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SOFTWARE FOR RESISTANCE PREDICTIONROUND BILGE CATAMARAN (MOLLAND)
A catamaran is a multiHulled watercraft featuring two parallel hulls of equal size. It is a geometrystabilized craft, deriving its stability from its wide beam, rather than from a ballasted keel as with a monohull sailboat. Catamarans typically have less hull volume, higher displacement, and shallower draft (draught) than monohulls of comparable length. The two hulls combined also often have a smaller hydrodynamic resistance than comparable monohulls, requiring less propulsive power from either sails or motors. The catamaran's wider stance on the water can reduce both heeling and waveinduced motion, as compared with a monohull, and can give reduced wakes. Catamarans range in size from small (sailing or rowing vessels) to large (naval ships and car ferries). The structure connecting a catamaran's two hulls ranges from a simple frame strung with webbing to support the crew to a bridging superstructure incorporating extensive cabin and/or cargo space.


INSEL & MOLLAND’S METHOD FOR CATAMARAN RESISTANCE PREDICTION (1992)
The paper by Insel and Molland (1992) summarizes a calm water resistance investigation into high speed semidisplacement catamarans, with symmetrical hull forms based on experimental work carried out at the University of Southampton. Two interference effects contributing to the total resistance effect were established, being viscous interference, caused by asymmetric flow around the demihulls which effects the boundary layer formation, and wave interference, due to the interaction of the wave systems produced by each demihull.
All models were tested over a range of Froude numbers of 0.1 to 1.0 in the demihull configuration and catamaran configuration with separation ratios, s/L, of 0.2, 0.3, 0.4 and 0.5. Calm water resistance, running trim, sinkage and wave pattern analysis experiments were carried out. The authors conclude that the form factor, for practical purposes, is independent of speed and should thus be kept constant over the speed range. This was a good practical solution to a complex engineering problem at that point in time. The authors also conclude that the viscous interference factor γ is effectively independent of speed and should be kept constant across the speed range and it depends primarily on L/B ratio.
The authors further conclude that:
The paper by Insel and Molland (1992) summarizes a calm water resistance investigation into high speed semidisplacement catamarans, with symmetrical hull forms based on experimental work carried out at the University of Southampton. Two interference effects contributing to the total resistance effect were established, being viscous interference, caused by asymmetric flow around the demihulls which effects the boundary layer formation, and wave interference, due to the interaction of the wave systems produced by each demihull.
All models were tested over a range of Froude numbers of 0.1 to 1.0 in the demihull configuration and catamaran configuration with separation ratios, s/L, of 0.2, 0.3, 0.4 and 0.5. Calm water resistance, running trim, sinkage and wave pattern analysis experiments were carried out. The authors conclude that the form factor, for practical purposes, is independent of speed and should thus be kept constant over the speed range. This was a good practical solution to a complex engineering problem at that point in time. The authors also conclude that the viscous interference factor γ is effectively independent of speed and should be kept constant across the speed range and it depends primarily on L/B ratio.
The authors further conclude that:
 The vessels tested have an appreciable viscous form effect, and are higher for catamarans where viscous interference takes place between the hulls.
 Viscous resistance interference was found to be independent of speed and hull separation, and rather is dependent on demihull length to beam ratio.
 Generally higher hull separation ratios result in smaller wave interference, with beneficial wave interference between Froude numbers of 0.35 to 0.42.
 Catamarans display higher trim angles than monohulls, and that the trim angle is reduced with increasing hull separation ratios.
 A ship to model correlation exercise is required for the extrapolation techniques presented to be validated.
The catamaran or twinhull concept has been employed in highspeed craft design for several decades, and both sailing as well as powered catamarans are in use. For commercial purposes semiplaning type catamarans are predominant. The component hulls (demihulls) are of the planing type, featuring Vtype sections and a cutoff transom stern.The division of displacement and waterplane area between two relatively slender hulls results in a large deck area, good stability qualities and consequently a small rate and angle of roll.
