Update Star Charts by Atitude or Bearing 2 View Star Charts View Sun Stars Moon and Planet Positions F View Sun and Moon Rise and Set D View Background Data and Aries Corrections View Polynomial Coefficients Re un Some or All Sights Exit Systematic Navigation with save options Select an Option and Press OK 13 Systematic Navigation will halt for you on the chosen schedule for you to review the results If you want to re enter the sights you can press the Main Menu buttons on the schedule or select Main Menu from the pull down menus Press the button to save the results sheet with its chart plot to
70. bee eee 00 13 00 14 00 15 00 18 00 17 00 18 00 19 00 20 00 21 00 22 00 23 00 00 00 06 00 07 00 08 00 08 00 10 00 11 00 12 00 00 01 00 02 00 03 00 04 00 05 00 Zone GMT Moon phases Page 43 Manual v5 0 31 March 2011 Sflnav50 doc Systematic Navigation www sysmaps com 11 Corrected Altitude 11 1 Method All sextant angles Hs need to be corrected for index error and altitude to produce the Apparent Altitude H The model computes these adjustments automatically and calculates the Observed Altitude Ho by subtracting a correction for refraction For the Sun Moon Venus and Mars a correction for parallax is also applied to H and for the Sun and Moon a further correction for semi diameter is also required The detailed calculations are 1 dip D 0 0293 SORT h where h is the height of the eye above the horizon in metres 2 115 instrument or index error 3 Apparent Altitude H Hs I D 4 Refraction R 0 0167 tan 7 31 H 4 4 5 f 0 28 Pressure Temperature 273 Adjusted Refraction Ro f R 6 Calculate the parallax in altitude PA from the horizontal parallax HP and the apparent altitude H for the Sun Moon Venus and Mars PA HP cos H Sun HP 0 0024 Moon HP is calculated 7 Oblateness of the Moon OB minus 0 0017 cos H 8 Semi diameter for the Sun and Moon Moon S 0 2724 HP Sun S is 16 under Method A and computed under
71. cal search and routing All the maps allow a GPS signal feed from Franson GPSGate software and are location aware with Skyhook Loki which positions the maps based on wiFi signals There are also other services such as search and geocoding which provide addresses and latitude longitude positions See the Information page at www sysmaps com for a full specification Systematic Maps B SysMaps Ordnance Surve Systematic Maps 5 Free Maps 8 Directions Ordnance Surv Cloudmade Instant Access to Maps 8 Directions with the Free and Easy Maps Toolbar Cloudmade Help Maps alot com IGN France Ads by Google IGN Help OSM BKG Germany Map Systematic s mapping resource website for UK French German OpenStreetMap Help Cloudmade Google Bing Multimap Navteq and Yahoo maps with search information geocoding Loki WiFi position and Franson GPSGate live GPS capability amp Google Map Bing Multimap Select a Navteq SysMaps Information Mapping Links Astro Navigation Bundesamt f r Systematic Home Kartographie und Geod sie SSi INSTITUT MATIC Contact Us Google maps FRANSON GpsGate MAPS Specimen maps are on the next page UK Ordnance Survey Cloudmade open source French IGN Navteq Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 5
72. cents table 12 Mars coefficents table 13 Jupiter coefficents table 14 Saturn coefficents table 15 Read Me and Registration Please contact Alastair Day if you would like assistance or further information on this or any other of products We welcome suggestions and look forward to hearing from you Copyright c Systematic Finance plc All rights reserved All intellectual contents and any derivatives and improvements to this product Systematic Navigation are the property of Systematic Finance plc Data reproduced with permission from data supplied by HM Nautical Almanac Office Copyright Council for the Central Laboratory of the Research Councils The program has been extensively tested However no liability can be accepted regarding the use or accuracy of the programs whatsoever We wil make every effort to rectify any errors reported to us at the address below Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 72 20 2 Installation You need to install Systematic Navigation on a hard disk Follow the instructions below The system requirements are an IBM compatible computer with minimum 3 0 Mb spare disk capacity The software requirements are DOS 3 1 or later Windows and Excel and Windows The disk contains all the files for this application A B D E F Ti G H Start Windows and insert the disk with the PKZIP file SFLNavXX zip Unz
73. course line It then reduces the sights and derives an azimuth bearing plot and an intercept in miles from the DR position With two or more sights Systematic Navigation will statistically calculate a fix position in latitude and longitude The results sheet summarises the results for each sight and draws a plot of the revised position The table below shows the extent of automatic calculation of the Greenwich Hour Angle and Declination You can always use the model as a training aid and opt to enter all data and check your answers against the model Systematic Navigation uses both Method Aries coefficents or Method Polynomial coefficients Yes 1881 2015 Enter Almanac Data 1991 2015 Yes Enter Polynomial coefficents Enter Almanac Data 1881 2015 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 71 Systematic Navigation contains these separate schedules within the file 1 Input form for up to three sights of the sun moon stars and planets 2 Results with a chart plot and fix 3 Chart Plot and sun moon and planetary positions 4 Star charts at the DR time 5 Positions schedule of the sun moon stars and planets 6 Sun and moon rise and set fF Background calculations and aries coefficients 8 Polynomial coefficent data table for the DR month and year for the sun stars and planets 8 Stars coefficents table 10 Sun coefficents table 11 Venus caeffi
74. cted Cells Copy Results Schedule Fill Selection Down Fill Selection Across Re set All schedules Restore Excel Menus Save Current File with back up Close Application to Excel Exit to Windows with Save Option Print Print Print Preview Print All Schedules Information Read Me Overview Registration Information Version Data Window Arrange All Unfreeze Panes Freeze Panes Maximise Action Display Main Menu to start inputting or revising data Copy selected cells Copy results to a new file Normal fill down Normal fill across Set all schedules to top of page Restore normal Excel toolbars at the top of the screen Open save options Close Systematic Navigation without saving it to Excel Quit Excel and prompts for save file options Print current schedule Print preview current schedule and allow printer set up Print ALL application schedules takes 10 minutes Print and view installation and licence information View overview map of application Print and view registration form for other products Display details about Systematic Finance plc Display information on copyright and the author Tile all open windows into sectors Normal unfreeze panes Normal freeze panes Set the window size to the full screen You can access the Main Menu from most schedules by pressing the Main button at the top of the screen or from the pull down menus You can also scroll through the schedules by using the
