Investgatng salng styles and boat set-up on the performance of a hydrofolng Moth dnghy Abstract M W Fndlay, S R Turnock Flud-Structure Interactons Research Group, School of Engneerng Scences, Unversty of Southampton, UK Emal: matt.fndlay@soton.ac.uk, srt@soton.ac.uk The adopton of hydrofols n the Internatonal Moth class of dnghy has posed new challenges to salors both n terms of the set-up of the boat and hydrofols, and ther salng technques and styles. The experence of salors n the class ndcates that the heght above the water surface at whch the boat s flown (rde heght) and the amount of wndward heel (heel angle) are crtcal factors affectng performance, partcularly n upwnd salng. The fore-aft poston of the helm affects the stablty of the craft and, n conjuncton wth the aft fol settngs, alters the ptch orentaton of the craft and offers potental for sgnfcant gans n performance. A four degree of freedom velocty predcton programme (VPP) wth the capablty to nvestgate these factors s presented and used to demonstrate how the fore-aft poston of the helm and the aft fol may be used n conjuncton to maxmse speed. Nomenclature α Incdent flow angle [rad] c Chord of fol [m] X CB Movement of centre of buoyancy n X-drecton C Lft-curve slope of fol [rad - L 1 ] α X, Y, Z Dstance along X, Y, or Z- [m] axs, between centre of effort of th component of force and centre of mass of craft ρ Densty of ar [kgm - ar [m] D Drag [N] 3 ] D Spray drag [N] Spray D Drag due to wndage [N] W e Oswald effcency factor [-] ρ Densty of water [kgm - X, Y, Z F Force n X, Y, or Z- 3 ] drecton, actng on th component θ Heel angle [deg] I Moment of Inerta of craft H about centre of mass θ P Ptch angle [deg] L Length [m] AR Geometrc Aspect rato [-] L Lft [N] C Coeffcent of drag [-] M Total mass [kg] D C Coeffcent of nduced [-] D S Area of fol [m drag ] C Coeffcent of profle drag [-] t Thckness of fol [m] D p C Coeffcent of spray drag [-] Dspray C Coeffcent of lft [-] L C Coeffcent of waterplane WP area [N] [kg m ] v Apparent wnd speed [m/ a s] v Craft speed n X, Y, or Z- [m/ X, Y, Z drecton s] [-] W Total weght of craft and [N] crew z Vertcal dstance between [m] craft centre of mass and water surface
1 Introducton Hydrofols are lftng surfaces ftted to marne craft that act at speed to partally or fully lft the man body of the craft clear of the water wth the am of reducng total drag at speed and therefore offers potental for an ncreased top speed. The practcal applcaton of hydrofols to salng craft s dffcult for two man reasons [1]. Frstly, the power to weght rato of most salng boats s relatvely low because of the need to carry ballast n order to provde rghtng moment aganst the heelng moment from the sals. Ths generally lmts the applcaton of hydrofols to catamarans and dnghes whch can extend the crew weght on racks or trapezes to provde the necessary rghtng moment. Secondly, the operatng speed of salng craft s hghly varable, beng a functon of apparent wnd speed and drecton, and so the use of hydrofols s also largely a problem of developng sutable control systems to account for these fluctuatons. Nevertheless, snce 005, hydrofol-equpped Internatonal Moth dnghes have won every major champonshp [] demonstratng that n ths class hydrofols can be used successfully n a large enough range of condtons to consstently wn regattas aganst non hydrofolequpped craft from the same class. The mpressve speed of these craft (top recorded speed close to 30 knots [3]) has caused an exploson n nterest from both salors and the salng meda and development has taken place at a rapd pace posng many nterestng challenges to both desgners and salors. The major ams of ths paper are to gve an overvew of the Internatonal Moth dnghy (secton ), present a new velocty predcton program (VPP) for the Moth (secton 3) and use the VPP to look specfcally at the nfluence of aft fol settng and helm longtudnal centre of gravty (LCG) on performance (secton 4.) The Internatonal Moth Dnghy The Internatonal Moth dnghy s a 3.355m long, sngle handed, una-rgged monohull dnghy. The class rules do not lmt hull shape, materals or weght, but lmtatons are placed on length, beam and sal area. As a result the craft have evolved to be lghtweght (<30kg fully rgged), have a narrow waterlne beam (~0.3m), and large wngs (beam overall =.5m) from whch the helm hkes. Ths s a craft that has a large power to weght rato, low drag and s therefore a great platform for the use and development of hydrofols. Fgure 1. Internatonal moth. Showng narrow hull and wde beam overall due to wngs. Appendages (daggerboard and rudder) can be seen percng the surface and have lftng hydrofols mounted on the submerged ends. Photo by Hannah Kemlo. The class rules prohbt surface percng hydrofols, forcng desgners to adopt a b-fol arplane confguraton utlsng daggerboard and rudder mounted, fully submerged T-fols, wth a mechancal control system usng a bow-mounted sensor arm ( wand.).1 The control system An actve control mechansm s requred to control rde heght over a range of speeds and ths s acheved through the use of a bow-mounted wand sensor (fgure 3a) controllng a tralng edge flap on the forward (daggerboard-mounted) fol (fgure a) va a cam and push-rod
