Ogilvie 



immediate interest. The engineer who must evaluate the likelihood of fatigue 

 failures is obviously concerned with different data and different theoretical for- 

 mulations from the engineer who must design equipment for helping aircraft to 

 land on a carrier. One might say that the ship captain will not be satisfied with 

 statistical descriptions at all; he sets an absolute standard: the safety of the 

 ship. So we must state carefully what problem concerns us before we choose a 

 statistical model. 



Long term phenomena, such as the fatigue problem, must still be treated on 

 a strictly phenomenological basis. At present, we cannot hope to specify ship 

 motions or any other ship-related variables for the whole variety of conditions 

 which a ship encounters in its lifetime. Even if we could suddenly obtain perfect 

 oceanographic prediction data, such an enterprise would be out of sight in the 

 future — and probably not even desirable. 



Also beyond the scope of this paper is the problem at the other extreme, 

 that is, the prediction of the specific short-time motions of a ship, given its 

 immediate, detailed history. 



We shall here be concerned with a problem somewhere between these, 

 namely, to predict the probability of occurrence of various phenomena when a 

 ship is travelling in certain well-defined environments. Since we are limited by 

 the available tools of probability theory, we restrict ourselves to the case of a 

 stationary random sea. Such an environment is probably highly non-typical, but 

 its study does give valuable information and it is in any case the best we can do 

 at present. 



Following St. Denis and Pierson (1953) and others, we first describe the 

 seaway by the energy spectrum of the wave height. This function specifies the 

 fraction of the total energy which is associated with any given band of wave fre- 

 quencies. The assumption of an energy spectrum description implies nothing 

 about the possibility of linearly superposing wave trains on each other. It sim- 

 ply means that one measures the wave height at a point for an (in principle) in- 

 finitely long time and then calculates the spectrum by a standard technique which 

 is found in many textbooks. 



Next, one generalizes the spectral description at the point so as to obtain a 

 description valid over an area of the sea. It is here that the assumption is in- 

 troduced that the sea can be represented as the linear sum of elementary waves, 

 each travelling in the manner described by the classical Airy formulas of line- 

 arized water wave theory. If one starts with a wave height record at only a sin- 

 gle point, many possibilities are available for making the generalization. Of all 

 these possibilities, two have special meaning for us, because they correspond to 

 situations of physical interest: 



1. We may assume that all of the wave components travel in the same di- 

 rection. Such a thing does not happen in nature, of course, but it is the situa- 

 tion which many towing tank operators have attempted to produce. 



2. We may assume that the energy in any bandwidth is distributed among 

 wave components travelling in a continuous distribution of directions. Insofar 



8 



