state of the sea. The characterization of the roll- 

 ing effects is best approached from a categorization 

 based on sea state and berg size and wiU be treated 

 so below. It eliminates the need to measure 

 oscillatory periods and to further break down the 

 equation for a in a water environment. Thus the 

 intangible values of equation (8) must be combined 

 with the known constant terms of g and Cp and 

 will result in the simplified relationship a = R. 

 However, the value R will now be determined for 

 sea conditions as well as for berg size in order to 

 include the considerations of water velocity and 

 turbulent heat transfer. With this approach the 



heat transfer equation from the water environment 

 to the berg is given by : 



q=RT^ gm cals/cm^/sec (9) 



Bergs of characteristic size, shape and sea state 

 environment can be observed, cataloged and 

 their characteristic deterioration constants R and 

 F determined. 



To apply equations (7) and (9), a statistical 

 program would have to be initiated to determine 

 the constants of R and F in the air and water 

 environment. Bergs must be categorized into 

 groups and subgroups and the R and F values 

 assigned as follows: 



Water portion: 

 (R value) 



Rough 

 Moderate 

 Calm 



Sea 

 State 



Air portion: 

 (F value) 



Whereas the underwater portion will be affected 

 by sea state and size, the above the water portion 

 will be affected by size and deterioration type. 

 Evidence tends to indicate that certain bergs, i.e., 

 drydock and pinnacle types, deteriorate faster 

 than domed or blocky shaped bergs. Until a 

 technique is developed for observing the under- 

 water portion of a berg, this shape modifier will 

 have to be neglected for the water environment. 

 In order to obtain R and F, an empirical relation- 

 ship is developed to define the required measure- 

 ments as follows: 



Deterioration time 



heat of fusion + temperature change of ice 

 heat flux above and below the water 



Deterioration 

 Type 



where : 



A/=heat of fusion for fresh water 

 AMi=mass change above the water 



Ar° = change of temperature from —12° C. 

 to 0° C. 



AM2=mass change below the water 



Ta„ = air temperature, representative, away 

 from the berg's immediate environ- 

 ment 



7'Ki„=water temperature, representative, 

 away from the berg's immediate 

 environment 



t/^„„=fluid velocity, air, measured at approxi- 

 mately one-half the berg height, 

 away from the berg's immediate 

 environment 

 Cp=specific heat 



This can be further simplified because of the 

 known constants involved, therefore: 



D time (hrs) =0.024 [J^ 4^+^^J (10) 



With the above equation it is now possible to 

 solve for F or R. In order to do this, bergs must 

 be located in certain environments which will 



48 



