This dist nine is laid out along the principal line 

 through point H^ in the direction of the visible 

 horizon. The lens horizon is then drawn perpen- 

 dicular to the principal line through point (H). 

 Heights, in meters, of selected points on the ice- 

 berg can be determined in relation to the lens 

 horizon by using the following formula : 



(K)(H)(a-b) 

 a(K-b) 

 where; (K) is a constant equal to: 

 f/(sin0-cos0) 



H = Flying height in meters, 

 a = Perpendicular distance from lens horizon 



to the water line, measured in millimeters. 

 b = Perpendicular distance from lens horizon 



to the top of selected points, measured in 



millimeters. 



All angles are in degrees, and all photographic 

 measurements are in millimeters. 



Analysis 



A stereo pair for each iceberg was set up with 

 a random sampling grid. The parallax was 

 measured to each point on the grid. The mean 

 parallax for the iceberg was then determined 

 using a simple average. This mean parallax (P) 

 was converted to mean above water height (h) 

 for the iceberg by using the ratio of h to p for 

 each iceberg. The mean height multiplied by the 

 sea level cross-sectional area of the iceberg, as 

 determined on the a photo data quantitizer, then 

 equalled the above water volume of the iceberg. 

 The iceberg has a mean density of 0.8997 metric 

 tons per cubic meter (Smith, 1931) and sea water 

 in the area of study had a density between 1.024 

 and 1.027 g/cm 3 . The total volume, V, of the 

 iceberg is given by 



v=v a +v 2 



where Vi is the above water volume and V 2 is the 

 below water volume. The mass, M, of the ice- 

 berg is then given by its total displacement 



M = Psw V 2 



where p sw is the density of sea water. The mass 

 of the iceberg is also given by the expression 



M = Pi V= Pi (V 1 + V 2 ) 



where p; is the density of glacial ice. Equating 

 (2) and (3) gives 



p™=Pi(Vi+V,) 



solving for V 2 in terms of V, and using p { =.8997 

 ™L J and p 8w = 1.0255 em / cm 3 yields a result 



V 2 = 7.15 Vj 



V = 8.15 V, 



from (1) to (5). From equations (3) and (6), 

 assuming a uniform density for the iceberg, the 

 total mass metric tons of an iceberg is then 7.33 

 times the above water volume of the iceberg in 

 cubic meters. 

 M = 7.33 V, 



A least square analysis of V x as related to 

 product of the longest side (L), shortest side 

 (W), and the height of the highest point (H), 

 indicates that 



V, = .41 LWH 

 combining (7) and (8) yields 



M = 3.01 LWH 



The errors which contribute to the total error 

 of iceberg mass measurements originate in the 

 following ways. 



a. The measurement of the heights of selected 

 point on the berg has an error estimated at ±5%. 



b. The parallax measurements using the stereo- 

 comparagraph have an error of ±2%. 



c. Calculations of the mean berg height from 

 heights taken at random points have an error of 

 less than ±9% associated with it. 



d. The waterline cross-sectional area can be 

 measured by the optical image analyzer to within 

 ±1%. 



Combining the errors using a simple summa- 

 tion yields a total error of ±17% or less. 



Results and Conclusions 



The purpose of this study was to develop a 

 technique for easily and quickly estimating the 

 mass of an iceberg. Several relationships were 

 tried such as separating bergs into visual shape 

 classes, plotting height against berg mass, and 

 using a combination of these two approaches. 

 The correlation that appears to be most satis- 

 factory both from the point of view of simplicity 

 and also accuracy is the correlation between the 

 product of the longest side, shortest side, and 

 height of the highest point with the total mass 

 of the iceberg. This approximates the above 

 water portion of the berg with a rectangular box. 

 If the length, width and height are measured in 

 meters, then the total mass of the berg in metric 

 tons is estimated to be 3.01 times the product. 



64 