system (fgure 3b). Screw fttngs n the system allow the salor to set the wand angle whch gves a neutral flap poston but the rato of wand angle to flap angle s governed by the cam system and therefore effectvely fxed. The wand length can be vared (though not currently whlst salng) for the condtons. It s possble to adjust the aft (rudder-mounted) fol (fgure b) angle manually whlst salng usng a worm gear system whch n some cases alters the entre angle of ncdence of the fol relatve to the boat, and n others adjusts the angle of a tralng edge flap on the aft fol. (a) Daggerboard and lftng hydrofol ( Tfol ), showng tralng edge flap that s controlled by bow mounted wand sensor. Fgure Vews of typcal Int. Moth appendages and fols (b) Rudder mounted on gantry and showng lftng hydrofol ( T-fol ) at depth. Photo from [4] (a) Bow mounted wand sensor that tracks water surface and controls flap angle on forward hydrofol. Photo by Hannah Kemlo. Fgure 3 Vews of Wand sensor (b) The lnkage between the wand sensor and the push rod whch leads back to the daggerboard and mechancally controls flap angle. Photo from [5] There are a number of varables relatng to fol sze, shape and poston that must be fxed by the desgner to acheve the am of creatng a fast craft, and other varables that may be controlled by the salor relatng to the set-up of the craft n order to maxmse speed (or
stablty) n a gven wnd condton on any gven leg of the course. In the feld of yacht desgn these varables are chosen based on (n approxmately ncreasng order of cost and tme) emprcal evdence, understandng of solated components, modellng of the complete system usng a velocty predcton program (VPP), tank testng, use of computatonal flud dynamcs and two boat testng. Most tunng decsons are made based on emprcal evdence, full scale testng, two boat tunng and, less frequently, through the use of a VPP. In [1] approaches to fol desgn and confguraton for the Internatonal Moth were dscussed and a VPP presented and used to predct the performance of Internatonal Moth dnghes n context of the decsons faced by desgners, partcularly wth regard to fol selecton. It was noted however, that lmtatons of that VPP meant t was not sutable for examnng n detal technques for salng the craft, or set-up and tunng of the fol control systems.. Salng styles The nternatonal moth utlses an 8m sal whch, n combnaton wth the hgh apparent wnd speeds, generates a large amount of force. Ths force s drected approxmately perpendcular to the sal surface and ts sdeways component must be balanced by the sdeforce from the appendages to prevent sdeways acceleraton. The roll moment from the sal and appendage forces must be balanced by the rghtng moment from the acton of the helm hkng to prevent the craft rollng over. These forces are llustrated n fgure 4. When salng to wndward, the sal force s large enough that, wth the mast vertcal, the salor s unable to develop suffcent roll moment to counter t. Ths problem s solved by heelng the craft to wndward (see fgure 4), whch ncreases the perpendcular lever arm of the helm s weght and utlses a component of the weght of the craft and rg to ncrease the rghtng moment. Ths s smlar to the common style used by wndsurfers. Sal Force W Helm W Boat Fols lft Appndg Sde-force Fgure 4. Demonstratng the wndward heel angle and the showng the lft and weght forces. Note that drag and wndage forces are not represented. Photo from [4] A consequence of ths wndward heel s that a component of the weght now acts to oppose the sdeways sal-force, thus reducng the force requred from the appendages and thereby reducng leeway angle and nduced drag, wth the consequence that the craft may track hgher (to wndward) and have greater speed. However, as the effcency of the sal s reduced wth ncreasng heel angle [6], there s lkely to be an optmum angle of wndward heel; dependent on the wnd condtons, boat set-up and helm weght, and t s of nterest to nvestgate ths computatonally to examne the trade-offs and search for an optmum.
