Hydro s to tic fo rc e ^ Hydrodynamic force
Trim angle,r <
Lift according to Savitsky (neglecting friction):
A ; Wetted length—beam ratio r : Trim angle [°] b
Cv : speed coefficient , ^ (Beam Froude number)
Centre of pressure:
Lcp .'Distance from centre of pressure to trailing edge [m]
Fig 10.3 Forces on a flat planing surface to beam ratio of the wetted surface and the trim angle. Note that the beam is used as a reference length in the speed coefficient (corresponding to the Froude number) and the lift coefficient. The first term in the lift formula is the contribution from the hydrostatic contribution, while the second one is the hydrodynamic pressure.
At first glance it may appear as if both contributions to the lift would increase with an increasing length to beam ratio. However, this holds only for a lift coefficient which has been obtained by dividing by beam squared. Had this coefficient been defined in the usual way by the wetted surface the first term would have decreased with length to beam ratio. A wide and short planing surface is thus more efficient in generating dynamic lift than a long and narrow one. As we know from Chapter 6, this is also the case for wings. Wide hulls do, however, generate a much larger added resistance in waves, and in reality this puts a restriction on the beam.
Fig 10.3 also gives Savitsky's formula for the location of the centre of pressure of the planing surface. This location is important when determining the trim angle of a power boat, as will be seen below.
Deadrise A flat plate skimming along a water surface may be useful for explaining the basic principles of planing, and it may be of interest for surfboards and water skis, but power boat hulls almost inevitably have V-shaped sections, ie a so-called deadrise. The reason for this is the seakeeping qualities of the hull. A completely flat bottom would be impossible in a seaway, since the vertical accelerations would be too large. The ride would be extremely bumpy and put people on board in danger. V-shaped sections reduce the problem considerably: the deeper the V, the smaller the accelerations. However, the deadrise reduces the lift, so a larger wetted surface or trim angle is required, which both increase resistance.
The reason why deadrise reduces the lift force is that the water that hits the bottom of the boat mav now be deflected sidewards. In fact, for j /
a normal deadrise angle most of the spray goes this way. As explained above, the hydrodynamic pressure that lifts the boat is caused by the reaction forces from the water particles which have been forced to change their direction when approaching the hull. For a flat plate the change in direction is almost 180° in the part of the flow in front of the stagnation point (see Fig 10.2). This results in high pressure. If the spray goes out sidewards, however, the change in direction is much smaller and so is the reaction force. Further, this force is now tilted inwards, so a useless transverse component appears; see Fig 10.4, which also provides a formula for the change in lift due to the deadrise.
To understand the advantageous effects of the deadrise when it comes to seakeeping accelerations, compare the impact of a wedge hitting the free surface with that of a flat plate. In the latter case the entire surface of the plate hits the water simultaneously, while the wedge surface gets immersed gradually. The reaction force thus builds up much more slowly for the wedge.
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