75. culates Sun and Moon Stars Planets Almanac needed for Declination and GHA Planet Almanac also required for Variation hour Method Calculated Sun Stars and Planets 1991 2000 Coefficients needed for Planets and Moon Input Method to be used A A or Actual Sight Time 5 58 52 Enter as 01 01 01 Press ReDo to re enter OK to continue ReDo Input Observed Angle Input angle in degrees and minutes together with height of user s eye 1 the height above sea level There are also prompts for the index or instrument error and whether the upper or lower limb was observed Any items not required for the body observed will be dimmed Press OK to continue of Halt to stop for manual input If you select the latter the system will enter all data so far entered and recalculate the model Systematic Navigation Observed Altitude Enter the observed angle and adjustments TIE 37 25 00 Index Error Minutes On Off Arc N F F Height of User s Eye 6 Upper Lower Limb U L L Semi Diameter Minutes Semi Diameter not required for Sun Moon and Stars Press HALT to stop for manual input HALT Press to continue Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 19 8 9 10 The system now calculates GHA and DEC or prompts you for Almanac data for the day of the sight If you opted to control t
76. e signed Name Date 18 Oct 10 Serial lumber 10633 111 5 0 first used on 31 Jan 2011 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 74 20 5 Version and File Information This is the Version sheet which is the last schedule on Systematic Navigation The system displays this information at the bottom of each schedule A registered copy of Systematic Navigation is valid until 31 December 2015 After this date the application will not work properly and will display error messages Installation serial Mo Licence Type Application Version Expiry Date Price Contact Author Company Address 1 Address2 Town County Postcode Telephone Fax CompuServe Web 31 3 2011 05 00 00 10633 111 5 0 Registered Copy systematic Navigation oystematic Navigation Version 5 0 31 Mar 2011 31 Dec 2015 50 550 Systematic Navigation www sysmaps com Alastair Day Systematic Navigation Orchard House Green Lane Guildford surrey UK GU1 2L2 44 011483 532929 44 011483 538356 infog system co uk WWW Sysmaps com Original installation date Licence serial number Shareware or Registered licence Initial macro screen Title of the macro dialog boxes Appears on all sheets to identify the version Data valid until 31 Dec 2015 Normal price for Systematic Navigation Copyright holder displayed on all schedules Author and copyright holder
77. e program prompts for the coefficients above and the current year Answer or to amend or continue Note that all inputs should be in upper case for the model to run correctly i e N not n 2 A position is stored and the next prompt is to change the DR position 3 Body Observed Sun Star Moon and Planet as 1 2 3 and 4 respectively 4 Enter the time of the sight sextant angle and corrections for index error height etc If not known pressure should be input as 1010 Mb and temperature as 9 8 C 5 Answer for this sight and intermediate results displayed 6 Prompt for position change between sights 7 Enter the second sight as above 8 Program displays a calculated fix and prompts for printing results Planets and Stars require inputs from the Almanac as directed for GHA and DEC and hourly corrections 18 3 Example Two sights are taken as 50 N 46 0 15 W 18 0 during 8 December 1996 of Dubhe 27 and Procyon 20 A Dubhe 27 at GMT 23 20 52 at an angle of 39 29 0 B Procyon 20 at GMT 23 25 56 at an observed altitude of 30 13 0 The program calculates GHA aries however you have to input SHA and DEC Variable Sight 1 Dubhe Sight 2 Procyon Declination DEC 61 N 45 7 PN 13 8 Sidereal Hour Angle SHA 194 7 1 245 12 6 Sextant Angle Hs 39 483 30 217 Observed Altitude Ho 39 046 30 188 Computed Altitude Hc 39 472 30 215 Intercept 0 52 miles Away 1 62
78. edule of positions of all celestial bodies e Sun and Moon rise and set including Sun transits This guide does not try to teach astro navigation however it is particularly suited to students of navigation who wish to learn the methodology You can select calculation of hour angles and declination using Aries Corrections e Polynomial Coefficients see Compact Data in the Bibliography e Almanac Data Greenwich and Sidereal Hour Angles and Declination Knowledge of the basic theories is assumed A bibliography is given at the end of the guide in addition to the explanations of the formulae and algorithms used by the system We strongly recommend that you review each of the examples in turn with this manual and make sure that you understand the results produced Registration entitles you to support so please contact Alastair Day if you need help or more information Systematic Navigation also produces a combined astro and coastal navigation package This comprises three methods of astro navigation sun and moon rise and set estimated position course to steer tidal heights passage planning and satellite positioning for Astra and the other television satellites Copyright Systematic Finance ple 2011 rights reserved intellectual contents and any derivatives or improvements on the Systematic Navigation disk are the property of Systematic Finance plc The programs have been extensively tested however no liability whatsoever can be
79. ellatrix 23016368 2376364 237 38 18 276 7648 222 1364 6 18 6 3425 14 14 237 3548 23r 21 20 2764842 221 8548 22151 29 2656024 15 15 Alnilam 2348520 22348520 2345171 2759913 219 3629 219 21 77 1 2087 S 16 16 Betelgeuse 230 1261 230 1261 23 2 12545 214 6261 2143757 T 4026 17 17 Canopus 2228074 22280974 53 84 2540258 207 3974 2072384 5270015 18 18 Sirius 5776215 21762185 21737 29 28 2024215 202729 3 1571585 19 19 Adhara 574 2467 214 2467 214 14 87 2553751 198746 198448 2697235 20 20 Procyon 564 0906 204 0906 204 5 447 2452190 18850306 10683544 5 2308 21 21 Pollux 5525952 2025952 202 35 71 2437236 187 0952 1875 71 280325 22 22 Avior 553 2491 1932491 193 14 95 22 3 75 dIT 7491 1774495 5950135 3 23 Suhail 541 8979 181 3979 18153868 223 0263 166 3979 158 82368 4342035 24 24 Miaplacidus 540 5504 180 5504 180 33 62 221 6880 165 0604 155362 8970385 25 25 Alphard 537 0153 177 0153 177 0 92 218 1437 161 5153 15133092 6 64545 26 26 Regulus 526 3241 166 3241 166 49 44 207 9525 151 3241 151 19 44 11 9826 N 27 27 Dubhe 5129925 1529925 152 59 55 194 1209 137 4925 137 2955 61 7676 28 265 Denebola 501 6513 141 6513 141 39 086 182 7797 1261518 126 9 086 14 5905 29 29 Gienah 404 9641 1340641 134 57 84 176 0025 119 4641 119 27 84 17 52115 30 30 Acrux 4922612 1322612 132 15 67 173 3896 116 7512 116 4567 63 0749 5 31 31 Gacrux 491 1226 131 1226 131 7 35 172 2510 1
