This invention relates to a new form of hydrofoils for high-speed marine craft. The hydrofoils are configured such that they provide both high lift coefficients and high ratios of lift to drag over a wide range of craft speeds, whether running submerged in close proximity to the free surface of the water at lower speeds or planing thereon at higher speeds.

The invention has particular application to the use of high speed catamarans and other surface craft which can benefit from the greatly reduced power consumption and improved ride and handling provided.

Whilst the majority of applications are likely to be for faster craft, the lift and drag characteristics of the new hydrofoils are such that significant reductions in hull resistance have been recorded at displacement Froude numbers only a little above 1.0 such that the hydrofoils also have application to relatively heavy commercial and workboats .

Once fully planing the lift to drag ratio increases steadily with speed such that the power requirement remains relatively constant over a wide speed range, essentially only increasing due to the increasing wind resistance.

If the operational speed range is high enough the hydrofoils may pass through the four defined states of shallow immersion, planing, skating and ground effect with increasing speed.

The displacement Froude number Pny is given by the following expression:

where V is the velocity of the craft, Δ is the volume of water displaced by the hull when it is at rest and g is the rate of acceleration due to gravity {all in consistent units)

A number of prior art technologies have addressed the issue of the application of hydrofoils to high speed craft but few have achieved commercial success . A number of craft with surface-piercing hydrofoils have been successfully operated, particularly in inland lakes and waterways typically achieving about 38knots and a displacement Froude number of around 3.0. A relatively small number of craft with deeply submerged foils have been operated . Details of such craft are disclosed in US4159690 and US5404830. Such craft tend to have optimum ride comfort but suffer from a a limited speed range and demonstrate a considerable 'hump' at on-to- foil speeds . They are also relatively complex and require special lifting arrangements and protection systems . At speeds above about 44 knots it becomes difficult to manage cavitation and the lift/drag ratio starts to deteriorate significantly. A few prototype craft of this type have been fitted with super-cavitating hydrofoils but lift/drag ratios have been poor. A significant number of hydrofoil assisted catamarans using shallowly-submerged hydrofoils have been successfully operated. Details of a number of such craft are disclosed in WO2008007249, US4606291, EP0051073, EP0094673, EP0352195, US2003029370, US5520137 for instance. Such craft tend to have ride qualities intermediate between surface-piercing hydrofoils and deeply-submerged hydrofoils and to give improved performance, particularly in the 30/40 knot range and to demonstrate lift/drag ratios in the 8:1 to 11.· 1 range. Above this speed the lift/drag ratio tends to increase substantially as the hydrofoils get closer to the water surface and as the cavitation number falls away.

With increasing emphasis on fuel efficiency and the increasing demand for both good ride comfort and speed new technologies are required. High aspect ratio planing hydrofoils mounted to catamarans or other suitable hulls in accordance with this invention have been shown to operate at much higher lift drag ratios than any other systems at displacement Froude numbers above about 2.4, and to demonstrate remarkable lift/drag ratios at higher speeds .

The primary object of this invention is to provide means which enable a significant increase in top speed,

cruising speed and cruising range with a reduction or at least no increase in power or fuel capacity.

It is a further object of this invention to provide means to enable the effective design of hull surfaces adjacent to the described planing hydrofoils such as to optimise system performance of the hydrofoil and hull system.

It is a further object of this invention to provide improved ride comfort to the craft to which the hydrofoils are integrated.

In a first preferred embodiment simple hydrofoils without trailing edge flaps or other control means are described.

In a second preferred embodiment the hydrofoils comprise controllable flaps to control the craft trim and roll attitude. Preferred examples of the new hydrofoils will now be described with reference to the accompanying drawings .

