This invention relates to a new form of sections for hydrofoils for high-speed marine craft. The sections 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 or planing thereon. In this context the expression “running submerged in close proximity to the free surface of the water” means a hydrofoil which is designed to operate at a depth/chord ratio preferably of less than one.
The invention has particular application to the use of high speed catamarans d 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 sections are such that significant reductions in hull resistance have been recorded at displacement Froude numbers only a little above 1.0 such that the new sections 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.
The displacement Froude number Fn∇ is given by the following expression:
Fn∇=V/√(g·∇1/3)
where V is the velocity of the craft, ∇ 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)
This invention has for objectives:
- To provide hydrofoils having reduced variation in lift coefficient with immersed depth variation;
- To provide hydrofoil sections with much improved lift/drag ratios under deeply submerged, shallowly submerged and planing conditions;
- To provide sections ideally suited to the new concept of planing hydrofoils and the corresponding benefits of sharply reducing resistance with increasing speed;
- To provide rapid and certain means for designing and optimising hydrofoil sections, particularly those intended for shallow immersion and planing conditions
Preferred examples of hydrofoil sections will now be described with reference to the accompanying drawings.
FIG. 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;
FIG. 2 shows the variation of the lift coefficient of cavitating hydrofoil section operating at a constant angle of attack at varying depth of submergence;
FIG. 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;
FIG. 4 shows the variation the chord Froude Number Fc with craft speed for a hydrofoil section of unit chord;
FIG. 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;
FIG. 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;
FIG. 7 shows a hydrofoil section according to the present invention with construction lines for its creation;
FIG. 8 shows a detail of the leading edge geometry of the hydrofoil section of FIG. 7;
FIG. 9 shows a detail alternative hydrofoil section according to the present invention with construction lines for its creation;
FIG. 10 shows a modification of the hydrofoil section of FIG. 9;
FIG. 11 shows an evolution of the pressure distribution during the optimisation process of the design of a hydrofoil according to the present invention;
FIG. 12 shows a hydrofoil section according to the present invention;
FIG. 13 shows alternative hydrofoil section according to the present invention;
FIG. 14 shows the hydrofoil section of FIG. 12 operating at a depth below the free water surface;
FIG. 15 shows the hydrofoil section of FIG. 12 operating at a depth below the free water surface in which a cavitation bubble has formed close to the leading edge;
FIG. 16 shows the hydrofoil section of FIG. 12 operating at a depth below the free water surface in which the upper surface of the section is fully ventilated;
FIG. 17 shows the hydrofoil section of FIG. 12 in which a trailing edge flap is deflected downwards operating at a depth below the free water surface in which the upper surface of the section is fully ventilated;
FIG. 18 shows the hydrofoil section of FIG. 12 which is fully planing;
FIG. 19 shows the hydrofoil section of FIG. 12 operating at its design speed with a reduced effective chord between a forward spray root position and the trailing edge;
FIG. 20 shows the hydrofoil section of FIG. 12 which is fully planing with the flap deflected downwards;
FIG. 21 shows the hydrofoil section of FIG. 13 which is fully planing;
FIG. 22 shows the hydrofoil section of FIG. 13 which is fully planing with the trailing edge flap deflected downwards;
FIG. 23 shows the hydrofoil section of FIG. 13 which is fully immersed;
FIG. 24 shows the hydrofoil section of FIG. 13 which is fully immersed with the trailing edge flap deflected downwards;
FIG. 25 shows the pressure distribution around the hydrofoil section of FIG. 12 which is fully immersed;
FIG. 26 shows the pressure distribution around the hydrofoil section of FIG. 12 which is fully planing at its design condition;
FIG. 27 shows the pressure distribution around the hydrofoil section of FIG. 13 which is fully immersed and the distribution around a NACA 67A 709 section for comparison;
FIG. 28 shows the desired pressure distribution around the hydrofoil section of U.S. Pat. No. 3,946,688;
FIG. 29 shows the computed pressure distribution around the hydrofoil section of U.S. Pat. No. 3,946,688 under particular operating conditions;