In settng up the boat the salor also controls whether the craft fles hgher ( rdng hgh ) or lower on the fols. Combned wth wndward heel, rdng hgh may have a postve effect by ncreasng the lever arm over whch the weght of the craft acts to provde rghtng moment, yet there s also an ncrease n the lever arm by whch the sal force acts to oppose rghtng moment, and the payoff between the two must depend at least partally on the wndward heel angle. Increased rde heght also decreases stablty, makng the craft harder to sal, and ncreases the rsk of fol ventlaton whch may be catastrophc. Agan a trade-off must be made and t s of nterest to examne the behavour of the system. Affectng the forces on the lftng fols, rather than the sal force and rghtng moment, the foreaft poston of the helm, n conjuncton wth aft fol settngs, are known to affect the stablty, ptch orentaton and speed of the craft. At the 008 Internatonal Moth world champonshps n Weymouth, the Australan salors demonstrated superor upwnd speed n the stronger wnds by flyng hgh and wth a bow down orentaton. Another area of great nterest s therefore n nvestgatng why ths orentaton was faster than the tradtonal set-up used by the European compettors who used essentally the same equpment. 3 Development of the VPP There are many questons regardng the set-up of the Internatonal Moth, and those assocated wth the optmal fol settngs and salng styles are motvatng factors towards developng a computatonal smulaton of the craft. In ths paper a new VPP s presented n whch the craft s free n four degrees of freedom and may be used to examne the nfluence of hydrofol set-up and salng styles on performance. The VPP s used to specfcally nvestgate the relatonshp between fore-aft poston of the helm and aft-fol angle and ther mpact on rde heght, ptch orentaton (bow-down, bow-up), speed and stablty. The results gve nsght nto the progress n boat set-up and salng styles (partcularly for stronger wnds) made by Australan salors, usng essentally the same equpment as ther European counterparts, demonstrated at the 008 World Champonshps [7]. 3.1 Overvew The VPP replcates the geometry of the Internatonal Moth (crucally the wand-fol system) and ams to fnd the stable rde-heght, velocty and ptch orentaton at whch the craft converges for a gven boat set-up and true wnd condton. Ths s acheved by quas-steady calculaton of flud and weght forces to accelerate the craft from rest through dsplacement salng, take-off and ultmately stable flght. The result of nterest s the steady moton of the craft and the desgn of the VPP reflects ths by adoptng rudmentary but suffcent models of hull-related forces (whch are zero when fol-borne) and usng a dampng factor approach to account for added mass. Ths does not affect the fnal soluton but may affect the acceleraton of the craft. Nevertheless the tme-related moton of the boat s predcted and s of nterest because t ndcates the stablty of the set-up. Comparson of the predcted moton wth vdeo footage of a Moth acceleratng from rest shows that the tme-scales of the acceleraton (onto the fols and up to full speed) are smlar. The VPP constrans the craft s yaw and roll motons but leaves t free to move n all other dmensons (surge, sway, heave and ptch.) Any heel angle can be specfed n order to look at the effects of wndward heel and other model nputs nclude aft fol settng and helm LCG. The dmensons of the Moth dnghy used n the smulaton are those of the Flyng Lme (fgure 1), a Fastacraft bult Prowler desgn of Internatonal Moth, whch s avalable for measurement and future valdaton trals. Fol settngs are determned from the geometry of the wand system and ts poston relatve to the water surface, as n the real craft. Sal drve force s maxmsed under the constrant that heelng moment may not exceed the maxmum rghtng moment and standard aerodynamc emprcal formulae are used to fnd the lft and drag forces actng on the craft, whch are resolved nto the body axs system and govern ts behavour. The smulaton s coded n Matlab and uses a one step solver based on an explct Runge-Kutta formula usng a varable step sze based on dervatves and error tolerance crtera. One 60s smulaton can take between 0s and hours to run on a modern desktop PC dependng on the number of teratons to acheve convergence at each step.