80. he calculation of the GHA and DEC a box reminds you how the ephemeris is being calculated or alternatively the system asks you for data such as the SHA and DEC The information to calculate a position line is now complete and system prompts for a View result for this sight before continuing with other sights b Increase the number of sights to a maximum of three c Enter no more sights and view final results and fix if two or more sights entered d Continue with more sights The default setting continues with more sights if the sight number is less than the total entered on commencement If a is selected then the system calculates and the object bearing and azimuth are displayed together with the computed latitude and longitude position of the intercept The model allows you to re enter the sight details or press OK to accept this result and continue with the next sight When all sights have been entered the options are greyed and the model defaults to calculating a fix Systematic Navigation Options Information now entered for sight number Select option View result for this sight 3 Enter no more sights and view results and fix Continue with more sights The system enters all the data on the Inputs sheet as shown on the next page It is divided into DR Position Bodies observed time and method of ephemeris calculation Altitude correction GHA LHA and DEC Azimuth and Intercept Calculated positio
81. ion View star charts in SHA altitude or bearing order View visible 350 Sun Planets Moon and Stars chart View hour angles and declination for position date and time in Inputs View sun and moon rise and set for position date and time in Inputs Viewmoon rise and set for DR position using Chebyshev coefficients Moon GHA DEC calculations Annual altitude by hour for each day in specified year Annual rise and set chart Great Circle between two points vvith bearing and distance Background calculations Data Data for the date and time in Inputs Version Version information and entries for registration codes Data reproduced with permission from data supplied by HM Nautical Almanac Office Copyright Council for the Central Laboratory of the Research Councils Inputs Results Systematic Navigation www sysmaps com 3 Press Automated Data Entry and the system displays the Main Menu showing the data contained in the model Use Halt to stop here and enter all data manually to the Input sheet If you halt at this point the system does not recalculate and you should use the button or F9 to update the model Automated Data Entry will start a macro described in the following pages with input boxes for the DR position and each of the sights Any data in the model will be entered in the boxes as they open If you do not press this button use the combo box to jump to individual sheets or tab along the bottom in Excel You enter all da
82. ion has a probability P of being located within a confidence ellipse specified by the axes a and b and the azimuth 0 of the a axis where tan2 0 2 B A C a o k SQRT 0 2 5102 b o k SQRT 0 2 10 2 k SQRT 2 log 1 P 2 448 at a probability of 95 13 2 Example This example applies the theory from the previous sections to bring together the calculation of GHA LHA Declination with sight reduction and statistical fixes This example is taken from Compact Data On February 9 1996 at GMT 12 0 0 the DR position is assumed to be 32 N 45 15 W 30 Three sights have been taken along a course of 325 T at a speed of 12 knots The temperature is 9 8 C and the atmospheric pressure 1010 Mb The height of the eye above the horizon is 6 0 metres Sextant index error is assumed to 0777 Star Deneb 53 Time of Sight GMT Difference to DR Time Observed Angle Hs Adjusted Altitude Ho Declination GHA LHA Azimuth Bearing Intercept Distance Direction 6 58 52 5 01 h 217237 387 19 43 5 24 85 S 22 12 08 37 30 48 430 36 38 0 88 Miles Away 7 03 52 4 56 h 28 29 28 22 86 45 16 03 N 294 18 94 219 36 5 52 4 62 0 89 Miles Away 9 53 45 2 06 h 22 28 22 37 43 14 50 27 S 324 53 11 309 42 14 126 19 23 0 02 Miles Towards 7 This is the complete worked example from pages 18 and 19 of Compact Data 1996 The answer g
83. ip the files to a new directory C SFLNavXX In the Windows File Manager choose Run from the File Menu Windows displays the Run dialog box Type a setup in the Command Line Box Choose OK and follow the instructions on the screen The routine decompresses the files and sets up a program group and icons Click the icon twice to start the application Systematic Navigation 20 3 Starting the Application After installing Systematic Navigation open it following the instructions below A 0 Commands Print Information Window Click the icon twice and the system will load Excel and Systematic Navigation When you tirst open the system It will display copyright intormation Press to agree system opens Systematic Navigation Buttons at the top of the screen allow you to Clear the entries and Calculate to re calculate the screen if calculation is not set to automatic The main pull down menus items are Display Main Menu Runs Main Menu Copy Selected Cells Copy selected cells Copy Results Schedule Copy results to a new file Update Stars Charts Copy data and sort stars charts Fill Down Right Fill selection down or right Reset Restore Reset schedules restore normal Excel menus zero all schedules Save Current File Saves current file Close Closes all files and returns to Excel Exit to Windows Quits Excel and prompts for save changes Print Prints schedule Print Preview Print previe
84. ir number to check the attitude and bearing See the Stars section 7 below for a full explanation of the three options Latitude 32 Degrees 45 00 North or South N S Longitude 15 Degrees 30 00 East or West DR Zone Date 09 Feb 96 Enter a date in normal format Zone Time 11 00 00 Enter as hh mm ss GMT calculated by reference to longitude since 15 Degrees equals one hour Course 315 00 Degrees T 5peed 12 00 Temperature 9 8 Degrees Pressure 1010 Position at each sight time calculated against a running fix Number of Sights 3 Routine will allow up to three sights on one sheet When Complete Press OK Press ReDo to re enter The model prompts you for the body observed and the zone time or local mean time GMT 18 calculated by reference to longitude e g 100 W 100 W 360 per day 24 hours 6 67 hours rounded to 7 0 hours If the calculation of GHA and DEC 18 set to automatic as below the explanation is dimmed and the relevant method is shown A for Calculated Almanac and B for Compact Data Press OK to continue or Re Do to return to the Main Menu Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 18 7 Systematic Navigation Sight amp Method Input the Observed Body 1 Sun 2 Star 3 Moon 4 7 Planets Venus Mars Jupiter and Saturn Input Method used for calculating Declination and Greenwich Hour Angle Method Cal
