GB2171363A

GB2171363A - Yaw angle and life/drag ratio optimising hydrofoil keel

Info

Publication number: GB2171363A
Application number: GB08601748A
Authority: GB
Inventors: Merrick Levison Sims
Original assignee: Individual
Current assignee: Individual
Priority date: 1984-08-30
Filing date: 1986-01-24
Publication date: 1986-08-28
Also published as: GB8527393D0; GB8601689D0; GB2171361A; GB8503569D0; GB8527392D0; GB2171361B; GB2171362B; GB8601688D0; GB8601748D0; GB2164296A; GB2171363B; AU3293184A; GB8527394D0; AU567757B2; GB2164296B; GB2171362A; GB8527391D0

Abstract

The lifting surface area of a hydrofoil keel operating on a sailing vessel is determined so that when the keel is travelling through the water at the beating hull speed of the boat, it generates just sufficient lift at that angle of attack which gives the keel's highest lift/drag ratio to balance the side force generated by the vessel's sails throughout a given apparent wind speed range. The moment coefficient of the boat-sail combination is also adjusted so that when the above relationship is in force, the boat will be in rotational equilibrium at the keel angle of attack giving the keel's highest lift/drag ratio, so that rudder drag will also be minimised at this point. A means is also provided for varying the lifting surface area of the keel to allow it to maintain the equilibrium for wind speeds outside the abovementioned range.

Description

1 GB 2 171363 A 1

SPECIFICATION

Yaw angle and lift/drag ratio optimising hydrofoil keel This invention relates to a yaw angle and lift/drag ratio optimising hydrofoil keel for use on sailing ves- 5 sels.

To operate effectively, hydrofoil keels must be able to generate sufficient lift at low angles of attack, where the lift/drag ratio is highest, to balance the lateral air force generated by the sails, throughout the wind speed range in which the keel is designed to operate, thus minimising the yaw angles of the boats on which the keels are operating. Maintainance of a low angle of attack is important, not only to reduce 10 the yaw or leeway angle of the boat, but equally importantly because the lift/drag ratio of a keel may be up to three times as great at the angle of attack which optimises this ratio, as it is at the stalling angle of attack (around 16% Thus a sailing vessel on which the keel is operating at an angle of attack close to that which optimises that keel's lift/drag ratio, uses a smaller percentage of the lift generated by the sails overcoming keel drag, than does one operating at some other angle of attack, thus leaving a greater 15 percentage of the lift generated by the sails available as net driving force, to propel the boat.

Accordingly the present invention provides means by which the lifting surface area of a hydrofoil keel operating on a sailing vessel is determined so that when the keel is travelling through the water at the beating hull speed of the boat on which it is operating, it generates just sufficient lift at that angle of attack which gives the keel's highest lift/drag ratio, to balance the side force generated by the boat's sails 20 at the ambient apparent wind speed. The moment coefficient of the boatsail combination is also ad justed so that when the above relationship is in force, the boat will be in rotational equilibrium at the keel angle of attack giving the keel's highest lift/drag ratio, so that rudder drag will also be minimised.

A specific embodiment of the invention will now be described by way of an example with reference to the accompanying drawings in which:

Figure 1 shows a front sectional elevation of one preferred embodiment of the variable area version of the invention; Figure 2 shows a similar elevation of an analogous fixed area version; Figure 3 shows both the fixed and variable area versions in plan; together with a theoretical exposition of the basis of the keel's principle of operation, in which; L is the lift of the appliance involved, (keel or sails); M is the moment of the appliance involved; CL is the lift coefficient of the appliance involved; Cm is the moment coefficient of the appliance involved; A is the area of the lifting surface of the appliance involved; 1 is the reference length of the appliance involved, which is inserted into the moment coefficient equa tions in order to make C,, dimensionless, and depends of the configuration of the appliance; d is the density of the medium involved, (wind or water); V is the speed through the medium.