3. Computatonal Process The computatonal process s llustrated by the flow chart of fgure 5. TWA TWS LCG Fol Set Heel Craft specs Geometry Apparent wnd angle and strength Wand angle Fol 1 flap angle WSA, Vol, Centre of bouyancy of Hull Fols 1 & ncdent flow angle Appendages ncdent flow angle Vx, Vy, Vz, Z, Ptch speed, Ptch Angle Hydrodynamc Models Hull buoyancy, resstance and sde-force Appendages lft and drag Wndage Aerodynamc Models Use no net roll moment crteron to determne sal angle whch maxmses drve force wthout exceedng max. avalable rghtng moment Resolve Forces nto Body Axs Weght Wndage Lftng fols Hull Appendages Sal forces Net Forces and Moments Sum forces n X, Y and Z drectons Sum moments n ptch Integrate ODE15s solver, Matlab Fol Ventlaton? No OR T = 60s? Yes Termnate Fgure 5. Computatonal process for smulaton of Internatonal Moth 3.3 Governng Equatons The forces actng on the craft and ncluded n the VPP are attrbutable to the followng sources: hull sde-force, hull buoyancy and hull resstance, appendage (daggerboard and rudder) lft and drag, lftng fol (forward, fol 1, and aft, fol ) lft and drag, sal lft and drag, wndage and weght. Forces are calculated n the approprate flud axs and then resolved nto the body axs for X (longtudnal axs of boat, +ve at bow), Y (lateral axs of boat, +ve to wndward) and Z (orthogonal to X and Y, +ve towards mast tp) components. The moton of the craft s determned n a quas-steady approach by summng forces (or moments) n each axs usng the approprate components (1), and n the ptch drecton usng approprate moments (3). All motons are calculated about the centre of mass of the craft. v X 1 = t M F X vy 1 = t M F Y vz 1 = t M F Z (1)
z = t θ P t v Z 1 = I ( F Z X + F X Z ) ML I = 5 (4) Y Z Z Y ( F + F ) = 0 (5) The constrant that heel angle must reman constant allows the roll moment equaton (5) to be used to determne the sal forces. Frst the maxmum avalable rghtng moment s calculated based on the acton of the helm and craft weghts, and accountng for the appendage and wndage forces contrbutng to roll moment, then the sal s effectvely trmmed from maxmum n to maxmum out and the sal lft and drag are evaluated at each trm pont. The sal forces are resolved nto the body axs and the trm angle s chosen that maxmses the drve force wthout the moment due to sde-force exceedng the maxmum rghtng moment. 3.4 Component Force Models The ndvdual forces attrbutable to each component of the craft are calculated usng the models and assumptons descrbed next. These are based on standard aerodynamc or shptheory and a suffcent approxmaton approach. The most dffcult aspect of creatng the smulator s not the mplementaton of the models but establshng the correct geometrcal relatonshps wthn and across the varous flud axs systems as the craft experences changes n heave, ptch, surge and sway n the boat axs system. Geometrc calculatons are made at every tme step to establsh: Wand angle (the wand rotates n the body axs x-z plane and s assumed to track the surface at all tmes.) Apparent wnd strength and angle. Fol flow ncdence angle (ncludng fol settng, ptch angle, flow due to vertcal and rotatonal velocty, and (forward fol only) wand-flap system.) Appendage ncdent flow (leeway angle due to sway speed.) Fol tp dstance from the surface. Wetted length and areas of appendages. Locaton and amount of submerged volume of hull. The followng secton detals the ways n whch forces have been modelled n the VPP, startng wth the lft and drag forces on the sal, fols and appendages, then the wndage forces and fnally the hull resstve and buoyancy forces. 3.4.1 Fol lft The approach taken to model lft s consstently appled to appendages, fols, sal and the hull. The approach used s based on lftng lne theory to determne the lft coeffcent, C L, from the angle of attack, α, based on the effectve aspect rato, AR. [8] CL AR CL = α (6) α ( AR + ) In all cases, aspect ratos are large, 8, and the hydrofols are approxmately ellptcal. () (3) C L α s the D fol lft curve slope, whch can be determned from emprcal data or a program such as X-Fol. The lftng fols use a NACA6341 secton and the daggerboard and rudder are NACA001 sectons. Equaton 6 holds for small angles of attack but fals when the fol begns to stall. Incdent flow angles can be shown to be small but for the lftng fols, the lft coeffcent, C L, s lmted to 1.5,
and n the case of the sal the onset flow s lmted to 35 degrees (a stalled sal condton can sometmes be desrable due to the hgh drag, for example when runnng downwnd.) The centre of effort of the daggerboard s assumed to be located at ts centre, or mdway between the free surface and the tp of the daggerboard f folng. The centre of effort of the sal s assumed to concde wth the geometrc centre of area; at approxmately 1/3 the luff length above the gooseneck. The centre of effort of the lftng fols s assumed to be n the centre of the fol. 3.4. Fol drag For all lftng surfaces, the same basc approach s taken to calculate drag. The consttuent components are skn-frcton, pressure form, nduced drag and, for surface percng fols, spray drag. Profle drag s calculated usng a skn frcton coeffcent (from the ITTC 57 skn frcton correlaton lne) and a form factor (based on thckness chord rato) as n [9]. Induced drag s calculated usng lftng lne theory based on geometrc aspect rato and ncludng Oswald s effcency factor, e, to account for the nfluence of shape on effcency [8]. C = C + C (7) C D D D D p CL = (8) eπar In the case of the sal, e s related to heel angle to account for the decrease n effcency of the sal as the craft heels [6]: e =.8cos( θ ) (9) AR 0 H L S = (10) Spray drag s a drag force attrbutable to the formaton of spray, whch s always present on the rudder as t s hung from a gantry behnd the boat and therefore at all tmes a surface percng strut (fgure b). Spray drag s ncluded for the daggerboard only when the top of the board perces the surface. Spray drag s calculated usng a formula due to Chapman [10] that modfes a formula of Hoerner and s based on the thckness chord rato. t C Dspray =.009 + 0. 