Active control of pitching motions by means of fins may eliminate this problem. The resistance of a catamaran is mainly affected by the wetted surface ratio the slenderness ratio and the hull spacing (s/L). The wetted surface ratio is relatively high compared with planing monohulls of the same displacement. Consequently, catamarans show poor performance at low speeds (Fn 0.35) where skin friction is predominant. At higher
speeds (in the hump region, the low trim angles associated with the slender demihulls of the catamaran lead to a favorable performance . At planing speeds (Froude numbers around 1.0) the equivalent monohull (of equal displacement) will show an advantage, as the hydrodynamic
performance decreases with decreasing aspect ratio (the ratio of the wetted breadth of the demihull to its length.
He found that the catamaran had less resistance at speeds in excess of the catamaran had some 30 percent less resistance, this reduction increasing to about 45 percent at = 7.0. This advantage is due to the fact that at such high speeds the conventional boat is operating at a
very small trim angle and high resistance, while the catamaran operates at a higher trim angle nearer to that for minimum resistance. An indication of the relative performance of catamarans and planing vessels is given in Fig. 97.
The hull spacing ratio is associated with interference effects between the component hulls. These effects consist of wave interference effects and body interference effects. Wave interference effects are due to the superposition of the two wave systems, each associated with a component hull in isolation. The body interference effects are caused by the change of flow around one demihull due to the presence of the other demihull.
Several studies on interference effects on resistance have been undertaken, e.g. Fry et al (1972), Sherman, et al (1975), Yermotayev, et al (1977) and Ozawa, et al (1977). The main component of the changed velocity field associated with body interference effects results from
the induced flow of one demihull at the location of the other one. This induced flow is due partly to thickness effects and partly to lift effects. Consequently, the resuiting flow around a symmetrical demihull will be composed of a symmetrical and an asymmetrical part.
Vollheim (1968) and Myazawa (1979) have carried out velocity studies by means of pressure measurements.
These results referred to a displacement type of catamaran with symmetrical demihulls. Myazawa found an increase of the mean velocity both between the demihulls and on the outer sides. He also concluded that the asymmetrical contribution to the local velocity field was small. His results apparently do not agree with those of Vollheim, however. The asymmetrical onflow of one demihull and the possibly asymmetrical shape of that demihull will lead to hydrodynamic lift forces. On account of the finite aspect ratio, trailing vortices are shed leading to induced
velocities around the other hull. This effect is believed to be of less importance.
The wave interference may influence the resistance to a large extent. Everest (1968) showed from a wave pattern analysis that beneficial wave interference is achieved by the cancellation of part of the divergent wave systems of each demihull, whereas adverse wave interference arises on interaction of the transverse wave system.
Fig. 98 shows the influence of the wave interference effects on the resistance obtained by Tasaki (1962) for a mathematical hull form. Here the wave
where is the wave pattern resistance of the catamaran and is the wave pattern resistance of one demihull. In general, experiments confirm this behavior but smaller beneficial and adverse effects occur (Everest, 1968). Theoretical and experimental evidence for symmetrical demihulls indicates that wave interference becomes significant at Fnvalues of 0.2. Maximum beneficial effects occur at Fn 0.32 and whereas adverse effects are most pronounced around Fn = 0.4. For asymmetrical demihulls, Everest (1969) and Turner, et al (1968) have made measurements.
The generation of vertical hydrodynamic lift and the associated change of hull form because of trim and rise of the center of gravity, may have a significant effect on the interference effects. Therefore, for the semiplaning speed range other tendencies may be expected, see Fig. 99. Fry, et al (1972) show model test results from which it may be concluded that the interference effects are small at speeds exceeding Fn = 0.8. Only for small hull spacings do the effects still seem to be significant. These conclusions are in contradiction with those of Sherman, et al (1975) for which there is no satisfactory explanation presently. For measurements of planing catamarans with asymmetrical demihulls the work of Ozawa, et al (1977) and Sherman, et al (1975) may be mentioned. Design charts for planing catamarans have been published by Clement (1961). These are based on model tests. Application of these design charts is restricted to:
Furthermore, the effects of interference between the hulls and of spray on the tunnel roof were not included. Sherman, et al (1975) modified Savitsky's (1964) planing performance prediction method for catamarans. The program does not include interference effects on drag and trim. Resistance due to spray interfering with the tunnel roof is again not included.