For the lift of the keel to balance the lift of the sails, V2keel = 1. V2 Lk I = -i'.d ter.CL k.el.Akeel 2 del,.CL = 1-,,, 2 d It will be convenient in the following discussion to express the speed of the wind as a multiple of the hull speed of the boat, and hence of the speed of the keel. That is V,,, = k.V,,,,. Also it will be convenient to express the lift coefficient of the sails as a multiple of the lift coefficient of the keel, that is, CL,.ii = k' 'CCL k..I.

Since the density of water is about 800 times that of air, we have, 80O. CL,ee,Ak.el.V2 keel = CL sai,.A,ei,e.k2.

V2 ke., and AkeelAwl. must equal (CLsail/CL,ee,).k2/800 or kU21800. Now, the lift coefficient of the keel depends both on it's section and it's angle of attack and the lift coefficient of the sails can be adjusted by sheeting 50 variations to give a range of optimal values with respect to lift/drag ratio throughout a given wind speed range. Thus it is possible, by suitably arranging the ratio of the keel lifting surface area to the sail area, to design a system in which the lift of the sails, over a given wind speed range is balanced by the lift of the keel operating close to that angle of attack which affords the highest lift/drag ratio, thus minimising keel drag in the wind speed range and maximising the net driving force available to propel the boat. From the 55 above results it will be seen that for the lift of a hydrofoil keel to balance, throughout some range of angles of attack close to an optimal angle of attack, the lift of the sails over some given wind speed range, the ratio of the area of the lifting surface of the keel to the sail area of the boat on which it is to operate, must be approximately equal to the square of the ratio of the wind speed at the upper end of the wind speed range in which the keel is designed to operate effectively, to the hull speed of the boat 60 on which it is designed to operate, multiplied by the ratio of the lift coefficient equivalent to the highest lift/drag ratio of the sails at the upper end of the wind speed range given, to the lift coefficient of the keel at that angle of attack giving it's highest lift/drag ratio, all divided by 800.

Boat-sail combinations generate rotational moments when sailing, which, because sails (except spinna kers) are sheeted on the leeward side of the boat, usually constitute weather moments known as weather 65 2 GB 2 171363 A 2 helm which is balanced by the application of lee helm via the rudder. Under large wind loads weather helm can become quite large, and compensation for this induces significant rudder drag into the system. Hydrofoil keels also generate rotational moments when lifting and the possibility exists of balancing keel moments against boat-sail moments when beating, to reduce or even eliminate rudder drag under these conditions. For rotational equilibrium, the moment coefficient of a hydrofoil keel operating above it's stalling speed must be equal and of opposite sense to the moment of the boat sail combination. That is Mk-1 k,.A,,.V2 ke.l. Ike, must equal minus M.,, = 2 wind. Isalls.

C,,n, varies with both the angle of attack and the section used. If the coefficient is positive the keel generates weather moments and if it is negative the keel generates lee moments, so in order to offset the weather helm of the boat the moment coefficient of the keel must be negative. Also, since the angle 10 of attack of the keel is increased by increases of the weather helm of the boat, for stability, the negative value of the moment coefficient of the keel must increase with increases in the angle of attack.

Cm.,,, can be given almost any required value when building or sailing by a combination of the following devices:

(1) when building, by suitable location of the C.L.R. and the C.E. by appropriately positioning the keel 15 and mast step and by arranging for easy mast step and sheeting width adjustments; (2) when rigging and suiting, by adjustment of the many parameters involved; (3) when sailing, by sheeting and trim adjustments.

For rotational equilibrium IVI,,, must equal M.A SO 80O.CM k I.Ako.I.V2 k I.1k I C,i,.Ai,,.k2.V2 SO, Cm..iJCm I,.., = (800/k2).(A,,/Ai,).