Figure 1 shows the variation of the lift coefficient of typical sub-cavitating hydrofoil sections designed for operation at a depth below the water level operating at a constant angle of attack at varying depth of submergence ;

Figure 2 shows the variation of the lift coefficient of cavitating hydrofoil section operating at a constant angle of attack at varying depth of submergence;

Figure 3 shows the variation of the ratio of the lift coefficient at various depth/chord ratios relative to the lift coefficients at infinite depth of typical hydrofoil sections;

Figure 4 shows the variation of the chord Froude Number F _c with craft speed for a hydrofoil section of unit chord;

Figure 5 shows the variation of the lift/drag ratios with the lift coefficient based on the span of planing hydrofoils of aspect ratios varying between 2.5 and 12 operating at a constant angle of attack and with varying camber;

Figure 6 shows the variation of the lift/drag ratios with the lift coefficient of planing hydrofoils of aspect ratios of 5 and 10 having constant section operating at varying angles of attack;

Figure 7 shows a typical variation of the lift coefficient and the lift drag ratio for a planing hydrofoil at varying angles of sweep back of the 50% chord line;

Figure 8 shows the variation of the lift coefficient for typical planing hydrofoils of rectangular platform at various small angle of dihedral ; Figure 9 shows the variation of the lift coefficient and the lift drag ratio for typical planing hydrofoils of rectangular platform at various deflections of a 10% trailing edge flap;

Figure 10 shows a planform view of a hydrofoil with swept- back leading and trailing edges and a taper ratio fitted with trailing edge flaps;

Figure 11 shows a frontal view of a hydrofoil with dihedral;

Figure 12 shows a side view of prismatic planing surfaces of a hydrofoil with swept-back leading and trailing edges and with dihedral ;

Figure 13 shows a planform view of a hydrofoil with swept- back leading and trailing edges and a taper ratio fitted with trailing edge flaps with an alternative trailing edge profile;

Figure 14 shows a planform view of a rectangular hydrofoil fitted with trailing edge flaps;

Figure 15 shows a frontal view of a planing hydrofoil without dihedral and with a supporting strut fitted to a catamaran hull . The figure includes a sectional view of the water flow around the hydrofoil and adj acent hull profiles;

Figure 16 shows a frontal view of a planing hydrofoil with dihedral fitted to a catamaran hull in which the local deadrise angle of the hulls is similar to the dihedral angle of the hydrofoil. The figure includes a sectional view of the water flow around the hydrofoil and adj acent hull profiles ;

Figure 17 shows a frontal view of a planing hydrofoil with dihedral fitted to a catamaran hull in which the local deadrise angle of the hulls is similar to the dihedral angle of the hydrofoil in which the hydrofoil is fitted with struts such that it lies below the hulls. The figure includes a sectional view of the water flow around the hydrofoil and adjacent hull profiles;

Figure 18 shows a frontal view of a planing hydrofoil with dihedral fitted to a catamaran hull in which the local deadrise angle of the hulls is similar to the dihedral angle of the hydrofoil in which the hydrofoil extends over the full width of the catamaran hulls and is fitted with struts such that it lies below the hulls. The figure includes a sectional view of the water flow around the hydrofoil and adjacent hull profiles ;

Figure 19 shows an underside isometric view of a preferred embodiment of a planing hydrofoil with trailing edge flaps fitted to a hull with two forward sponsons have a step immediately aft of the hydrofoil ;

Figure 20 shows an isometric view the hydrofoil of the preferred embodiment of Figure 21 in which the surface area of the hydrofoil in contact with the water surface at in the condition at which it becomes fully planing is shown;

Figure 21 shows an isometric view the hydrofoil of the preferred embodiment of Figure 21 in which the surface area of the hydrofoil in contact with the water surface at the design condition is shown;

Figure 22 shows an underside isometric view of a preferred embodiment of a forward planing hydrofoil fitted to a hull with two forward sponsons have a step immediately aft of the hydrofoil which also comprises two aft planing hydrofoils; Figure 23 shows a preferred section for a planing hydrofoil with indications as to the water surface under various operating conditions ;

Figure 24 shows an alternative section for a planing hydrofoil;

Figure 25 shows the pressure distribution around a preferred hydrofoil section operating deeply immersed in water or air;

Figure 26 shows the pressure distribution around a preferred hydrofoil section operating in ground effect.