013 c 1 DSpray tcv S ρcdspray 0 (11) = (1) Tp loss drag, assocated wth the acceleraton of flow across the tp of a fol, juncton drag, assocated wth the nteracton of boundary layers at ntersectng sectons, and fol wavemakng drag, assocated wth the generaton of waves when the fols are operatng very close to the free surface, are consdered neglgble [11], [1]. 3.4.3 Wndage The components of wndage are helms-person, wngs, hull, foredeck and rggng. Mast and boom are assumed mplct n the sal model and fols above water (aerodynamc) drag and wand drag are neglected. No blanketng effects are accounted for and the projected area (n the plane perpendcular to the apparent wnd) of each component s used as the dmensonalsng area, S. Drag coeffcents are approxmated based on the shape of the components and usng data from Hoerner [13] and are gven n table 1. D = 0.5 v ( S C ) W ρ (13) ar a D
3.4.4 Hull Forces The man purpose of the hull wthn the VPP (and ndeed n real lfe) s to support the craft pror to t becomng fully folng, and therefore the models are rudmentary. In ths nvestgaton the hull has no bearng other than at the begnnng of a run when the craft ntally accelerates. Hull sectons are assumed to be rectangular wth vertcal sdes and flat bottom. The hull s assumed to have no rocker and be symmetrcal about md-shps (so that the bow and stern are dentcal.) The hull s assumed to have a coeffcent of waterplane area, C WP, of 0.75. The wetted surface area and volume are estmated usng the average draft; calculated geometrcally accordng to the rde heght and ptch angle of the craft. The centre of buoyancy s assumed to move wth ptch angle accordng to: L 5 CB X = (1 e θ P ) (14) So that as ptch angle changes the buoyancy forces moves quckly towards the ends of the hull, but never qute gets there. Ths s a suffcent approxmaton. The model accounts for no lateral (sdeways) movement of the centre of buoyancy as the craft are very narrow. Ths smplfes the calculaton of maxmum avalable rghtng moment whch s therefore solely due to the acton of weght. Physcally the boat cannot be heeled much when the hull s n the water as the wngs wll make contact wth the water surface. Forces due to the hull are buoyancy, sde-force and resstance. Vertcal force due to the acton of the hull as a planng surface and assocated drag forces are neglected. Buoyancy force acts n the opposte drecton to gravty and wth magntude equal to the dsplaced weght of water. The hull s assumed to act as a very low aspect rato fol, based on geometrcal calculaton of wetted length and average draft, and thereby generates sde-force and nduced drag n accordance wth (6) and (8). Hull resstance s calculated usng skn frcton and a form factor, as n [9], wth Reynolds number based on wetted length. Resduary resstance s neglected on the bass that the craft are very slender (L/B ~ 10) and only operate at low Fn (the craft are fully fol-borne at hgher speeds). Added resstance n waves s also neglected on smlar bass that the craft s fully fol-borne when there s enough wnd to generate waves. 3.4.5 Other assumptons The centre of effort of wndage s assumed to be on the fore-aft centrelne of the boat. As a consequence there s no moment due to the Z- (upward) component of the wndage force. Smlarly, to smplfy the geometrcal calculatons, the centre of effort of the sal s assumed to be on the fore-aft centrelne. The Moth, beng a hgh speed craft, usually sals wth the boom closely sheeted to the centrelne so ths assumpton probably also has a low mpact. The centre of mass of the boat (excludng helm) s assumed to be on the centrelne mplyng that the moment due to the weght of boom and sal (the only components not symmetrcal about the centrelne) s neglgble. Ptchng s neglected from the aerodynamc model for sal force calculatons; beng relatvely nsgnfcant n comparson to forward speed, wnd speed and heel angle. Leeway (as a result of sway velocty) s neglected from the model of hydrofol lft as t s relatvely nsgnfcant n magntude and affects the effectve sweep angle of the fols rather than the angle of attack. Smlarly ptch angle s neglected from the appendage models for exactly the same reason. 3.5 Implementaton Measured and estmated values for overall dmensons and coeffcents used n the smulaton are gven n Table 1. Centres of mass were estmated by lftng the fully rgged craft to fnd the balance pont n each axs. The centre of wndage of the craft s assumed to be postoned at the boat centre of mass. The centre of wndage of the helm s assumed to act at the centre of mass of the helm. All postons are defned wthn the VPP relatve to the centre of rotaton of the wand whch was arbtrarly chosen as the orgn for measurements on the boat.
