To accurately determine the total mass of an 

 iceberg, the above water volume and mass must 

 first be determined. This involved three types of 

 photographs; horizontal, oblique and vertical. 

 In all cases the 500 EL/M 70mm cameras were 

 used. Black and white negative film was used, 

 with all analysis done from positive prints. 



Horizontal and oblique photography was ob- 

 tained by using a leveled tripod from inside the 

 helicopter. Slow, level passes at selected altitudes 

 and offset distances were made at four locations 

 around the iceberg. These were usually 90 de- 

 grees apart. Both horizontal and oblique photo- 

 graphs were obtained at each station. Vertical 

 photography was obtained using the previously 

 described camera mount. Adequate overlap was 

 obtained by taking repetitive frames at pre- 

 determined time intervals. Utilization of each 

 type of photography is explained in the pilot 

 study and analysis sections which follow. 



Pilot Study 



After several attempts to contour the iceberg 

 in a manner similar to a topographic map, we 

 came to the conclusion that such a straightfor- 

 ward method was impossible due to the extreme 

 surface gradients found on a typical iceberg. A 

 new approach was then tried which proved suc- 

 cessful. A grid of randomly selected points was 

 used to locate the position of the parallax meas- 

 urements. Since no point on the berg was more 

 likely to be sampled than any other, it was pos- 

 sible by sampling a sufficient number of randomly 

 selected points to determine the average height 

 of the iceberg to any desired accuracy. An ac- 

 curacy of better than ±2 meters was chosen and 

 a pilot study was conducted to determine the 

 sampling density required. It was determined 

 that a sampling density of .02 points per square 

 meter would give a mean height that had a stand- 

 ard error of less than two meters. 



A grid of .02 random points per square meter 

 at an average scale of 1 :2000 was used. The 

 variations in actual size of the icebergs resulted 

 in variations of photographic scale. In all but a 

 few cases, the number of random sample points 

 exceeded the minimum density. 



Change in Height Versus Change in Parallax 



The stereo pairs used had no real reference 

 level, since the sea surface had no detail in the 



photographs. Therefore, it was necessary to con- 

 struct a linear relationship between the change 

 in height (Ah) and the change in parallax (Ap) 

 for each iceberg. To construct such a graph, 

 points on the iceberg were chosen on the hori- 

 zontal and oblique photographs and the actual 

 heights of these points were computed. These 

 same points were then located on the stereo pair 

 and the parallax was measured. Using a least 

 square fit to these points (four to eight for each 

 iceberg) , a ratio of Ah to Ap was established for 

 each iceberg. This ratio was used to convert the 

 iceberg's mean parallax (Ap) to mean height 

 (Ah). By comparisons with actual height meas- 

 urements we determined that the heights from 

 the oblique photographs were more reliable than 

 those from the horizontal photographs. This was 

 because the only scale reference for the horizontal 

 photography was the presence of the helicopter 

 in the field of vision. Depth of field, orientation 

 of the helicopter (e.g., level or not) and its posi- 

 tion in relation to the plane of the icebergs were 

 not constant or definable. The oblique mensura- 

 tions on the other hand did not require a scale 

 reference. 



Therefore, we used only the oblique photog- 

 raphy to determine the ratio of Ah to Ap. 



Oblique Mensurations 



The principal point (P) is the center of the 

 photographic format. A line drawn through 

 (P) perpendicular to the visible horizon is the 

 principal line (PH,), the point of intersection 

 being (H a ). The depression angle (#0 between 

 the optical axis of the camera and the visible 

 horizon is calculated : 



tan e 1 = PH 1 /(f-M) 



where (f) is the focal length of the camera in 

 milimeters and (M) is the enlargement factor of 

 the photograph. The dip angle (D) between the 

 visible horizon and the lens horizon is computed. 



D = 9.03\/H 



where (H) is the flying height of the helicopter 

 in meters. The depression angle (8) between the 

 optical axis of the camera and the lens horizon is 

 found by 6 = 6 1 + T>. The distance (PH) meas- 

 ured along the principal line to the lens horizon 

 is calculated : 



PH = fTan 0-M 



63 