FIG. 30 shows the computed pressure distribution around the Speer H105 hydrofoil section operating deeply immersed;
FIG. 31 shows section profiles for the sections of FIGS. 12 and 13 together with a NACA 67A 709 and a Speer H105 section in which the thickness is shown exaggerated;
FIG. 32 shows deeply immersed characteristics of the profiles of FIGS. 12 and 13 together with a NACA 67A 709 and a Speer H105 section;
Referring to FIG. 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 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 FIG. 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 FIGS. 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/√(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 FIG. 4 shows the variation of Fc 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 FIGS. 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 FIGS. 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. FIG. 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. FIG. 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 FIG. 7 and FIG. 8 a hydrofoil section 401 is shown together with details 300 for designing such profile. An upper section 4014 may be created by drawing a conic between points 302, 305 and 306 in which a weight may be assigned to curve point 305. A straight line may be drawn between points 306 and the trailing edge point 307. An aft lower section 4017 may be created by drawing a further conic between points 307, 308 and 309 and a weight assigned to the curve point 308. A mid lower section 4018 may be created by drawing a further conic between points 309, 310 and 311 and a weight assigned to the curve point 310. A line may be drawn between points 311 and 303 to create the forward underside section 4015. Referring to FIG. 8 a leading edge section 4012 may be created by drawing a conic between points 303, 301 and 302 which passes through the leading edge point 304. Alternatively the leading edge section 4012 may be created by drawing two conics between points 303, 3031 and 304 and between 304, 3021 and 302 and weights assigned to curve points 3021, 3031. In order to fine tune the pressure distribution around the leading edge it is sometimes beneficial to move the leading edge point 304 upwards or downwards along the line between points 3021 and 3031 and to consider assigning different weights to curve points 3021 and 3031 in order to provide a local inflexion in the mean camber line in the leading edge section 4012. Straight lines and conical sections are preferentially arranged to be tangent continuous other than at the curve or apex points of the conical sections and at the trailing edge.
Referring to FIGS. 9 and 10, a mixture of conics and lines may be used to create sections 402 and 403 using the above techniques.
Referring to FIG. 11, the selection of curve points and weights and feeding the resulting profiles into a computational fluid dynamics (CFD) analysis software package the pressure distribution and other sectional attributes may be produces for deeply immersed, shallowly immersed or planing conditions. FIG. 11 shows pressure distribution curves 100 acting on the upper surface and 110 acting on the lower surface of hydrofoil sections produced using FIG. 9 with curves 101, 102, 103 and 104 produced by assigning different curve point weights to points 3021, 3031 and 305 and by omitting or including point 306. By combining a point creation code and a CFD code sections conforming to particular design criteria may be produced and optimised automatically providing much faster and much smoother sectional profiles than have been heretofore possible. This is particularly the case for shallowly immersed sections and for planing sections for which neither software nor standard profiles are available. Whilst planing profiles have not heretofore existed, shallowly immersed sections for use with hydrofoil assisted catamarans and other hydrofoil craft have generally been poorly specified.
Referring to FIGS. 12 and 13 profiles 401 of FIG. 7 and 402 of Figure have been extracted. FIG. 12 shows a new profile for planing or shallow immersion characterised by a pronounced ‘bustle’ 4017 at the aft end of the lower surface an inflexion curve 4018 ahead of the ‘bustle’, a flat or slightly convex forward section 4015 and a relatively sharp leading edge 4012. For some applications a more curved leading edge similar to curve 4022 of FIG. 13 may be applied. FIG. 13 is more similar to classical aerofoils but with key differences which are described below. This profile is generally better suited to slower craft and relatively deeper immersion. Flaps 4011, 4021 (not illustrated) may be applied to the sections shown.
