NAVIGATIONAL HINTS 



LATITUDE BY 

 MERIDIAN ALTITUDE BELOW THE POLE 



Polaris is probably the most useful of all the stars in the higher 

 northern latitudes and provides the mariner with his latitude, under 

 reasonably favorable conditions, at any hour of the night. There is 

 also another excellent, but seldom used, method of obtaining a 

 much-desired latitude. This method involves finding the altitude of 

 a circumpolar star when it is on the observer's meridian below the 

 pole. While the method can be used in both the higher northern 

 and southern latitudes, it is especially useful in the southern hemi- 

 sphere where no guardian of the south celestial pole, such as Polaris, 

 is available. 



A circumpolar star is by definition a star which revolves around 

 the elevated pole without setting. This situation occurs when the 

 polar distance of the star is less than the observer's latitude and 

 both have the same name. 



Figure 3 



In figure 3, AWBE is the diurnal circle of a circumpolar star 

 in the southern hemisphere. Line AB is the observer's meridian. 

 At A the star is on the observer's meridian, bears south and has 

 reached its highest altitude. During the next six hours, the star 

 will fall towards the west. Then, continuing to fall, the bearing will 

 curve eastward for six hours until the star reaches point B. At B 

 the star is again on the observer's meridian, bears south, and has 

 reached its lowest altitude. From point B the star will rise towards 

 the eastward for six hours, then while still climbing, it will curve west- 

 ward completing one day's revolution when it again reaches point A. 



To find the latitude, subtract the star's declination as tabulated 

 in the Nautical Almanac for the appropriate date from 90°. The 

 result is the star's polar distance. Add, to the polar distance, the 

 corrected observed altitude when the star was at point B; the sum 

 equals the latitude. The following example demonstrates the ease 

 of the process. 



On July 4, 1965, after several days of squally overcast weather, 

 conditions improved and the navigator observed Achernar close to 

 being on his meridian below the pole. A series of observations were 

 taken and finally a low reading of 20°12.r was obtained. Knowing 

 the height of eye was 44 feet and having no instrument correction, 

 the navigator laid out the work: 



MERIDIAN ALTITUDE OF ACHERNAR BELOW POLE 



OBSERVED ALTITUDE 20° 12.1' 



ALTITUDE CORRECTION ( — ) 02.6' 



HEIGHT OF EYE (-) 06.5' 



TRUE ALTITUDE 



20" 03.0' 



NOTE: Corrections obtained from Nautical Almanac 



FIX RELIABILITY 



The pinpoint fix, whether obtained by stars, cross bearings of 

 terrestrial objects, radio bearings or other means, is always a source 

 of confidence to the navigator in that he knows his exact position at a 

 specific time. Unfortunately, this single point is often very elusive 

 and a round of stars or bearings leaves the navigator with a triangle 

 or square for a fix. Some interesting hints about the latter merit 

 review. 



First, let us look at the case of star sights. As previously 

 mentioned, a systematic error is often introduced in the observation 

 of stars. Based on the assumption that this error is equal for each 

 star, a very reasonable assumption, it becomes apparent that we can 

 improve the fix reliability by properly adjusting the various lines 

 of position. 



Proper adjustment means that each line of position must be 

 moved equally in distance and direction, either all towards or away, 

 from the bearings of the observed bodies. When this is done, the 

 navigator many times is able to completely close the triangle or 

 square. The amount of adjustment necessary is found by trial and 

 error. Occasionally, the actual position will be foimd to be outside 

 the original fix shape altogether. 



Figure i. 



—n— 



In figure 4, the solid lines represent the position lines of 3 stars 

 after being advanced to a common time. The bearings of the 

 observed bodies are indicated by the small arrows. The dashed 

 lines represent the new lines of position after the navigator has 

 shifted them equally towards the bearings, figure 4, (A) and (C), or 

 away (B), in order to make them cross at a common point. Looking 

 at (A) and (B), it is at once apparent the actual position does lie 

 within the original triangle. In (C), however, it is obvious that the 

 lines will cross only at some point outside the original triangle. The 

 value of placing the small arrows on the various position lines, to 

 indicate bearing, cannot be over emphasized. 



The desirability of taking stars to the north and south of the 

 zenith has already been discussed. If, in addition, it is possible to 

 take sights to the east and west of the observer, the best possible 

 indication of fix reliability is obtained. In figure 5, the position lines 

 of 4 stars are shown, with their bearings lying in the direction of the 

 arrows. Looking at (A) and (B), it is again apparent that the actual 

 position lies within the square and that the fix is reliable in both 

 latitude and longitude. In (C), however, the latitude is rehable but 

 the longitude is doubtfiil. 



Figure 5. 



Before looking at the problems of reliability of terrestrial fi:es, 

 let it be stated with the utmost emphasis that whenever three or more 

 charted objects are available, a fix should consist of a minimum of 

 three cross bearings. Even if the compass error is known, there is no 

 check that a two bearing fix has been properly plotted on the chart. 

 The third bearing will make any error in plotting immediately appar- 

 ent. Frequently, a round of bearings, properly observed and plotted 

 on an accurate chart, still do not cross at a common point. There is 

 only one answer under these circumstances and that is compass error. 

 This unknown compass error will affect each bearing by the same 

 amount. By trial and error, the navigator can shift all the bearings 

 clockwise, then counterclockwise until the bearing lines do cross at a 

 common point. Often the vessel's actual position will be outside 

 the original triangle. The navigator has not only accurately deter- 

 mined his position, but has also obtained the compass error which 

 equals the number of degrees necessary to adjust the bearings. This 



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