Figure 27 shows the lift generated by particular hydrofoils comprising the section of Figure 26 operating in ground effect mode .

The following describes the general principles governing the invention.

Referring to Figure 1 curves 1 show a rapid reduction in lift coefficient for sub-cavitating sections as the hydrofoil nears the water surface . Although not shown on this figure the lift/drag ration also falls away due to the an increasing effect of the friction drag. Initially this reduction is quite slow, but as the value of d/c approaches 0.25 the reduction in the lift/drag ratio becomes increasingly marked. Curve 11 shows the variance of the lift coefficient with the depth/chord ratio for an efficient hydrodynamic section with a slightly concave under surface . Curve 12 shows the variance for a more classic aerofoil section which a slightly convex under surface . The difference is due to the increasing reliance on the pressure distribution on the lower surface as a cavitation bubble increasingly grows on the upper surface which becomes fully ventilated at some point. Both sections have a 2D lift coefficient of 0.63 when deeply immersed.

Referring to Figure 2 the opposite effect is evident for cavitating sections. For the flat plate shown by curve 2 the lift coefficient doubles between deep immersion and zero immersion with most of this occurring when the hydrofoil is very close to the surface . The curve for more efficient cavitating sections follows the same trend although the overall increase in lift coefficient is reduced from 100% to generally 25% to 50%. The lift/drag ratio for a cavitating section tends to improve as the surface is approached. The frictionless value tends to be little changed but the friction coefficient has a reducing effect as the lift coefficient increases close to the surface .

Referring to Figures 3 and 4 it is evident that the lift coefficient is increasingly reduced as the depth/chord ratio reduces, particularly in the region around a chord Froude number of 1, where the chord Froude number is given by the expression

Fc = V/V(g . C)

where V is the velocity of the craft, C is the chord of the hydrofoil section and g is the rate of acceleration due to gravity {all in consistent units) .

Line 4 of Figure 4 shows the variation of F _c with craft speed for a chord of one metre from which it can be seen that a significant reduction in lift coefficient is to be expected as the hydrofoil section approached the surface, particularly in the range of speeds from 5 to 10 m/sec at which a high lift coefficient may be required to get a craft foil borne. It will be evident from Figures 1, 2, 2 and 4 that the design of a suitable section is highly dependent on the range of immersion depth intended, particularly if operation within the range of immersion depths between 0.5 and zero is expected.

Referring to Figures 5 and 6 the benefit is shown of using the a planing hydrofoil section arranged for constant wetted span in which the chord reduces and by consequence the aspect ratio increases as the speed increases. Figure 5 shows the rapid improvement in the lift/drag ratio as the aspect ratio is improved. It also shows that the camber and associated value of the lift coefficient based on span must be carefully selected to lie within a desired range of lift/drag values. Figure 6 shows values of CL and the lift/drag ratio for hydrofoils having aspect ratios or 5 and 10 with the same section with the lift coefficient varied by changing the angle of attack. These curves show the importance of maintaining an optimum angle of attack with the performance dropping away rapidly as the angle of attack is increased. The aspect ratio is equally of key importance.

Referring to Figure 7, line 6 shows the variation in the lift coefficient for a typical planing hydrofoils with varying angles of sweep back at 50% chord. The 50% chord point is taken as the centre of sections adapted to such hydrofoils typically have centres of pressure at around 50% of the chord. Preferred sections for use in this invention typically have a centre of pressure at around 75% or even further back in the design condition. Line 6 shows the variation of the lift/drag ratio for the same hydrofoil . This Figure shows that no significant difference in the lift coefficient is to be expected at sweep back angles below 35degrees and that no reduction in the lift/drag ratio is to be expected at sweep-back angles below 45 degrees.

