## Propeller and Engine

1 Assume that the velocity at the propeller is equal to the yacht speed, as before.

2 Compute the total resistance and assume that this is equal to the thrust, as before.

4 Find the point on the loading curve in Fig 9.14 that corresponds to the computed value, and read the advance ratio and the torque coefficient on the same vertical line.

5 Compute the rate of revolutions from the definition of the advance ratio and the power from the torque and the angular frequency.

Fig 9.14 Interpolated 2-bladed propeller characteristics quantities must match the output curve of the engine, as we will sec.

If the thrust coefficient is divided by the advance ratio squared, a quantity independent of the rate of revolutions is obtained. This quantity, KT/J2, is often referred to as the propeller loading, and it can be computed from the characteristics. This has been done in Fig 9.13. The computation may now proceed as follows:

All formulae required arc given in Fig 9.15, which also presents calculations for the YD-40 at the three speeds used above. The results are plotted in the form of power versus rate of revolutions in Fig 9.16. Two curves are given, corresponding to the calm and rough weather cases. The limits for the engine are also indicated, representing the maximum engine output and the maximum rate of revolutions,

Fig 9.15 Computation of power required for non-optimum propeller -YD-40

 Caim weather Rough weather V = V [knots] 7 8 8.5 7 8 8.5 V = V [m/s] j. 60 4. 1 1 4.37 3.60 4. 1 1 4.37 ■i 7/^.1 r> —7 r* /—1 4000 T zr /r "7 T = R [N] 1300 275O 33o 7 4880 6169 D (given) [m] 0.53 O. 53 0.53 0.53 0.53 0.53 0.563 0.724 0.896 1.000 Coefficient 0.347 1.118 J (diagram) 0.475 0.415 0.385 0.355 O. 34 O 0.330 K^ (diagram) 0,0084 O. O 10O 0.0107 0.0114 O.Oi 18 0.0122 n [rps] 14.3 18.7 21.4 22 8 25 O ^ * v* Po [kW] 6. 60 17.5 23.2 21.4 37.6 51.2

PD - 2TT • K ' p • D5' n3 = 0.269 • KQ • nJ

respectively. The top corner of the 'allowable region' is the point for which the optimum propeller was designed, ie 26 kW and 20 rps. Due to the fact that the chosen propeller is not optimum this corner is not reached. At the maximum rate of revolutions the engine develops 22 kW with this propeller and the speed is about 8.2 knots in calm weather. As we have seen above, 8.4 knots would be reached with the optimum propeller. In rough weather we will use 25 kW at maximum rps and the speed will be around 7.2 knots, a reduction by about 0.3 knots, as compared to the optimum. This is very reasonable, however, and we are on the right side of the corner.

There are two reasons for being to the rieht of the corner. First, if the resistance for some reason gets larger than expected in rough weather, more power is required at all rates of revolution and we will move in the direction of the corner. There is thus a certain 'spare power' available for extra difficult situations. Had we been on the other side of the maximum, the power would have dropped under extra load. Secondly, we have used diagrams for fixed propellers in the design process, and they are certainly more efficient than the folding ones, so the actual power required is higher than that computed. The difference is hard to estimate, since characteristics for folding propellers are not available, but it could well be 20% in terms of efficiency, which would move the power curve to the other side of the corner. The efficiency would then be around 0.5 rather than around 0.6. as in the calculations above. For lack of better information we will consider the propeller designed as adequate. 