Referring to FIGS. 14 to 17 section 401 of FIG. 12 is shown at generally increasing speed and decreasing immersion. In FIG. 14 the section is fully immersed and fully wetted. The leading edge is shown at a depth d below the free surface 201. The water surface 202 immediately ahead of the hydrofoil 401 and for some distance (not shown) aft of the hydrofoil is distorted by the thickness or the hydrofoil and by the lift it generates. In the submerged state the camber line 502 shows a significant camber 503 from the chord reference line 500. Although the mean camber line 502 is shown following aeronautic practice it is generally more useful for hydrodynamic purposes to consider the camber of the upper and lower lifting surfaces separately. FIG. 15 shows a cavitation bubble 205 starting to form at the leading edge. FIG. 16 shows the upper surface of hydrofoil 401 fully ventilated with an upper ventilation boundary 203 and a low ventilation boundary 204. FIG. 17 shows a reduced immersion depth d, with a trailing edge flap 4011 deflected downward increasing the camber 503, This would correspond generally to a ‘lift-off’ condition for a craft.
Referring to FIGS. 18 to 20 which show hydrofoil profile 401 operating in a fully planing state. In FIG. 18 the profile is just fully planing with the free surface water level 201 at or close to the leading edge. The camber 501 is now defined by the lower surface of profile 401 and reference line 500 drawn between the trailing edge 4013 and a point tangential to the lower curved leading edge section 4012 or to the intersection between the lower surface of the leading edge section 4012 and the forward underside section 4015 of FIG. 12. The camber is much reduced relative to the camber 503 of the immersed section of FIG. 14 indicating a large reduction in lift coefficient compared to the fully immersed section. However, as above noted for hydrofoil sections it is more useful to consider the cambers of the upper and lower sections separately rather than the shape of the mean camber line 502 usually considered in aeronautic practice. If so considered there is less significance between the camber of the lower immersed surface and the planing surface of the section 401. The camber to effective chord ratio is given by the length of line 501 divided by the length of the effective chord line 500 and is 2.15% in this condition for this section 401. The maximum camber point is well aft being situated 82.4% from the front of the effective chord line. By reference the maximum camber of the lower surface of a NACA 67A 709 section measured in the same manner is 0.64% at 80.2% chord. FIG. 19 shows the profile at or close to its design condition in which the forward end of the chord is now defined by the spray root generated by the planing section. The camber 501 is somewhat increased in this condition such that the camber/chord ratio is substantially increased to 4.5% positioned 65.5% along the effective chord line indicating a significant increase in lift coefficient. In this condition the angle of attack is substantially reduced such that the lift/drag ratio is substantially increased. FIG. 20 shows the hydrofoil profile 401 with a trailing edge flap deflected downwards resulting in a further increase in camber 501 to 3.6% of the effective chord positioned 84.4% along the effective chord line. This condition corresponds to the status immediately post becoming foil-borne for a preferred case where a flap is fitted.
FIGS. 21 and 22 refer to section 402 of FIG. 13 without and with the presence of a downwardly deflected flap 4021 and in the fully planing state. For the unflapped case the camber 501 is very small for this section with a camber/effective chord ratio of 1.11% at 83.5% of chord. Due to the relatively larger leading edge thickness of section 402 compared to section 401 it can be expected that the spray root point will form at a point 515 some distance aft of the leading edge. With a downward flap deflection of 10 degrees these figure become respectively 3.8% and 80.7%.
FIGS. 23 and 24 correspond to the hydrofoil profile of FIG. 13 in the fully immersed and fully wetted condition and show the high camber 513 for this section in this condition.