Table 1. Desgn Parameters of Modelled Moth Hull 3.35 Length 5 m BWL 0.3 m wng half beam 1.1 5 m hkng dstance max 0.3 m mass helm 65 kg mass boat 45 kg C WP 0.75 form factor 1.06 Daggerboard Length 1 m Chord 0.1 m Thckness 0.00 8 m e 0.7 Rudder Length 0.9 m Chord 0.1 m Thckness 0.00 8 m e 0.7 Fol1 Length 1 m Chord - root 0.1 m Chord - tp 0.07 m Thckness 0.00 8 m e 0.7 set deg Fol Length 0.8 m Chord - root 0.1 m Chord - tp 0.07 m Thckness 0.008 m E 0.7 Sal form factor 1.05 luff length 5.585 m Area 8 m Other Craft MoI 47.63 3 kgm helmcd 1. foredeckcd 0.8 shrouddam 0.003 m shroud length perp 5 m shroudcd 1. wandneutralangle 70 deg wandfolrato 0.15 3.6 Valdaton It has not been possble so far to conduct trals of an nstrumented hydrofol Moth n order to verfy the predctons of the VPP. However, the results of the VPP regardng upwnd salng speeds (of approxmately 1 knots n 15 knots of true wnd) and hgh end speeds (approxmately 5 knots downwnd n knots of true wnd) are smlar to those observed on the water. In addton, vdeo records of the craft salng and acceleratng from standstll show that the tme-scale over whch the craft transton to fol-borne mode and approach top speed s comparable wth that gven by the VPP (eg. <4 s onto fol). 4 Results Fgure 6a gves an example of the predcted moton of the craft from the VPP. The frst fve seconds of ths run are shown n detal n fgure 6b to help dentfy the surge and sway motons. The craft can be seen to accelerate quckly from rest, adoptng a small sway velocty as a result of the sal sde force. The sway velocty decreases as the forward speed ncreases. Intally the craft ptches bow-down due to the moment generated by the sal drve force and the hydrodynamc resstve forces. Ths ptchng moment s opposed by the shft n hull centre of buoyancy at about -5 degrees but ths effect dmnshes as the craft ncreases rde heght to become fully fol-borne after about 5 seconds. In ths example the craft contnues to accelerate for about 0s, reachng a top speed n the regon of 8.5 m/s before apparently comng so close to the surface that the sway velocty ncreases sgnfcantly to account for the reduced wetted surface of the appendages. Ths ultmately leads to one of the fol tps encroachng the crtcal dstance wthn the surface and the smulaton s ended (the VPP equvalent of catastrophc fol ventlaton.) In other smulatons (fgures 10 and 11)
the craft can be seen to converge at a steady speed, n whch case ths s the speed taken as representatve of that run. (a) Smulaton lastng approx 0s Fgure 6. Example of VPP Output (b) Enlarged vew of frst 5 seconds The partcular varables under nvestgaton are the aft fol settng (alpha) and longtudnal poston of the weght of the helm (LCG). The range of values for LCG are from 1.6m, whch represents the helm sttng as far forward as possble (by the mast), to 3.1m whch represents the helm sttng as far back as possble (at the transom.) Aft fol angle s adjustable by a few degrees whle salng but can be set at any partcular regon by adjustment of the gantry. Intally results were gathered for aft fol angles n the regon -9 to +10 degrees, and ths showed that the regon n whch the aft fol s most effectve s 6-10 degrees, whch s where subsequent efforts were focussed. In order to manage the case study, all varatons of alpha and LCG were appled to just one arbtrary wnd condton and heel angle: true wnd speed of 6 m/s, true wnd angle of 10 degrees, and a wndward heel angle of 10 degrees. The results of ths test matrx are gven n table. Table. Results matrx of smulatons. Values are speed n m/s. Alpha LCG -9-6 -3 0 3 4 5 6 7 8 9 10 1.6 3.81 4.9 4.80 5.75 7.10 7.55 7.96 8.8 8.34 8.37 0 0 1.9 3.69 4.07 4.71 5.51 6.9 7.40 7.84 8.0 8.40 8.45 0 0. 3.56 3.88 4.37 5.19 8.3 7.1 7.69 8.09 0 0 0 0.5 3.47 3.73 4.11 4.75 0 7.00 7.40 7.95 8.09 0 8.35 0.8 3.37 3.58 3.86 4.34 0 0 7.4 8.01 8.18 0 8.34 0 3.1 3.7 3.43 3.6 3.9 0 0 7.13 8.40 8.50 8.68 8.33 8.00 It can be seen from the table that there are four dstnct regons. On the left the confguratons whch faled to acheve full folng because the aft fol angle s smply too low. Here the speed s lmted to 3 or 4 m/s and an example (LCG =.5, aft fol = 0) can be seen n fgure 7. The craft ntally ptches bow down due to the moments from sal force and resstve forces but ths ptch angle s opposed by the longtudnal movement of the centre of buoyancy of the hull (whch remans n the water) and the craft settles at a ptch angle of about -0.5 degrees.
