# Propeller and Engine

The most difficult quantity to estimate is the added resistance in waves. In Fig 5.4 it was assumed to be 10% of the sum of the other components, which may be reasonable for the conditions in question. However, now we will have to consider much worse conditions for the rough weather case. We will make use of the added resistance curves of Fie 5.30 com-puted by Prof Gerritsma et al. These were obtained for 10 m Lw, yachts at a Froude number of 0.35 and a wave angle of 135° measured between

the directions of motion of the waves and the Yacht. The waves were thus 45° from head seas. To make use of the results some assumptions must be made. First, a dimensionless resistance is obtained by dividing by the weight (mass displacement times acceleration of gravity). This can be done for each curve of Fig 5.30. since the length/displacement ratio is known, as well as the length (10 m). Note that we only know the values for the canoe body. If the waves and yacht were geometrically scaled, and the Froude number was the same at two scales, the dimensionless resistance could be used for all scales. This is not quite true, since the shorter waves are comparatively higher, ie steeper, but if we restrict the discussion to yachts with an Lwl between 5 and 15 m we can adopt this approximation for the present purposes.

The second approximation is related to the Froude number. Although 0.35 corresponds to a reasonable speed by engine, we do not know whether we will obtain that speed exactly. However, we are only-interested in the maximum value of the added resistance, ie the peaks of Fig 5.30, and these are likely to be about the same for other speeds (although they will be obtained at different wave periods).

Finally, we assume that the maximum added resistance is the same in head seas as in the computed 135° seas. This is reasonable, since the possible coupling between roll and pitch is not considered in the calculations, which take into account only heave and pitch.

It should be mentioned that if the computation is to be carried out for other waves than those of Fig 5.31, a good approximation is obtained by multiplying the values presented in Fig 9.3 by the square of the ratio between the actual wave height and the present one. The specification of the waves is the most uncertain part of this computation. The waves of Fig 5.31 are typical for unsheltered waters off the coast in many sailing areas of interest. However, on the oceans the waves are longer, and in certain other cases (such as in a shallow area or a narrow passage with head seas), the waves could be considerably steeper.

The result of the above discussion is shown in Fig 9.3. The estimated maximum added resistance in dimensionless form is plotted versus length/displacement ratio. This figure may be used for yachts of different sizes and slenderness. Numbers for the YD-40 arc included, and it can be seen that the maximum added resistance for this hull is 730 N. This value has been used in Fig 9.4, which shows the total resistance of the YD-40 in calm and rough weather. The different contributions at 7, 8 and 8.5 knots are given in the table. To be on the safe side we have here assumed a wind speed of 15 m/s, which is somewhat higher than the speed for which the maximum added resistance occurs. 