3362 HYDROGRAPHIC MANUAL PaGE 228 



of value to assist in controlling a dead-reckoning line of soundings. If the survey of an 

 offshore area is controlled by astronomic observations, the positions of the sounding 

 lines may frequently be strengthened by the observation of numerous bearings on an 

 isolated island which is passed by the sounding Ime at a considerable distance. 



For the survey of an isolated shoal one survey buoy is frequently anchored at the 

 approximate center of the shoal, the area being developed by a system of soimding lines 

 radiating from the buoy. Bearings are useful to control the sounding lines in azimuth 

 relative to the buoy, the distances from the buoy being determined by vertical or 

 depression angles or dead reckoning, as described in 368. 



3362. Distance by Depression Angle 



The distance between the survey vessel and an object at sea — usually, but not 

 necessarily, a survey buoy — may be determmed by the measurement with a sextant of 

 the small depression angle between the waterline at the object and the horizon beyond. 

 The distance varies with the observed angle and the height of eye of the observer; for 

 a given horizontal distance the greater the height of eye the more accurate will be the 

 determination. The distance may be computed from the furmula 



j^__ HQOt (a+d) 

 3.28 



in which D is the distance in meters to the object, H is the height in feet of the eye 

 above sea level, a is the observed angle, and d is the dip of the sea horizon. 



The dip may be taken from a table which will be found in any epitome of navi- 

 gation (e. g., table 18 in the American Practical Navigator— Bowditch) or may be 

 computed from the formula 



d^Br^/lT 



d and H being the same as above. 



Tables or curves as illustrated in figure 57, showing the distances in meters for 

 various angles and heights of eye may be prepared to facilitate the computation if 

 frequent use is to be made of such angles. 



This formula does not include any correction for curvature or refraction. It 

 should be used only for short distances. Table 11 in Bowditch (page 138) is based 

 on this formula. 



The height of eye should be determined and the sextant angles should be measured 

 accurately. The sextant should be in adjustment -or a correction made for any index 

 error. The vessel on which the observer is stationed is unstable, and if the object 

 is a survey buoy, it too is unstable, due to the motion of the water. The angle 

 should be marked at a time when the vessel is on an even keel and when the 

 level of the sea at both the vessel and the buoy is as near average as can be estimated. 

 The buoy rises and falls with the waves and an attempt must be made to measure the 

 angle to the mean position at which the buoy would rest if the sea were calm. 



Used in conjunction with three-point fix control, a depression angle of 3° or more 

 will usually give the required accuracy; and if an observation from the bridge of the 

 vessel would result in a smaller angle, an attempt should be made to measure the angle 

 from a greater elevation. In general, a depression angle of 1° or less will be too in- 

 accurate for use in connection with any kind of well-controlled hydrographic surveying. 

 An angle of 1° will correspond approximately to a distance 50 times as great as the 

 height of eye. 



