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Published online by Cambridge University Press: 23 November 2009
Having been concerned in the mid-fifties with developing the general equations of most economic flight and applying them to the profitability of an airline, I was surprised to discover when I was a ship financier in the early seventies that the much simpler equivalent marine problem had never been addressed by our clients, nor did the question arise apparently in the negotiation of their time charters with oil companies which are not conspicuously unsophisticated in some matters. I was therefore most interested to read Captain P. M. Alderton's paper on ‘The optimum speed of ships’, this Journal, 34, p. 341. If it were not for his charming reference to Napier's paper on the same theme dated 1865 one would be tempted to think that this was a case where the air leads the sea by decades.
1 There are altogether more dimensions to the air problem. For example, by changing altitude one gets a different range of possible true airspeed, a different fuel consumption for a given speed, all depending on temperature, and usually a different headwind component.
2 In a bad market a vessel may be mortgaged for more than its market value and the owner be unable to find the cash which is therefore required to sell it. As we shall see, this affects the optimum speed of a fleet but not of a single ship.
3 Kibbitzers will note that as the number of ships in a fleet,n, can only be a whole number, a function of which it is a variable cannot be differentiated. We evade this difficulty by defining the problem formally in a different way so as to make n continuous. It is analagous to chartering in at own operating cost. If, on this purely formal exercise we determine, say, an optimum fleet of 18·6 vessels, we run our real exercises with n invariant at 18 and 19.