85. isplays the Run dialog box 5 Type a setup in the Command Line Box where a is the drive letter 6 Choose OK 7 Follow the instructions on the screen The system decompresses the files on the floppy disk and then sets up a program group called Systematic Navigation It then creates icons the main application file SFLNavXX xls and the ReadMe and Registration files The command lines should be correct based on your answers during the set up routine If you experience any problems check the command lines to make sure Windows starts Excel or Notepad and then the application file Note that you can always load file manually when you already have Excel loaded To start Systematic Navigation click the icon twice quickly to load Excel and the application A copyright box appears Click and the system displays a description of the information needed See Section 3 2 an overview map of the application and Section 4 for detailed instructions When you first open the application click Halt at the description dialog box and manually tab along the sheets to the end schedule Version Enter the name and code as given to you on your invoice to register the Systematic Navigation Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 7 2 3 Pull Down Menus The pull down menus at the top of your screen are Menu Command Commands Display Main Menu Copy Sele
86. iven is 32 6554 N 32 N 39 3 15 5387 W 15 W 32 3 a 1 257 nm b 2 485 nm azimuth 37 using the same methods for four observations Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 48 Computed Position Position Azimuth 1 Course Distance U 90 6 Take out Excess 300 True Azimuth Bearing Z Plot Position Direction Distance Bearing Miles Latitude Longitude Revised Fix Position Minutes 410 606 315 00 T 1 0038 140 605 039 389 T 0 58 mis 0 654 0 013 E 14 680 W 40 8225 sight 2 037 92 T 0 70 mis 0 703 W 0 013 W 14 721 W 126 3271 T 036 32 T 0 02 mis 0 019 E 0 000 E 15 182 W 10 9464 F Fix Method of Least Squares 1 2564 mis 0 9763 mis 1 2573 mis 1 351 Standard Deviation Deviation Longitude Deviation Latitude 2 Atan 2 Ellipse Azimuth 333 255 Probability P 0 95 Scale Fac 2 4477 3 2776 mis 2 1123 mls A C Sights No of Sights AC B 2 The Model uses the Method of Least Squares to compute a fix at the DR Time of 32 N 38 59 15 W 32 17 This position is on a bearing of 199 45 T 6 66 miles from the DR Position The confidence ellipse is a 3 27 nautical miles b 2 11 nautical miles and the azimuth 0 is 333 25 POSITION 1100 ZT 9 1996 FIX 32 30 59 15 32 17 W 6 66 MLS 196 55 T B DR 327 45 15 30 W 2 00 DR 32 45
87. l v5 0 31 March 2011 Page 60 19 Worked Examples 19 1 Sun Moon and a Star on 21 June 1994 Check the Scenarios in the application 2003 Tools Scenarios 2007 Data What if Scenarios as all the examples are included in the model A ship at ZT 22 0 0 GMT 23 0 0 on 21 June 1994 calculated its DR Position as 32 0 N 15 0 W and has followed a course of 325 00 T at a speed of 8 knots per hour for several hours Three sights have been taken and a fix is now sought to check the transferred positions The individual sights are 1 Sun at ZT 18 0 0 GMT 19 0 0 at an altitude of 11 57 0 2 Moon at ZT 18 23 30 at an altitude of 11 34 0 3 Star thought to be Kochab 40 at ZT 21 23 20 at an altitude of 46 31 0 and a bearing of 356 0 0 At 15 W the model calculates the local time as GMT 15 W 360 24 GMT I hour the usual convention for West and South is negative The star finder and identification routines are used to ensure the accurate selection of the star A following page shows the location of all Navigational Stars for the DR time and position in this example Summary of results Star Kochab 40 Time of Sight GMT 19 00 00 19 23 00 22 23 20 Difference to DR Time 4 h 00 m 3 h 36 m 0 h 36 m Observed Angle 11 57 0 11 34 0 47 31 0 Adjusted Altitude 12 8 35 12 44 94 47 30 09 Declination 23 26 29 N 20 17 28 S 74 10 93 N GHA 104 33 7 314 48 56 23 1 61 LHA 89 53
88. lculation option set to iteration If you start the application from an icon the system should suppress this message The systems sets up the calculation method as it opens so you need take no further action Systematic Navigation Copyright Registered version of Systematic Navigation 31 Dec 2015 All rights reserved All intellectual contents and any derivatives or improvements are the property of Systematic Finance Limited The application has been extensively tested however no liability can be accepted regarding the accuracy of the application and its associated data Reproduced with permission from data supplied by HM Nautical Almanac Office Copyright Council for the Central Laboratory of Research Councils Select language for reports and charts Language 8 English Deutsch Enter Working Directory if different C Windows system32 c Systematic Navigation Orchard House Green Lane Guildford Surrey UK GU1 2LZ Press to continue Tel 44 0 1483 532929 Fax 44 0 1483 5 Email No info system co uk Version 5 0 31 Mar 2011 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 15 2 Press OK and the system displays the Main Menu showing the data contained in the model Use the control to select Inputs directly or press Automated Data Entry to enter data via dialogue boxes The options are ReadMe Overview Registration Inputs Results
89. lination for GMT 0 0 0 on the day of the sight Planets also need the correction per hour and this is also found on the daily page in the Almanac Press Re Do to re enter information or OK to continue to the Options Box at the end of the Sight Example The GHA and DEC of Mars on 28 March 1996 at GMT 12 0 0 From The Nautical Almanac the GHA and DEC at GMT 0 0 0 is 182 57 3 and 0 N 16 6 respectively The variations per hour are 15 011458 and 0 791667 and the model interpolates the data Publications such as The Nautical Almanac provide shorter intervals by displaying data in hourly intervals The interpolation formula is GHA day 0 at GMT 0 0 0 decimal hours GHA GHA day o 24 In this case 182 966 12 360 183 230 182 966 24 182 966 12 15 011458 363 0925 Removing multiples of 360 GHA 3 0925 37 5 5 Mars GHA and DEC Mars GHA 182 955 Mean Variation 15 0115 Correction 12 hours 180 1374 Calculated GHA 213 0237 Mars GHA 3 0925 3 5 549 Mars DEC 0 276667 N Daily Variation 0 316663 Hourly Variation 0 013194 Variation 12 hours 0 158332 Mars Declination 0 434999 0 N 26 099 This is an extract from the Inputs sheet showing both methods The left hand column shows the results using Method A and the right hand column Method B see next page Input Mars DEC O N 16 60 Calc DEC O N 0 00 Mea
90. n Variation Hour 0 0 79 0 0 00 Corr 12 0 0 GMT 0 946 0 0 00 Mars Declination 02508 North Mars DEC 26 12 North Input Mars GHA 187 51 20 Calc GHA 0 0 00 Variation Hour 15 0 69 0 0 00 Corr 12 0 0 GMT 180 6 20 0 0 00 Mars GHA LHA 3 5 58 j3 5 55 Mars J55 355 Azimuth Bearing 2187 0 21 218 0 21 216 1 00 218 1 09 Intercept Miles 123 08 mils Towards 123 04 mls Towards Calc Position 0 16 5 1 0 16 5 N 1 56 9 W Example from the tables on page 68 of The Nautical Almanac 1996 GHA 3 091667 37 5 5 DEC 0 4350 0 N 26 1 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 40 9 2 Method B Polynomial Coefficients The model contains all the coefficients ag to for GHA and DEC together with ao and a for the semi diameter The system looks up the coefficients from the relevant schedule There are separate schedules for Venus Mars Jupiter and Saturn providing monthly data for each month from January 1991 to December 2015 Using the example above the polynomial coefficients are Mars GHA and DEC a 11 7031500 8 4901000 a 0 5327300 9 7093000 0 0473400 0 6257000 0 0140400 0 3136000 0 0013800 0 0052000 Check Sum 12 2705600 1 5365000 Days X 0 8906 87 230 Calculated 12 2061 0 4353 GHA and DEC 363 0917 0 4353 Degrees 3 5 502 0 26 118 HP ag 0 00100 HP a 0 00000 Check Sum