Referring to line 7 of Figure 8 it is evident that a significant increase in lift coefficient may be achieved by arranging the hydrofoil with a dihedral angle . It will be seen later that this implies the application of an appropriate sweep-back angle depending on the angle of attack. The variation in the lift/drag ratio has been found not to follow any such simple variation with dihedral angle and needs to be optimised for specific conditions .

Referring to figure 9 in which line 8 shows the variation in the lift coefficient and line shows the corresponding variation in the lift/drag ratio. Whilst the figures are only applicable to a particular hydrofoil it is generally the case that increasing the flap deflection provides an increased lift coefficient and a decreased lift/drag ratio. Sections of the preferred type generally show much more desirable characteristics if such a variation in lift coefficient is achieved by variation of the sectional camber indicating that use of flaps should be limited as much as possible during operation.

Referring to Figure 10, a planform view of a hydrofoil 20 having both sweep back and a taper ratio is shown. The hydrofoil has a leading edge 201, a trailing edge 202 and tips 203. It also has a span b, a root chord C _R and a tip chord C _R and a fully wetted area S. The geometric aspect ratio A for the fully wetted hydrofoil is given by the expression:

A = B ² /S

The taper ratio TR is defined by the expression: TR = CT/CR Hydrofoil 20 preferentially embodies trailing edge flaps

205 extending preferentially over the majority of the span b.

The preferred trailing edge 202 is arranged to be generally normal to the centreline 204 as it crosses the centreline . An alternative straight trailing edge form is shown in Figure 13. The centreline of Figure 10 results in smoother flow conditions which is particularly important if the flow would otherwise impinge on an after hull body or if an additional hydrofoil or other lifting surface is fitted aft of hydrofoil 20. When planing, a spray root is formed at the intersection of the waterplane and the hydrofoil under-surface . Such spray- root defines the forward edge of the pressure surface and by consequence defines the forward end of the wetted chord. For prismatic planing surfaces the spray root line is approximately straight and is shown by line 208 at an angle γ to the centreline 204

The basic relationship between the root spray angle , the angle of attack and the dihedral angle for prismatic surfaces is given by the expression below

Where: γ is the angle in radians between the spray root line and the centre line in plan view for prismatic planing surfaces, τ is the angle of attack in radians and β is the dihedral angle in radians

For the preferred cambered sections of this invention the spray root line becomes curved as shown by line 209. Although approximate expressions are available for the computation of such lines it is generally sufficient to compute the straight line and prior to computing a more precise geometry using computational fluid dynamics tools.

Referring to Figure 11 the hydrofoil 20 is shown having a lower surface 206 which is generally wetted in both planing and non-planing conditions and an upper surface 207 which is generally wetted in the submerged condition but generally dry in the planing condition. For the purposes of the planing hydrofoil a dihedral angle β is defined by the inclination of the under lifting surface 206 to the horizontal.

Referring to Figure 12 showing a prismatic planing surface 206 bounded by the spray root line 208, the trailing edge 202 and proportions of the tip chords 203 and the centreline chord 204, the centreline chord is at an angle T _c and the tip chord at an angle t _T to the horizontal wherein a median value of τ is used in the expression above for the angle γ.

Referring to Figure 13 showing an alternative swept planform with a line between the 50% tip and root chord points describing a sweepback angle Δ ₅₀ ».

Referring to Figure 14, a hydrofoil 20 with a simple rectangular planform is shown with a span b and a chord C is shown with one or more trailing edge flaps 205.