Fgure 7. Not enough lft from aft fol to promote folng and consequent low speed. The next regon of the test matrx s hghlghted by the 0 entres n the bottom left. These sgnfy that the craft was unstable and dd not converge to a steady moton wthout crashng. In the bottom left regon are low aft fol angles and hgh LCG values, whch forces a relatvely bow up condton. The craft s able to attan a fully folng state but the wand s not able to remove enough lft from the forward fol and ths ultmately breaks the surface. Ths s a common occurrence for novce folers who st too far back n the boat. Fgure 8 shows an example. Fgure 8. Helm too far aft or not enough lft from aft fol. In the opposte corner of the test matrx, agan hghlghted by the 0 entres, the opposte occurs. In ths regon (hgh aft fol angles and low LCG values) the craft s forced to adopt a bow-down orentaton as the excessve lft from the aft fol produces a trmmng moment that s not suffcently balanced by the helm s weght. The aft fol ultmately breaks the surface. Fgure 9 shows an example where the craft accelerates over about 4 seconds nto a catastrophc ptch pole a frustratng and tedous experence!
Fgure 9. Helm too far forward or too much lft from aft fol. The mddle regon of the table s of greatest nterest because t ndcates where the set-up s both fast and stable. A typcal example of ths s shown n fgure 10 where the craft attans a top speed of just over 8m/s. Sgnfcantly ths regon of the table shows that for lower aft fol angles the craft speed ncreases as the helm moves forward (reducng LCG), and for hgher aft fol angles the craft speed ncreases as the helm moves aft (ncreasng LCG.) The lmt can be seen by the 0 entry at LCG =.m, alpha = 7 deg, when the system acheves such a hgh speed that t smply generates too much lft. Ths s the case of fgure 6a. Fgure 10. Fast and stable folng. 4.1 Analyss The data clearly ndcates that the hghest speeds are attaned when the weght of the helm and craft s supported by the combnaton of aft fol and forward fol, and that postonng the weght solely over one of them s less effcent. Ths s due to the reducton n total nduced drag when the weght s supported by lft from both fols rather than just one of them, due to the squared power relatonshp between lft and nduced drag (8). In the partcular case examned t appears that hgher speeds could have been acheved had less total lft been
generated (the case of fgure 6) whch suggests that an optmum set-up for the condtons would use less bult n angle of attack on fol 1 (currently degrees), a shorter wand or smaller wand neutral angle. 5 Dscusson In addton to the reducton n total nduced drag observed makng more use of the aft fol, there are secondary benefts to ths set-up. Wth ncreasng aft fol angle to support the moment due to ncreasng helm LCG, the craft adopts an ncreasngly bow-down orentaton whch s nterpreted by the wand sensor n the same way as an ncrease n rde-heght (snce the wand rotates relatve to the craft), and the acton of the control system s to reduce the lft on the forward fol. Ths cycle results n decreased angle of attack on the fols and means that the control system can be set more aggressvely relatve to a bow-up condton. Ths n turn s benefcal because for the same change n rde-heght, the wand moves through a larger angle the closer t s to vertcal. Ths gves a tghter control at the fols by effectvely ncreasng the rato of change n fol angle wth change n rde-heght. In turn ths reduces the mpact of ptch varatons on flap control relatve to heght varatons. The feature of the control system of decreasng lft wth decreasng ptch angle, and vce versa, s destablsng n ptch, and therefore reducng the mpact of ptch varatons on flap control s favourable. Tghter control could also be acheved by reducng the wand length, whch wth the correct systems, should be possble to mplement whlst salng. The aft-wards movement of LCG drectly reduces the ptch-stablty of the craft by decreasng the moment arm over whch the aft fol can exert restorng moment for small changes n ptch (aganst postve feedback from the forward fol.) Ths effect was not observed n these smulatons (though t may be partly responsble for the consequences of fgure 9) and a calculaton suggests that the helm needs to be postoned vrtually over the aft fol for t to become sgnfcant. 