But we know from the previous section that A,,1A,,,=k.k2/800 So for equilibrium C1I.A.1CM k..I (CL5ai[JCL over the wind speed range in which the keel is designed to operate. Thus, if C,.i,, is arranged by means of the devices outlined above to bear approximately the same ratio to C,,,., as does CL. nil. to CLk.,I for all wind speeds in the design range and the keel section is so selected that CNIk-1 is negative throughout the range of angles of attack corresponding to the 25 wind speed range and the differential coefficient of CM k..I with respect to angle of attack is also negative throughout the same range of angles of attack, the boat will be rotationally stable throughout the design wind speed range and will beat at an angle of attack close to that affording the highest lift/drag ratio for the keel section selected. Note also, that since M,, andMk..I come to equilibrium through small adjust- ments in the angle of attack of the keel it is not necessary for C,, to be exactly equal to k-CM keet"kel 30 over the whole wind speed range involved. As long as the above relationship is reasonably close, once equilibrium is established within the range, any change in M,,, induced by a change in wind speed, will induce whatever small change is required in the angle of attack of the keel to deliver the required change in CM k.el to restore the rotational equilibrium. Note also, that the system will be stable under changes in wind direction. Any change in IVI,,, due to change in wind direction will induce a change in the angle of attack of the keel in the correct sense required to restore the rotational equilibrium at the old angle of attack oriented to the new wind direction. With this system operating when beating, the rudder can be neutralised or even withdrawn from the water, thus significantly reducing rudder drag and allowing the boat to beat automatically, close to the keel angle of attack affording the highest lift/drag ratio, and thus allowing the boat to sail at the highest speed commensurate with the driving force available. Since the 40 keel angle of attack giving the highest lift/drag ratio is about 5' for camberless keels and can be about 00 for cambered ones, it will be obvious that significantly higher tracks can be attained with the above sys tem than are attained at present with conventional keels. Another advantage of the system is that it leaves the crew free to devote it's undividied attention to maintainance of the optimal sail setting for the ambient wind conditons without the hazard of variation from the optimal setting of the sail platform due to steering errors.

The reason why the keel angle of attack is optimised for the highest wind speed in the design range and not the average wind speed in the range, is because at wind speeds corresponding to keel speeds below the hull speed of the boat a reduction in wind speed automatically includes a reduction in both Lk.W and IVI,, through a reduction in V2 ke., and the equilibrium is maintained, leaving both CLke, and CMk close to their original values and consequently leaving the keel angle of attack close to it's original opti mal value. For reefed suits of sails C,,,nf.d.,i,, can be arranged by the many devices available to equal C,,,,, adjusted for the changed sail area, so that rotational equilibrium can be maintained throughout virtually the entire wind speed range.

An alternate method of maintaining the required rotational equilibrium outside the design wind speed 55 range would be to lock or set the amount of helm required to restore the equilibrium on to the rudder and the keel would again function as outlined above, the only penalty paid being the small amount of induced rudder drag. For wind speeds outside the design range, the ratio of keel lifting surface area to sail area to suit the new wind speed range can be obtained by varying the keel lifting surface area rather than by reefing the sails. One arrangement for varying the area of the keel lifting surface is shown in Figure 1 which depicts in front sectional elevation, a keel adapted for this function. In this arrangement the keel is constructed in two major parts consisting of: an upper part shown as 1 in figure 1, rigidly fixed to the hull of the boat and extending vertically downward to a level shown as 6 in figure 1, slightly above the maximum ballast level in the keel when the keel is in a configuration affording the minimum lifting surface area and with the planform of this upper part 1 being the same as the planform of the 3 GB 2 171 363 A 3 vertically sided upper part of the keel shown in figure 2 in front sectional elevation and in plan in figure 3; and a lower part shown as 2 in figure 1 having the same general configuration as the lower two thirds or so of the keel of figure 2 except that it's upper part 3 is shaped to form a sliding sleeve fitting with a waterproof seal outside the vertical sided upper part 1, the sleeve being extended vertically upward to a point where, when the keel is in the configuration affording the lowest lifting surface area, the top of the 5 sleeve 3 is level with the top of the upper part 1. The arrangement also requires a two way pressure water pump 4 situated either within the keel or within the boat and able to pass water as required be tween the watertight compartment within the keel and the water in which the boat is floating. When water is extracted from the watertight compartment in this operation, the pressure of the atmosphere acting through the water outside the keel will raise the lower part, 2, of the keel thus reducing the keel's 10 lifting surface area. Conversely, adding water to the watertight compartment will increase the lifting sur face area. Since the atmospheric pressure is equal to a head of about 2' 6' of mercury, the system will operate for a depth of lead ballast inside the keel, shown as 5 in figure 1 of up to about X, which for a keel of the configuration in question is more than enough for almost all operational purposes. For very large boats where the depth of the keel is a significant fraction of the head of water which the atmos phere will support, higher maximum ballast depths within the keel can be achieved by locating the two way water pump, 4, near the level, 6, within the keel, since the water head, 6-4, would then be above the pump andnot below it. Some restraining means connecting parts 1 and 2, such as chains or cables of appropriate lengths situated within the keel, must also be fitted to prevent the lower part of the keel from failing away in the event of a pressure failure within the keel. Maintainance of a watertight compartment 20 within the keel requires that this compartment must be effectively separated from the bilge. This condi tion requires that boats to which the above keel is to be fitted must have their hulls shaped so as to incorporate a bilge, separate from and independent of the space within the keel, in an arrangement, one form of which is shown at the tops of figures 1 and 2.