Referring to Figure 15, a catamaran hull 30 is shown with a hydrofoil 20 without dihderal . The hydrodoil 20 is attached to the inner walls 3013 of the hulls 301a and 301b such that the lower face of hydrofoil 20 is approximately aligned to the inner edges of the two hull surfaces 3012. A strut 211 may be required to stiffen hydrofoil 20. A tunnel is defined by the inside walls 3013 of the hulls, the under face of the bridge structure 302 and the water surface 40 The lower surfaces 3012 of hulls 301a, 301b are arranged with a deadrise angle β _Η . At sufficient speed the spray- root angle for the hydrofoil will be 90deg whereas the spray root angle for the hulls will be lower than this depending on angle β _Η and the angle of attack of the hulls. Some form of complex spray jet pattern will result in this region as indicated by 402. The water surface at the hydrofoil will thus be represented by line 401 and patterns 402.

Referring to Figure 16, a catamaran hull 30 is shown similar to that of Figure 15 together with a hydrofoil 20 with a dihderal angle β. The hydrodoil 20 is attached to the inner walls 3013 of the hulls 301a and 301b such that the lower face of hydrofoil 20 is approximately aligned to the inner edges of the two hull surfaces 3012. A tunnel is defined by the inside walls 3013 of the hulls, the under face of the bridge structure 302 and the water surface 40

The lower surfaces 3012 of hulls 301a, 301b are arranged with a deadrise angle β _Η similar to the dihedral angle for the hydrofoil 20 At sufficient speed the spray root angle for the hydrofoil and the hulls will be similar and will generally result in improved flow conditions and a significant increase in the effective aspect ratio will result. The spray jet 402 will be directed upwards and the sides of the hull 3011 will tend to form some form of fence or tip further improving the hydrodynamic efficiency of the lifting surfaces. The water surface at the hydrofoil will thus be represented by line 401 and patterns 402.

Referring to Figure 17, a catamaran hull 30 is shown similar to that of Figure 16 together with a hydrofoil 20 with a dihedral angle β. The hydrofoil 20 is attached to the inner walls 3013 of the hulls 301a and 301b my means of fences or struts 212. A tunnel is defined by the inside walls 3013 of the hulls, the under face of the bridge structure 302 and the water surface 40

The lower surfaces 3012 of hulls 301a, 301b are arranged with a deadrise angle β _Η similar to the dihedral angle for the hydrofoil 20. However, in this case the hydrofoil is arranged below the bottom extremity of the hulls 301a _? 301b which will consequently ride clear of the water at sufficient speed. In this case the hydrofoil foil area S and/or the aspect ratio of the hydrofoil will be reduced due to the reduced span. The spray jet 402 will be directed upwards and the sides of the fences or struts 212 will tend to form some form of fence or tip which may make up some of the deficiency due to the lower aspect ratio of the hydrofoil 20. At sub-planing speeds the hydrofoil 20 will be more deeply immersed such that by reference to Figure 1 it can be seen that it will generate more lift, however, once planing its performance can be expected to be inferior to a full width hydrofoil . The water surface at the hydrofoil will thus be represented by line 401 and patterns 402.

Referring to Figure 18, a catamaran hull 30 is shown similar to that of Figure 17 together with a hydrofoil 20 with a dihedral angle β. The hydrofoil 20 is attached to the outer walls 3011 of the hulls 301a and 301b my means of fences or struts 212. A tunnel is defined by the inside walls 3013 of the hulls, the under face of the bridge structure 302 and the water surface 40

The lower surfaces 3012 of hulls 301a, 301b are arranged with a deadrise angle β _Η similar to the dihedral angle for the hydrofoil 20. However, in this case the hydrofoil is arranged below the bottom extremity of the hulls 301a, 301b which will consequently ride clear of the water at sufficient speed. Compared to the arrangement of Figure 17 the hydrofoil 20 can be arranged with increased span qnd will have improved performance. The spray jet 402 will be directed upwards and the sides of the fences or struts 212 will tend to form some form of fence or tip to further increase the hydrodynatnic efficiency. At sub- planing speeds the hydrofoil 20 will be more deeply immersed such that by reference to Figure 1 it can be seen that it will generate more lift. It will also have improved performance compared to the other arrangements in the planing configuration due to the continuous hydrofoil. The water surface at the hydrofoil will thus be represented by line 401 and patterns 402.