91. n and confidence ellipse Further pages detail the calculations for GHA and LHA DEC Observed Altitude Ho Computed Altitude Hc and the derivation of the statistical fix and error probability Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 20 DR Position Calculated Position A English DR Latitude 32 H 45 00 a2 N 38 57 Confidence 95 00 DR Longitude 15 W 30 00 15 W 32 23 Ellipse DR Zone Date 9 Feb 96 Friday Distance 6 696 mls Latitude 2 12 mls Zone GMT 11 00 00 12 00 GMT Bearing 196 92 T Longitude 3 28 mls Course Speed 315 00 T 12 00 kn Bearing 333 24 T Sight 2 Sight 3 Which Sight 3 2 Star 1 Sun Method Calculated B Polynomial A Calculated Actual Sight Time 5 58 52 06 58 GMT 6 03 52 07 03 GMT 8 53 45 09 53 GMT Time Diff Miles 5 01 hrs 60 23 mls 4 55 hrs 59 23 mls 2 06 hrs 25 25 mis Revised DR Position 32 2 4 N 14 38 47 W 32 3 1 N 14 40 27 W 27 1 MH 15 8 87 W DR Star Altitude 0 00 0 0 00 0 0 00 0 DR Star Bearing 0 00 0 0 00 0 0 00 0 Star Number 1 Input Star No 53 Deneb 0 0 DR Alt Bearing 38 1478 230 34 6 28 29 15 52 792 22 35 1 126 23 02 Observed Angle 25 00 28 29 00 22 28 00 Index Minutes 0 00 0 00 0 00 On Off the Arc M F F Off Arc F Off Arc F Off Arc Height of Users Eye 6 00 mtr 6 00 mtr 6 00 mtr Upper Lower Limb L Lower L Lower L Lower Moon HP SD
92. o Moon Set Hext day 05 45 AM 12 04 05 07 AM 04 28 03 46 AM 11 54 AM SYSTEMATIC NAVIGATION RISE AND SET 50 0 N 0 VV ON 26 MAR 1996 05 45 00 12 04 59 05 07 07 04 28 02 03 46 41 11 54 47 I I I I I T I I I I Sflnav50 doc Set onetime G T UT 06 25 PM 18 25 58 07 03 19 03 51 07 43 PM 19 43 01 08 24 zZ0 24 28 03 06 AM 03 06 57 29 Mar 56 848 18 6 2 65 41 47 180 0 59 12 203 0 899 6o 10 97 290 49 03 50 28 08 31 92 To 0 25 261 6 99 Manual v5 0 31 March 2011 Page 52 6 46 N 18 84 M 31207291 F EZM 19 44 M DAM F 20 17M F 4 56 N F 20 76 M 16 6 72M 15 5 16 20 24 ZT 254 55 63 15 41 2356 45 15 104 44 287 245 44 097 114 31 717 124 53 79 263 57 14 fo 231 264 55 63 15 41 390 45 15 104 44 287 245 44 097 114 31 717 124 53 79 263 57 14 fo 23 17 Moon zet 15 Great Circle The application provides a separate sheet for calculating e Destination latitude and longitude given a bearing and distance as below e Bearing and distance from start and destination latitude and longitude positions next page Inputs Results Date Destination Date Time ETA Time Units Hours Taken Degrees Minutes 1 Destination Starting Latitude Starting Longitude Destination Latitude 0001 2 Bearing Distance Destination
93. one Time of Sight Object Sun 59 Stars Moon Venus Mars Jupiter Saturn Method chosen under automatic calculation Type Aries Almanac Coefficents 1891 2015 1891 2015 1991 2015 lated 1991 2015 alculated 1991 2015 Calculated 1991 2015 Calculated 1991 2015 Sextant Altitude Hs Corrections Index Height On Off Arc Upper Lower Limb Calc Input Data Displays result of each sight intercept and azimuth Statistical if applicable 1 View input sheet and halt for manual input 2 View results summary and chart plot 3 View chart plot and positions of sun moon etc 4 Update star chart by bearing or altitude 5 View Stars Charts 6 View positions of sun moon planets and star T View sun and moon rise and set 8 View background calculations and aries coefficients View polynomial data for date of sights 10 Re run some or all of the sights 11 Halt for manual input 12 Exit Systematic Navigation with save file options Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 11 For completeness this is a listing of all the schedules in Systematic Navigation When you open the application you enter data to dialog boxes which the system enters directly to the Inputs sheet This sheet calculates the results and retrieves data from other background schedules The system displays the plots on the Results SightCharts StarsCharts and Posi
94. r Systematic You have a limited licence to use the software for the period of time stated on this software copyright notice and to make copies of the software for backup security purposes only This is a single copy software licence granted by Systematic You must treat this software just like a book except that you may copy it onto a computer to be used and you may make an archival backup copy of the software for the purposes of protecting the software from accidental loss The phrase just like a book is used to give the licencee maximum flexibility in the use of the licence This means for example that this software can be used by any number of people or freely moved between computers provided it is not being used on more than one computer or by more than one person at the same time as it 15 being used elsewhere Just like a book which can only be read by one person at a time this software can only be used by one person on one computer at one time If more than one person is using the software on different machines then Systematic s rights have been violated and the licencee should seek to purchase further single copy licences In the case of multiple licences or network licences the number of users may only equal the number of licences You may not make any changes or modifications to the licenced software You may not decompile disassemble or reverse engineer the licenced software You may not rent or lease the software to others If yo
95. rection to the altitude for refraction instrument error height etc e Computing the position of the body observed Local and Greenwich Hour Angles and Declination e Sight reduction computation of the altitude and bearing at the time of sight e Position lines comparing the sight reduction with the actual sight and plotting a sight line and distance from the assumed position Entering further sights to derive and plot a statistical fix Position lines are generally assumed to be straight over distances up to a few hundred nautical miles The observer lies along or close to each calculated position line so that the intersection of several position lines increases the accuracy of the fix To determine the position line the altitude of the body is observed above the horizon with a marine sextant The observer applies corrections to the observed altitude It can then be compared with the calculated altitude of the centre of the body as if seen from the centre of the earth with no atmosphere Corrections include instrument or index error height of the observer s eye above the horizon and the upper or lower limb of the body observed PATH OF INDEX MIRROR rmn es wath the index armi MIRROR half sibeered to refhect image of a heavenby body one side The other part is clear to see the Horizon OB SERVER S EVE 725 i i i x GRADUATED SCALE