Referring to FIG. 25 which shows the pressure distribution for the hydrofoil profile 401 of FIG. 12, the upper line 101 shows a relatively high negative pressure extending across virtually the whole chord. A High negative pressure spike just aft of the leading edge will result in the early formation of a cavitation bubble in the area and assists the transition to fully ventilated flow. The key feature of this profile is the high positive pressure acting on the underside of the profile particularly ahead of the trailing edge and the complete absence of areas of negative pressure at all expected angles of attack as shown by curve 111S. About 33% of the total lift is due to the positive pressure acting on the underside of the hydrofoil section. At slow speed the high lift coefficient has the effect of lifting the craft. As the speed builds the upper part of the section start to ventilate, but the positive pressure acting on the underside increases in line with curve 2 of FIG. 2.
Referring to FIG. 26, line 111P shows the positive pressure distribution acting on the underside of section 410 in the design planing state. Under this condition the effective chord is designed to reduce to about 55% of the total chord as the section lifts partially out of the water. The figure of 55% will vary from section to section and depends on the ratio of foil-borne speed to maximum design speed for the craft in question. Comparing curve 111P with the aft 55% of curve 111S of FIG. 25 it can be seen that the pressure distributions are virtually the same except that in the planing state the pressure coefficient tends to zero rather than unity. The section characteristics show q relatively high lift coefficient and an extremely high lift/drag ratio compared to other planing or cavitating sections. This is due to the fact that a higher ‘bustle’ can be used for this innovative planing section than would be possible for a cavitating submerged section in that the upper cavity is ventilated and consequently higher than for a submerged section and that the extended chord increases the height under the cavity boundary. Also, once planing there is no flow over the hydrofoil section other than, perhaps, under wave conditions so any notion of cavity thickness fall away.
Referring to FIG. 27, pressure distribution curves are shown for the hydrofoil profile 402 of FIG. 13 and for a NACA 67A 709 section under deep immersion conditions. It can be seen that curve 102 showing the computed negative pressure for profile 402 is more constant and extends over a greater area than for the NACA profile consequently increasing the lift with little or no effect on cavitation or ventilation inception. The greater differences are however between curves 112 and 113 showing the pressure distribution on the underside of the sections. Here it will be seen that the positive pressure is higher for curve 113 right across the chord, but particularly so towards the trailing edge. This has a major impact on the lift/drag ratio. Additionally, the NACA section has a negative pressure zone on the underside which will result in cavitation on this surface at higher speeds which will have a very negative impact on performance at higher speeds. The new section 402 shows no negative pressure zone on the underside all normal angles of attack.
With reference to FIGS. 28 and 29 shown for the much studied sections according to U.S. Pat. No. 3,946,688, whilst FIG. 28 shows a moderately advantageous pressure distribution, the distribution calculated for the case of FIG. 29 is very poor with large areas of negative pressure on the underside both in the region of the leading edge d the flap pivot. The lift would fall away very quickly for this section as it approached the free surface.
With reference to FIG. 30, the pressure distribution is shown for a much used Speer H105 hydrofoil section. This section was designed specifically for use with hydrofoils but is very unsuited to shallow immersion operation. Lines 104 and 114 show the pressure distribution for the upper surface and the lower surface of the profile respectively. The large negative pressure extending over much of the lower surface will result in a sharp fall in lift as the section approaches the water surface. Even for normal operation the fact that both the upper and the lower surface produce negative lift with only a small pressure differential means that the lift/drag ratio is poor. The peak negative pressure on the upper surface is not high, but it is high relative to the lift coefficient.
With reference to FIG. 31, section data for the new profiles 401/4011, 402/4021 is shown together with NACA 67A 709 profile 403/4031 and Speer H105 sections 404/4041.
With reference to FIG. 32 it is shown that the new sections no only exhibit much improved pressure distribution, but also higher lift coefficients and very much higher lift/drag ratios. The overall thickness for the sections is similar other than for the thicker Speer section. Critically, the positive lift generated by the underside of the section is significantly higher for the new sections.
Whilst the figures show two particular preferred embodiments of the current invention it will be clear that the methodology of the present invention may be used to design optimised hydrofoil profiles for any condition of depth, speed and required lift coefficient.