Referring to Figure 19, a craft hull 30 is shown with forward sponsons 401a, 401b. A full width flapped hydrofoil according to the present invention straddles the two sponsons. This preferred embodiment is in accordance with Figure 16,

Referring to Figures 20 and 21, a hydrofoil 20 of Figure 19 is shown at the point at which it starts to plane in Figure 20. The whole under face 23 of the hydrofoil shown shaded is wetted and subject to a generally upwards positive pressure. Figure 21 shows the same hydrofoil at higher design speed such that the wetted surface 23 is now of smaller area. For a hydrofoil according to this invention the span remains generally constant such that the aspect ratio of the planing surface is increased. Figure 21 also shows a preferred arrangement in which the ratio of the wetted chord at the tip to the wetted chord at the centre of the hydrofoil is in the range of 15% to 75% in the design condition and preferentially under all normal high speed operating conditions. This is due to the fact that the drag coefficient rises substantially outside this range.

Referring to Figure 22 a craft 30 comprising forward sponsons 301a, 301b stepped at 309 comprises both a front hydrofoil 20 and rear hydrofoils 206a, 206b according to the present invention. Propulsion units 215 are provided aft of the rear hydrofoils. At a design speed only an aft portion of the front and rear hydrofoils will be wetted as shown in Figure 21. It will be evident that unlike a planing hull operating in a seaway, the overall surface area which may be expected to come into contact with the water is limited to the area of the hydrofoils and the forward sponsons so that slamming forces are relatively limited.

Referring to Figure 23, a preferred hydrofoil section demonstrates improved lift and lift/drag ratios compared to existing sections . The hydrofoil section 20 comprises a leading edge 201, a trailing edge 202, a lower surface 206 and an upper surface 207 and preferentially comprises a trailing edge flap with a pivot 205a. The lower surface 206 comprises a generally straight forward section 206a, a cambered "belly" section 206b, a pocketed concave section 206c and a downwards inclined trailing edge section 206d.

At slow speeds hydrofoil 20 is fully submerged at a depth d below the undisturbed water surface 403. Although the undisturbed water surface is shown immediately ahead of the leading edge of the hydrofoil the flow of the water past the hydrofoil will actually influence the water level some way ahead of the leading edge and a long way aft of the trailing edge. The disturbed water level is shown pictorially at 4031. At some increased speed "the planing speed" the leading edge will break through the surface and a spray jet with an associated spray root will become established at point 410 just behind the leading edge 201 of the section corresponding to a water surface 404. At this point the effective planing chord of the hydrofoil is shown as C. As the speed increases the surface area required to generate the required lift will reduce. At some speed the water surface will be situated at 405 and the corresponding spray root will be located at point 411 corresponding to an effective chord C _E . As the speed is further increased to some design speed corresponding to a design displacement the water surface will be situated at 406 and the corresponding spray root at point 412

An aspect of this new section when used for a planing hydrofoil is that as the hydrofoil rides up over the water surface the chord reduces and progressively the angle of attack also decreases. By ensuring the dihedral angle, the spray root angle and angle of attack continue fit the expression for the spray root angle, the full hydrofoil span will remain wetted and the aspect ratio will increase in the proportion to the reduction in the effective chord. Using the new section, the effect of reducing the chord results in an increase in both the section lift coefficient and the section lift/drag ratio The combined effects of increasing the aspect ratio and increasing section performance results in a rapid reduction in drag or hull resistance as indicated in Figure 5.

At some speed, which is normally taken as the design speed for a particular displacement, the chord will reduce to C _DBS - The ratio Cms/C largely determines the ratio between the design speed and the planing speed for the hydrofoil. This chord ratio is shown as about 50% in Figure 23, but can be arranged to be of the order of 25% or less. Assuming a constant lift coefficient this lower ratio results in a speed ratio of about 2.0 between the planing speed and the design speed Assuming a typical displacement Froude number of 2.4 for the planing condition the resulting design value of F _nV will be 4.8.

