Fig 9.1 8 Computation of blade area required -YD-40

The relevant formulae are given in Fig 9.17. First, a cavitation number is defined. This is the "margin" to cavitation at the propeller shaft in dimensionless form. The nominator thus contains the difference between the static pressure at the shaft and the vaporization pressure at the temperature in question, while the denominator is the dynamic pressure at 70% of the propeller radius. The static pressure at the shaft is the sum of the atmospheric and hydrostatic pressures at this depth, as shown in the Fig 9.17.

Having computed the cavitation number the diagram in Fig 9.17 maybe used for finding the maximum value of the quantity x for non-cavitating conditions. This value is simply read from the line and used in the formula for the minimum blade area ratio. Note that this ratio is defined by the developed area, ie the sum of the areas of the blades considered 'flattened out and untwisted" and the area of the propeller disk.

In Fig 9.18 the blade area is checked for the YD-40. The worst case is the one having the largest loading KT./J2. In the calculations of Fig 9.15, this is the 7 knots heavy weather case. The 8 and 8.5 knots will not be reached, as we have seen. Using the values of the table in Fig 9.15 and a propeller depth of 0.48 m, the minimum blade area ratio becomes 0.285. As we have already noted, the Troost propeller designed had a ratio of 0.3, so this is large enough. ITad the area been too small a larger diameter would have helped. Three-bladed propellers have larger blade area ratios, but they cannot be folded and have a very large drag when sailing.

Calculation according to Fig 9.17

p. =101300 [Pa] atm pp - 101300 + 1025 - 9.81 • 0.48 = 106127 [Pa]

Worst case — rough weather, 7 knots (see Fig 9.15): VA= 3.60[m/s]

° 0.220 • 0.5 - 1025 - 3.602■ [1 + (q'J$5 f] - (1.067 - 0.229 • 0.62) - 0.25 • tt - 0.53

Propeller resistance

The propeller resistance when sailing may be estimated using the frontal area of the propeller and some suitable drag coefficient. To obtain the area an approximate relation shown in Fig 9.19 may be used, and the drag coefficient for a fixed propeller, locked in position and outside the wake of the keel, may be set to 1.2. The resistance is then obtained easily as shown in the figure. If the propeller is completely free to rotate, its resistance is reduced to only about one fourth of that of a locked propeller. This is, however, an ideal situation. In practice the clutch and the friction will slow down the rotation. Outstanding from a resistance point of view is the folding propeller with a resistance that is normally less than 5% of that of the fixed and locked one.

In Fig 9.19 the resistance of the YD-40 propeller has been plotted for varying speeds. If a propeller with fixed blades and locked in position was to be used, the resistance at the typical upwind sailing

Fig 9.19 Propeller resistance when sailing

Propeller resistance, YD—40 (D-0.53 m ; P=0.33 m)

Fixed blades, locked

/ Folding

Fixed blades, free to rotate

/ Folding

Frontal area of propeller: A

Resistance:

CQ = 1.2 for fixed blades, locked CD = 0.3 for fixed blades, free to rotate CQ = 0.06 folding speed of 6.8 knots used in Fig 5.4 would be 460 N. This is 29% of the total resistance without propeller, and it would reduce the speed by about 0.8 knots for a given driving force. If the propeller were completely free to rotate the effect would be four times smaller, ie a 0.2 knots speed reduction. Most yachtsmen prefer to reduce the speed loss even more and use a folding propeller, for which the loss in our case would be less than 0.04 knots.

\ A HIGH SPEED 1U HYDRODYNAMICS

A lthough the emphasis of this book is on sailing yachts, much of A\ the theory presented is the same for power boats. There is no Jl JL difference in the hull geometry definition or the principles for producing a drawing, manually or using a CAD system. The displacement of the yacht, as well as its static and dynamic stability properties, are computed in exactly the same way as for the sailing yacht. Neither is there any basic difference in the flow around the hull nor in the associated viscous and wave resistance components. The upright resistance may thus be obtained by the formulae presented in Chapter 5 up to a Froude number of about 0.7 and the same is true for the added resistance in waves. Heel resistance is obviously irrelevant, but induced resistance as well as lift is of importance in the design of efficient power boat rudders. Both planform and profile need to be considered. A reader only interested in power boats can safely skip the two chapters on sails and balance, but he should pay keen interest to the preceding chapter on propellers and engines.

An area not covered in the foregoing is the special hydrodynamics of high speed craft, ie craft operating in the planing mode. Few sailing yachts reach this speed range, although some very special sailing craft like windsurfers or extremely light dinghies may be fast enough. Planing power boats are, however, becoming more and more popular, and to satisfy the interested power boat enthusiasts the present chapter on high speed hydrodynamics has been included.

Planing According to Archimedes, the buoyancy of a body wholly or partly submerged in a fluid is equal to the weight of the displaced volume of fluid. The buoyancy, which is caused by the hydrostatic pressure in the fluid, was dealt with in Chapter 4. At zero speed this force balances exactly the weight of a floating body. However, as soon as the body starts moving, the hull puts water particles into motion by exerting a force on each particle. The same force, but in the opposite direction, is exerted on the hull. This force per unit area may be called the hydro-dynamic pressure. Although not distinguished in this way, we have seen this pressure in Fig 5.4, and we have found in Chapter 5 that it is responsible for both the viscous pressure resistance and the wave resistance. These two resistance components are caused by the longitudinal component of the pressure force over the hull surface. In the vertical direction the hydrodynamic pressure causes the hull to sink (or rise) and trim. At high speed this vertical pressure force may be considerably larger than the buoyancy, lifting the hull more or less

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