Active control of pitching motions by means of fins may eliminate this problem. The resistance of a catamaran is mainly affected by the wetted surface ratio the slenderness ratio and the hull spacing (s/L). The wetted surface ratio is relatively high compared with planing monohulls of the same displacement. Consequently, catamarans show poor performance at low speeds (Fn 0.35) where skin friction is predominant. At higher
speeds (in the hump region, the low trim angles associated with the slender demihulls of the catamaran lead to a favorable performance . At planing speeds (Froude numbers around 1.0) the equivalent monohull (of equal displacement) will show an advantage, as the hydrodynamic
performance decreases with decreasing aspect ratio (the ratio of the wetted breadth of the demihull to its length.
He found that the catamaran had less resistance at speeds in excess of the catamaran had some 30 percent less resistance, this reduction increasing to about 45 percent at = 7.0. This advantage is due to the fact that at such high speeds the conventional boat is operating at a
very small trim angle and high resistance, while the catamaran operates at a higher trim angle nearer to that for minimum resistance. An indication of the relative performance of catamarans and planing vessels is given in Fig. 97.
The hull spacing ratio is associated with interference effects between the component hulls. These effects consist of wave interference effects and body interference effects. Wave interference effects are due to the superposition of the two wave systems, each associated with a component hull in isolation. The body interference effects are caused by the change of flow around one demihull due to the presence of the other demihull.
Several studies on interference effects on resistance have been undertaken, e.g. Fry et al (1972), Sherman, et al (1975), Yermotayev, et al (1977) and Ozawa, et al (1977). The main component of the changed velocity field associated with body interference effects results from
the induced flow of one demihull at the location of the other one. This induced flow is due partly to thickness effects and partly to lift effects. Consequently, the resuiting flow around a symmetrical demihull will be composed of a symmetrical and an asymmetrical part.
Vollheim (1968) and Myazawa (1979) have carried out velocity studies by means of pressure measurements.
These results referred to a displacement type of catamaran with symmetrical demihulls. Myazawa found an increase of the mean velocity both between the demihulls and on the outer sides. He also concluded that the asymmetrical contribution to the local velocity field was small. His results apparently do not agree with those of Vollheim, however. The asymmetrical onflow of one demihull and the possibly asymmetrical shape of that demihull will lead to hydrodynamic lift forces. On account of the finite aspect ratio, trailing vortices are shed leading to induced
velocities around the other hull. This effect is believed to be of less importance.
The wave interference may influence the resistance to a large extent. Everest (1968) showed from a wave pattern analysis that beneficial wave interference is achieved by the cancellation of part of the divergent wave systems of each demihull, whereas adverse wave interference arises on interaction of the transverse wave system.
Fig. 98 shows the influence of the wave interference effects on the resistance obtained by Tasaki (1962) for a mathematical hull form. Here the wave
where is the wave pattern resistance of the catamaran and is the wave pattern resistance of one demihull. In general, experiments confirm this behavior but smaller beneficial and adverse effects occur (Everest, 1968). Theoretical and experimental evidence for symmetrical demihulls indicates that wave interference becomes significant at Fnvalues of 0.2. Maximum beneficial effects occur at Fn 0.32 and whereas adverse effects are most pronounced around Fn = 0.4. For asymmetrical demihulls, Everest (1969) and Turner, et al (1968) have made measurements.
The generation of vertical hydrodynamic lift and the associated change of hull form because of trim and rise of the center of gravity, may have a significant effect on the interference effects. Therefore, for the semiplaning speed range other tendencies may be expected, see Fig. 99. Fry, et al (1972) show model test results from which it may be concluded that the interference effects are small at speeds exceeding Fn = 0.8. Only for small hull spacings do the effects still seem to be significant. These conclusions are in contradiction with those of Sherman, et al (1975) for which there is no satisfactory explanation presently. For measurements of planing catamarans with asymmetrical demihulls the work of Ozawa, et al (1977) and Sherman, et al (1975) may be mentioned. Design charts for planing catamarans have been published by Clement (1961). These are based on model tests. Application of these design charts is restricted to:
 lowaspectratio hulls, i.e., 0.1 AR 0.3,
 small deadrise angles, i.e., 0 deg 10 deg.,
 high planing speeds, where buoyant forces are small.
Furthermore, the effects of interference between the hulls and of spray on the tunnel roof were not included. Sherman, et al (1975) modified Savitsky's (1964) planing performance prediction method for catamarans. The program does not include interference effects on drag and trim. Resistance due to spray interfering with the tunnel roof is again not included.