While the above description contains many specifications, these should not be construed as limitations 25 on the scope of the invention, but rather as an exemplification of one preferred embodiment thereof.

Accordingly, the scope of the invention should be determined not by the embodiment illustrated, but by the appended claims and their legal equivalents.

Claims

1. A keel having hydrofoil shape, the ratio of the area of the lifting surface of said keel to the sail area of the boat on which said keel is adapted to operate, being approximately equal to the square of the ratio of the wind speed at the upper end of the wind speed range in which said keel is designed to operate, to the hull speed of said boat multiplied by the ratio of the lift coefficeint of the sails at their setting giving 35 the highest lift/drag ratio at the upper end of said wind speed range, to the lift coefficient of said keel at the angle of attack giving it's highest lift/drag ratio, all divided by 800.

2. A keel as defined in claim 1 wherein the ratio of the moment coefficient of said keel about the line of action of the sum of the hydrodynamic lift forces normal to the line of movement of said keel through the water at the angle of attack giving the keel's highest lift/drag ratio, to the moment coefficient of the 40 boat-sail combination about the line of action of the sum of the aerodynamic lift forces normal to the apparent wind direction at the sail setting giving the highest said lift/drag ratio at the upper end of said wind speed range, is approximately equal to the product of the ratio of the lift coefficient of said keel at that angle of attack giving it's highest lift/drag ratio, to the lift coefficient of the sails equivalent to their highest lift/drag ratio at the upper end of said wind speed range, and the ratio of the average total chord 45 of the sails to the average chord of the keel.

3. A keel as defined in claim 2 wherein the moment coefficient is negative throughout the range of angles of attack in which it is designed to operate.

4. A keel as defined in claim 3 wherein the differential coefficient of the moment coefficient with re spect to angle of attack is negative throughout the range of angles of attack in which the keel is designed 50 to operate.

5. A keel as defined in claim 1 wherein the area of the lifting surface is variable either by withdrawal of the upper part of the keel into the hull of the vessel or by extending the length of the keel with a sleeve arrangement.

6. A keel as defined in claim 5 comprising: a first hydrofoil shaped portion adapted to be fixed to the 55 boat hull; a second hydrofoil shaped portion telescopically attached to the first portion; and a means adapted to controllably extend and retract said first and second portions relative to one another.

7. A keel as defined in claim 6 wherein said first portion is of hollow constant section along the direc tion of telescopic movement, said second portion includes a sleeve of constant section fitting over said first portion and said keel further including sealing means between said first and second portions and a 60 pump controlling the volume of water within said keel.

8. A keel as defined in claim 7 further comprising restraining means imposing a maximum extension of said first and second portions relative to one another.

4 GB 2 171363 A

9. A keel as defined in claim 2 being attached to a craft, the rudder of which is provided with a fixing or setting means whereby the rudder helm can be fixed to any required degree of weather helm, of lee helm or to zero helm.

10. A keel substantially as described herein with reference to figures 1, 2 and 3 of the accompanying 5 drawing.

4 Printed in the UK for HMSO, D8818935,7186,7102. Published by The Patent Office, 25 Southampton Buildings, London, WC2A lAY, from which copies may be obtained.