Fig 10.4 The influence of dead rise on spray and pressure forces
The spray from a bottom with deadrise normally increases the frictional resistance, since most of the spray actually goes backwards. Savitsky measured this effect and devised a spray correction to the wetted length to beam ratio. This correction is shown graphically for different deadrise and trim angles in Fig 10.5, which also gives the appropriate formulae for computing the frictional resistance.
Forces on a planing hull Fig 10.6 shows a planing hull with the most important forces acting on the hull displayed. N corresponds to the pressure force in Fig 10.3 (hydrostatic and hydrodynamic contributions) and Rr is the friction. There is also the propeller thrust T and the resistance of the propeller drive, denoted Ra, where the index 'a' stands for appendage. For a hull with a propeller on a shaft the resistance from all appendages like the shaft, shaft brackets and rudder must be considered. Useful formulae for streamlined shapes and inclined circular cylinders are given in Fig 10.7. The direction of the appendage forces vary somewhat, but without too much loss in generality they may be assumed parallel to the keel
Edge of spray
Lk : Wetted keel length [m]
¡3 : Deadrise angle [°] CLp : Lift coefficient, non—zero deadrise
Edge of spray
Fig 10.5 Calculation of the frictional resistance of the hull
Frictional resistance: Rf : Friction [N]
Sw : Surface wetted by water and spray [m ] CF : Skin friction coefficient (see Fig. 5.8)
AX : increase in wetted length—beam ratio due to spray
S = -kr-'b ' T- - (X + AX)'-^-^-w b cosß K y cosß
AX is obtained from the following figure
Dead rise angle, ß, degrees
Lever arm for Rf : (ff and VCG, see Fig. 10.6) ff = VCG - - tan ß [m]
line. Some lift may be generated by the appendages, particularly the shaft, but this is neglected in the following.
The weight is shown as a force mg acting vertically through the centre of gravity G. To compute the moments this point may be taken as the origin. It is seen that N, Rf and Ra create a moment to trim the boat by the bow and that their respective lever arms are e, ff and fa. The propeller thrust, on the other hand, creates a bow-up moment with the arm f. The hull automatically attains a trim angle where the moments cancel, ie the net moment is zero. Thus, for example, if there is a net moment to trim the boat by the bow the trim will become smaller and the force N moved forwards until balance is achieved.
If a bow-down moment is applied to a hull originally at an optimum trim angle, the new smaller trim means that the hydrodynamic pressure is reduced. On the other hand, the wetted surface is increased, so it may
Fig 10.6 Forças on a planing hull
Fig 10.7 Appendage resistance
Resistance of rudders and brackets:
Rr : Rudder or bracket resistance [N]
Sr ' Wetted surface [m
Crr - Skin friction coefficient (see Fig. 5.8)
Resistance of propeller shaft:
Rsh ' Shaft resistance [N]
d : Shaft diameter [mj s : Shaft angle relative to flow [°]
CFsh Skin friction coefficient based on shaft length
Rrsh = 0.5 - p-V2' I -d - (1.1 • sin3 s + TT-Crsh)
Edge of spray r- Sta tic wate rlin e
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