96. ring of 107 38 degrees from the DR position DR Position Calculated Position Position Error DR Latitude 32 N 1 00 32 M 0 02 Confidence DR Longitude 7 14 W 38 00 14 W 34 45 Ellipse 95 00 DR Zone Date 14 Sep 11 Wednesday Zone GMT 5 30 00 06 30 GMT Distance Bearing Latitude 1 50 mis Course Speed 315 00 T 12 00 kn 3 15 mls 107 38 T Longitude 2 99 mis Temperature amp Pressure 9 60 C 1010 00 mb Bearing 011 31 T Sight 1 Which Sight 3 Moon 2 Star 5 Mars Calc Almanac Palynomial B Polynomial B Polynomial B Polynomial Star Number 49 18 Sirius 0 Actual Sight Time 4 54 57 05 54 GMT 5 05 21 06 05 GMT 5 15 23 06 15 Time Diff Miles 0 35 hrs 7 01 mis 0 24 hrs 4 93 mls 0 14 hrs 2 92 mls Revised DR Position 31 55 14 32 27 W 31 57 5NM 14 33 9 W 3156869 14 35 67 W DR At Bearing 31 24 260 13 21 a2 S462 143 15 08 47 1 49 91 54 05 Observed Angle 30 26 596 32 425 471047 Index Error Minutes 0 00 0 00 0 00 Height of Users Eye DIP 4 31 4 317 4 317 Refraction R Ro f 1 61 1 55 0 93 Parallax in Altitude 45 60 0 007 0 05 Semi Diameter 14 717 0 00 0 00 Corrected Altitude 31 21 82 32 37 04 47 522 Calc Declination 8 45 45 North 16 43 82 South 21 35 81 North Moon GHA 12 52 1 58 19 94 342 47 9 328 14 01 327r 28 1 312 52 54 Azimuth Bearing 260 15 24 807 13 21 1437 15 08 143 15 08 91 54 05 97 4 05 Intercept Miles
97. rizontal Parallax of Sun Moon Venus or Mars PA Parallax in Altitude of Sun Moon Venus or Mars HP COS 5 Semi diameter of the Sun or Moon Add lower limb and subtract upper limb Ho Observed Altitude apparent altitude corrected for refraction and if appropriate corrected for parallax and semi diameter H R OB 5 Calculated or Computed Altitude see section 11 2 Azimuth true measured clockwise around the horizon from 0 to 360 Defined as the arc of the horizon between the meridian of a place and a vertical circle passing through a celestial body Intercept of a sight Ho Hc Towards positive Away negative Atmospheric Refraction Course or track measured as for azimuth from 0 to 360 Speed in knots 242170 Latitude and longitude may be written in degrees with decimals minutes You usually enter degrees and minutes which the application converts to decimal degrees Similarly longitude can be converted to time since 15 is equivalent to one hour Local Mean Time is referred to as Zone Time ZT and GMT are calculated by reference to longitude GMT or UT Zone Time west longitude or east longitude converted into hours 1 e 15 W plus one hour Declination DEC is equivalent to the latitude of the body observed and measured in degrees north or south For example the Sun moves from the furthest position in the South on 21st December to the 21st June in the Nor
98. rred to in this manual as Compact Data The model derives a series of coefficients to calculate the GHA Declination and if applicable the horizontal parallax and semi diameter of the body observed The model computes the DEC and GHA and adds the longitude to convert to LHA Local Hour Angle The most convenient method for calculating GHA and Declination for each body is shown below The model will prompt you for the method to be used on all sights Similar to Methods A and B the celestial bodies are referred to throughout the model by their numbers below 1 2 3 4 Sun Under A GHA and DEC are calculated for 1989 2015 and under Method B the coefficients for 1991 2015 are contained in the model If you enter an observation for another year Method B will prompt you for the coefficients applicable to the month and year Stars The model requires the SHA and DEC under Method A however the data under Method B for the years 1991 2015 are contained in the model The apparent position of the Stars does not vary month to month and therefore the coefficients are contained on just two five year tables Moon Method A and B are calculated for 1989 2015 Method B uses monthly Chebyshev coefficients contained in the model Planets These are denoted as 4 Venus 5 Mars 6 Jupiter 7 Saturn Under Method A the Greenwich Hour Angle and the Declination together with hourly corrections must be input The pol
99. s OB 0 0017 cos H Horizontal Parallax HP Parallax in Altitude PA HP cos H Semi Diameter S add lower limb Corr Altitude Ho H R PA OB S 0 0000 0 068 1 0 0423 1 0184 0 0024 21 3283 21 2602 0 043 1 0 0000 0 0022 0 2684 21 4878 0 0000 0 068 1 0 0251 1 0184 0 9922 33 4600 33 3919 0 0256 0 0014 0 8284 0 2704 34 4637 0 0000 0 0681 0 1801 1 0184 0 0021 4 5433 4 4752 0 1834 0 0000 0 002 1 0 0000 4 2940 2 Example from page 281 of The Nautical Almanac 1996 Answers given 21 4877 34 4644 and 4 2935 The slight differences on the Moon and Venus are explained by 0 005 variation in the horizontal parallax Their example also ignores the oblateness of the Earth which yields a small variation P Note that with a bubble sextant no correction for height is needed Formula from a paper by Bennett 1982 Journal of the Institute of Navigation volume 35 page 255 9 Add lower limb and subtract upper limb Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 45 12 Sight Reduction 12 1 Method The model uses the classic Marcq Saint Hilaire method to reduce the sights as the mathematical link between the observer and the celestial body If you know your latitude and longitude you can predict the true bearing and the height of
100. ta on the Inputs sheet and the calculations are used on all the other sheets and charts The following pages show the automatic sequence Reset to top of page resets all sheets to the top ready for saving Use Custom Toolbars and Excel Toolbars to toggle between the application and Excel toolbars Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 16 Systematic Navigation Information Astro Navigation fixes positions with up to three sextant sights by two distinct methods using 1 Sun 2 Stars 59 Navigational Stars 3 Moon 4 Planets Venus Mars Jupiter and Saturn Input 1 DR Latitude Longitude Date Time Course and Speed 2 Body Observed Time Observed Altitude U Lower Limb and Height 3 Dedination Greenwich Hour Angle GHA Calc Sun and Moon Almanac needed for Stars SHA and Declination Planets GHA and Declination plus Hourly variation Polynomial Coefficients from Compact Data for Navigation and Astronomy for 1991 2005 No inputs for the Sun Stars Planets Coefficients needed for the Moon from Compact Data inputs for the Sun Moon on Method A and the Sun Stars Planets on Method Azimuth Intercept displayed Fix given for two sights or more Press HALT or OK to continue HALT c Systematic Navigation Version 5 0 31 Mar 2011 4 Press OK and the system requests you to select general options for
101. tationery Office and the UK Hydrographic Office www ukho gov uk Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 76 22 Bibliography We would like to thank the authors of these publications which proved to be invaluable reference guides in the preparation of Systematic Navigation 10 11 12 13 14 15 16 LT The Nautical Almanac 1994 HM Nautical Almanac Office ISBN 0 11 772737 7 The Nautical Almanac 1996 HM Nautical Almanac Office ISBN 0 11 772814 4 The Macmillan and Silk Cut Nautical Almanac 1994 Macmillan ISBN 0 333 58729 4 The Macmillan and Silk Cut Nautical Almanac 1996 Macmillan ISBN 0 333 61049 0 0 333 660536 Astro Supplement Yallop B D and Hohenkerk C Y 1991 Compact Data for Navigation and Astronomy for the Years 1991 1995 Cambridge University Press ISBN 0 521 38731 0 Yallop B D and Hohenkerk C Y 1995 Compact Data for Navigation and Astronomy 1996 2000 HMSO ISBN 011 772467 X Yallop B D and Hohenkerk C Y 2000 Compact Data for Navigation and Astronomy for the Years 2001 2005 The Stationary Office ISBN 0 521 38731 0 Yallop B D and Hohenkerk C Y 2004 Compact Data for Navigation and Astronomy 2006 2010 TSO The Stationary Office ISBN 011 887331 8 NavPac and Compact Data 2006 2010 FERES um Fames m d m m nc Yallop B D and Hohenkerk C Y 2010 Navpac and Compact Data 2011 2