At yet higher speeds the incoming water surface 405 largely misses the underbelly 206b of hydrofoil 20 and a spray jet is created just forward of the trailing edge 202. Under these conditions a pressurised mixture of air, water and water vapour is created in the under pocket 206c. Under such conditions the chord is not substantially reduced from the value C _DES but the pressure reduces such as to decrease both the lift coefficient and the drag coefficient . The lift/drag ratio becomes extremely high due to the almost equal areas over which the pressure acts in the sense of the longitudinal axis . At the same time the gaseous mixture reduces the skin friction such that the craft effectively skates on a gas/water film. At yet higher speeds the hydrofoil acts increasingly as a high aspect ratio airfoil under ground effect at virtually zero height with the high pressure under the section depressing the water surface . Under these conditions the lift/drag ratio could increase to 250 and the lift coefficient to 1.3 for the new section and with hydrofoils according to the present invention.

Referring to Figure 24, an alternative preferred hydrofoil section also demonstrates improved lift and lift/drag ratios compared to existing sections. The hydrofoil section 20 comprises a leading edge 201, a trailing edge 202, a lower surface 206 and an upper surface 207 and preferentially comprises a trailing edge flap with a pivot 205a. The lower surface 206 comprises a generally straight forward section 206a and a downwards inclined trailing edge section 206d.

As for foil 20 of Figure 23 the hydrofoil 20 of Figure 24 is fully submerged at slow speeds. At the planing speed a spray jet with an associated spray root becomes established at point 410 just behind the leading edge 201 of the section corresponding to a water surface 404. At this point the effective planing chord of the hydrofoil is shown as C. As the speed increases the surface area required to generate the required lift will reduce. At some speed the water surface will be situated at 405 and the corresponding spray root will be located at point 411 corresponding to an effective chord C _E . As the speed is further increased the effective chord will continue to decrease .

As for the section of Figure 23 this new section when used for a planing hydrofoil the chord reduces as the hydrofoil rides up over the water surface. By ensuring the dihedral angle , the spray root angle and angle of attack continue fit the expression for the spray root angle, the span will remain wetted and the aspect ratio will increase in the proportion to the reduction in the effective chord. Whilst using the new section of Figure 24 results in an increase in aspect ratio with increasing speed, there is little variation in either the section lift coefficient or the section lift/drag ratio as both the angle of attack and the maximum camber remain sensibly constant such that the reduction in drag or hull resistance will still be generally as indicated in Figure 5, but will be less advantageous that results for a hydrofoil using the section of Figure 23. None-the-less the fact that the section of Figure 24 exhibits no minimum value for the effective chord CE can be beneficial in certain circumstances .

Referring to Figure 25, a pressure distribution around the section of Figure 23 is shown at deep immersion. This shows a relatively high negative pressure coefficient of between about 0.6 and 0.8 extending over a large majority of the upper surface and an high positive pressure coefficient extending over a large majority of the lower surface .

Referring to Figure 26, a pressure distribution for the section of Figure 24 is shown for a condition in which the section is just fully airborne, riding over the top of the water surface. For this case the negative pressure over the top of the section is reduced to between about 0.25 and 0.45 extending over a large majority of the upper surface and an exceptionally high positive pressure coefficient approaching 1.0 extending over virtually the whole of the lower surface. In this condition the lift coefficient for a typical hydrofoil is around 1.37 and the lift/drag ratio is well in excess of 200.

Referring to Figure 27, the lift relative to the lift required for the craft to become airborne based only on the areas of the hydrofoils is shown, the craft effectively flying in very close proximity to the water surface at a displacement Froude number of about 17.5. In this condition the list/drag ratio for the hydrofoils is substantially in excess of 200:1.