102. th Hour Angles are the equivalent of longitude except that longitude 18 measured up to 180 degrees whereas hour angles have values up to 360 degrees Three kinds of hour angle are used to calculate positions e Sidereal Hour Angle SHA are based on a meridian line c f Greenwich for longitude and in the heavens this is the first point of Aries The SHA 18 the degree s difference to Aries the hour equivalent of the Greenwich meridian e Greenwich Hour Angle GHA is the addition of the Aries position and the Sidereal Hour Angle e Local Hour Angle LHA completes the calculation as the addition of the GHA and Longitude West is subtracted Therefore LHA GHA aries SHA observer s longitude Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 13 4 Using Systematic Navigation 4 1 Method Systematic Navigation incorporates two different methods of computing the Local Hour Angle and Declination of the observed body The two methods are denoted as A or B throughout the model A B Almanac Calculated The model will compute the position of the Sun and Moon automatically and will prompt for Almanac data on the SHA and DEC for Stars and the GHA and DEC Planets You will find this information on the page in an Almanac containing the day of the observation Polynomial Coefficients These are extracted from Compact Data for Navigation and Astronomy by Yallop and Hohenkerk refe
103. the sights These are set to true and they must be clicked to de select them The options are a Keep DR Dead Reckoning position and time b Calculate GHA and DEC automatically c Keep existing sight results Clicking a or c will cancel the sights held in the system If the selection is left untouched the system will load the currently saved entries into the dialog boxes for cancellation editing and amendment Sight Data can be changed and this option does not prevent future editing Clicking b allows you to choose the method of computing the GHA and DEC Select to continue or Re Do to return to the previous screen Explained in section 4 1 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 17 5 6 Systematic Navigation DR Position A box requesting the DR position and zone time together with any course and speed between the DR position and the sights if applicable The zone time is calculated with reference to longitude and no account is taken of any local time differences e g Winter and Summer time You should also enter the number of sights maximum three However if one or two are entered and you chose the retention of current data any sight numbers above the number of sights chosen will be erased when calculating fixes Press OK to continue or Re Do to return to the Main Menu For stars there is a subroutine for identifying stars or using the
104. tions schedules There are two input methods you can enter data directly to the Inputs or use the dialog boxes to enter the data in stages The doalog boxes check your inputs and should remove most input errors ReadMe 1 On line notes on Systematic Navigation Overview 2 Useful map of the application previous page Registration 3 Shareware registration document Inputs Main input sheet and results sheet with workings Results 5 Summary inputs and results with chart plot SightCharts 6 Chart plot and positions plot of the Sun Moon and Planets StarsCharts 7 Star chart plotted in number order or by altitude bearing or SHA Positions 8 Calculated position of all bodies at the dead reckoning time RiseSet 9 Sun and Moon rise and set including Sun transits Moon 10 Moon rise and set using Chebyshev coefficients Altitude 11 Altitude by hour and day for a year for selected object Aries 12 Background calculations Data 13 Derived polynomial data for the dead reckoning date Stars 14 Polynomial data lookup table four tables for 1991 1995 1996 2000 2001 2005 and 2006 2015 Sun 15 Monthly polynomial data lookup table Jan 1991 December 2015 Moon 16 Monthly polynomial data lookup table Jan 1991 December 2015 Venus 17 Monthly polynomial data lookup table Jan 1991 December 2015 Mars 18 Monthly polynomial data lookup table Jan 1991 December 2015 Jupiter 19 Monthly polynomial data lookup table Jan 1991 December 2015 Sa
105. ts It uses these expressions Calculate t where cos t sin h sin Lat sin Dece cos Lat cos Dece h 0 8333 for Sun rise or set 6 for civil twilight and 12 for nautical twilight sunrise 90 Longitude t GHAg 15 sunset 270 Longitude t 15 The model uses similar expressions for the Moon however the passage of this body is more complicated The system iterates an answer despite the possibility of rising and setting on different days The model also derives Sun transits T 12 Longitude converted to hours Time 24 Longitude in hours y where y is GHA GMT in hours evaluated at time Phases of the Moon Sun s Rays View from Earth a Inferior Waxing Conjunction Crescent Crescent First Last Quarter Quarter Waxing Opposition Waxing Gibbous 4 e Gibbous Full 3 Moon Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 51 14 2 Example This example is for March 28 1996 at 50 N 0 0 E 0 Rise Oe tine GMTSUT Rise and Set Position Data Azimuth Declination 1 55 Example from The Nautical Almanac 1996 Answers given Rise Nautical 04 31 Civilian 05 10 Sunrise 05 43 Moon 11 53 Set Sunset 18 28 Civilian 19 00 Nautical 19 39 Moon 02 20 Sun transit 12 05 Systematic Navigation www sysmaps com Sun Sun Transit Civilian Nautical Astr
106. turn 20 Monthly polynomial data lookup table Jan 1991 December 2015 Version 21 Version data on Systematic Navigation Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 12 3 4 Glossary All distances are given in sea nautical miles One nautical mile 1 Metres 1 852 00 metres 1 85 kilometres Yards 2 026 08 yards 1 metre is 1 094 yards English Miles 1 15 miles 1760 yards to the mile A nautical mile corresponds to one minute of latitude and is made up of ten cables thus sixty miles is equal to one degree of latitude Units of longitude vary with latitude and cannot be calculated in this manner Explanation GMT Greenwich Mean Time Synonymous in this context with Universal Time UT Lat or B Latitude north positive south negative Shown as 15 N 12 33 or 15 2055 Long or L Longitude east positive west negative GHA Greenwich Hour Angle GHA aries SHA measured in degrees E from 07 to 360 SHA Sidereal Hour Angle 360 Right Ascension DEC Declination measured in degrees north positive and south negative LHA Local Hour Angle GHA Longitude measured in degrees E from 0 to360 Hs Sextant Altitude measured by the observer s sextant 1 Instrument or Index Error D Dip of horizon height of the observer s eye above the horizon H Apparent Altitude sextant altitude corrected for instrument error and dip Hs I D HP Ho
107. u wish to pass your software licence to another person you may However you must provide all original disks documentation and remove the software from your own computer s to remain within the single copy licence agreement In addition you must inform Systematic in writing immediately in the event of any such transfer and provide the new holder s name company telephone and fax number To do otherwise will violate Systematic s rights Systematic warrants that the supplied media are free from physical defects If the media appear to be faulty then Systematic will supply free of charge replacement disks up to thirty days from the despatch date Systematic warrants that the software will perform substantially in accordance with the documentation supplied with it Systematic does not warrant that the functions contained in the software will meet your requirements or that the operation of the software will be uninterrupted or error free This warranty does not extend to changes made to the software by third parties nor does it extend to liability for data loss damages or lost profits due to the use of the software Systematic does not accept any responsibility for software failure due to changes in the operating environment of the computer hardware or operating system made after delivery of the software Copyright O Systematic Finance plc 2011 Crown Copyright and or database rights Reproduced by permission of the Controller of Her Majesty s S
108. ulations on the two other pages on the Inputs schedule This is the first page of workings showing the Greenwich Hour Angle Declination Polynomial Coefficients if used and the corrected altitude The methodology follows The Nautical Almanac These figures are summarised on the first page and on the Results schedule You can improve the position fix by selecting iteration on the Inputs sheet This will attempt to converge and improve the solution Calculation Method a Mo iteration use first answer O Use iteration to improve fix Example from pages 18 and 19 of Compact Data 1996 Fix with four sights including Kochab 40 327 39 3 15 W 32 3 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 21 A GHA and DEC Workings Sun DEC amp GHA Sun DEC Convert to Radians V DEC E Declination in Degrees X Add to 180 Calculated Sun GHA Star DEC and GHA SHA Calc GHA Aries Calc Star GHA and DEC Coefficient 40 Coefficient A1 Check Sum SemiDiameter 5 0 Minutes B Calculated GHA and DEC Moon GHA Mean Variation Final DEC Mean Variation Variation Moon Declination sight 1 6 00 hrs 0 0 0000 sight 1 GHA 0 0000000 0 0000000 0 0000 Polar Stars on Alt Azimuth Corrected Altitude Decimals Altitude Observed Hs Index Error 1 DIP Height D 0 0293 5qrtH Apparent Altitude H
109. ws and allows printer set up Print All Prints all schedules Read Me Displays information and licence agreement Overview Flow chart of application Registration Displays and prints registration document Version Displays version information Information Displays copyright and registration information Arrange All Windows Tiles all open windows into sectors Unfreeze Freeze Panes Unfreeze or freeze current window panes Maximize Window Sets the window size to the full screen Save this file with your results whenever you exit Systematic Navigation All reports were prepared with an HP laser printer if you have problems adjust the magnification in Print Preview Keep all files in the same sub directory they will not work correctly if split between different directories Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 73 20 4 Registration This registration form can be used to register evaluation copies of Systematic Navigation or other products The cost is GBP 30 or equivalent as listed from time to time on the web site Systematic Navigation Version 5 0 31 Mar 2011 Registered Copy Thank you for your interest in our products You can register the Systematic Navigation in two ways 1 Post Complete the details below and send the form to Alastair Day at Systematic Navigation together with your remittance UK cheque or equivalent 2 Credit Cards only at the website ww w s
110. ynomial coefficients for 1991 2015 are in the model for Method The above provides some flexibility the model and the results will be very similar To reduce the complexity of the above you can decide to compute the GHA and DEC automatically and in this case the routine will choose either Calculated Almanac or B Compact Data as follows 1 2 3 4 Sun Method B for 1991 2015 otherwise Method A The model derives the coefficients for 1991 2015 and will also calculate the semi diameter accurately as opposed to using the single figure of 16 used in Method This will account for any resulting small differences between the two methods Stars Method B polynomial coefficients provided for the years 1991 2015 Moon Method and with no inputs needed Method is more accurate using the Chebyshev coefficients Planets Method B polynomial coefficients provided for the years 1991 2015 Systematic Navigation www sysmaps com Sflnav50 doc Manual v5 0 31 March 2011 Page 14 4 2 Procedure 1 Double click Systematic Navigation in the program group or load SFLNavXX xls and the application displays a copyright box and requests confirmation of the working directory and language for the reports If the system displays the circular errors box press OK and continue This is merely informing you that the workbook may contain circular arguments and needs the ca
111. ystem co uk Important The secure server is for orders only any questions about the status of the shipment of the order refunds registration options product details technical support volume discounts dealer pricing site licences etc must be directed to Systematic Navigation When ordering by credit card be sure to quote your full details This is a secure web site managed by Vlorldpay part of the Royal Bank of Scotland plc Errem VISA 1 payments powered by WorldPay Mark above the application and number of you require remittance the sum 25 00 is enclosed Where did you obtain your evaluation copy These items are software and Value Added Tax Sales Tax will be where appropriate We will send you by email the most recent version on a disk together with a full manual containing worked examples of all options and a password to access the add ons You will also be entitled to free and all upgrades and additions to Systematic Navigation soon as they become available Worldwide postage and packing will also be added where appropriate Please contact Alastair Day at the address above if you would like any further details or informati Hame Please enter your name and address Company Mame Full Address Postcode Zip Code Telephone Number Fax Number E Mail Other Information Other Information and Suggestions on the software Delete as applicabl

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