6 Conclusons A new Velocty Predcton Program has been developed to examne the mpact of set-up and salng styles on the performance of hydrofol-equpped dnghes. The VPP gves a more realstc smulaton of the craft than prevous work by ncludng wndward heel angle, the wand-fol control system, postonng of the helm and aft fol settngs, whch are all crtcal elements of salng the Internatonal Moth. The VPP predcts the moton of the craft and s therefore useful for dentfyng unstable set-ups as well as stable confguratons. A case study for the Moth shows that utlsng the aft fol to generate a proporton of the lft rather than just as a control surface mnmses the total nduced drag and therefore ncreases top speed. Ths requres that the salor sts further back n the craft and the craft adopts a bow down orentaton. The boat set-up for the case study appears not to be optmal because t s possble for the craft to generate too much total lft at the hghest speeds, despte beng stable and well balanced ndcatng that a set-up adjustment s requred. 6.1 Future work A common use for VPPs s to allow the generaton of polar dagrams that ndcate the maxmum speed of a yacht for any gven true wnd strength and angle. It s possble to use the new Moth VPP, n conjuncton wth an optmsaton procedure over varables ncludng wndward heel angle, aft fol settng, LCG, and wand settngs, to produce a polar dagram for the Moth and assocated optmum settngs for each wnd condton as predcted by the VPP. The large number of varables nvolved and functon calls makes ths a computatonally ntensve task but could gve salors not only target boat speeds for upwnd and downwnd legs, but also ndcate the set-ups requred to acheve those boat speeds and gve an understandng of how varatons to the set-up affects boat speeds. Most useful would be an analyss of the condtons for maxmum velocty made good (VMG) n upwnd and downwnd salng as the usual race course comprses only upwnd and downwnd legs.
Specfc case studes of nterest are the relatonshps between wndward heel angle, and rde heght (due to wand settngs) on boat speed (at or near optmal angles for maxmum upwnd and downwnd VMG) and the VPP can be used to undertake ths. At tmes there are dfferng requrements for salng style between take-off and steady speed salng such as movng body weght aft to assst take off before returnng to the steady LCG condton. Ths opton s ncorporated n the VPP, although t was not used for these results and t would be of nterest to salors to understand how movement of body weght can be used to maxmse the acceleraton to top speed. The VPP could therefore be used to look at the dynamc performance of the craft as they accelerate at starts or out of tacks and gybes although t would be desrable to adopt a more comprehensve added mass approach. Extenson of the VPP for ths purpose would also nclude the effects of small course changes ( heatng t up ) and pumpng of the sal for temporary larger sal force to overcome the drag hump near take-off. Fnally the VPP also offers great potental for examnng the control system partcularly n waves, where the water surface could be represented by any functon rather than a flat surface and the resultng craft behavour, based on the wand trackng the surface and the fols proxmty to t could be examned. References 1. Fndlay, M.W. and S.R. Turnock, Investgaton of the effects of hydrofol set-up on the performance of an nternatonal moth dnghy usng a dynamc VPP, n Innovaton n Hgh Performance Salng Yachts, 008, London, UK, Royal Insttuton of Naval Archtects, Lorent, France. p. 43-56.. http://www.moth-salng.org/mca/faces/worldchampons.jsp. World Champons. [webpage] 008 [cted 008 01-10]. 3. http://www.nt-moth.org.uk/newpages/vavavoom.htm. Speed Matters. [webpage] 008 31-8-08 [cted 008 01-10]. 4. http://www.nt-moth.org.uk/newpages/desgn.htm and A. May. Fol ventlaton. 008 16-03-08 [cted 008 01-10]. 5. http://www.fastacraft.com/moth_hulls_prowler.html and J. Illet. Fastacraft Internatonal Moth Hydrofols. [cted 008 01-10]. 6. Wellcome, J.F., Aerodynamcs of Sals, n Salng yacht desgn: theory, A. Claughton, J. Wellcome, and R. Sheno, Edtors. 1998, Addson Wesley Longman Lmted. 7. http://www.moth-salng.org/worlds/008_uk.xml. 008 World Champonshps Results. 008 [cted 008 01-10]. 8. Abbott, I. and A. Von Doenhoff, Theory of Wng Sectons. 1959: Dover Publcatons. 9. Keunng, J.A., The hydrodynamcs of hull, keel and rudder, n Salng yacht desgn: theory, A. Claughton, J. Wellcome, and R. Sheno, Edtors. 1998, Addson Wesley Longman Lmted. 10. Chapman, R.B., Spray Drag of Surface Percng Struts, n AIAA/SNAME/USN Advanced Marne Vehcles Meetng:. 197: Annapols, MD. 11. Chen, 1960. Optmum Wng-Strut Systems for Hgh Speed Operaton Near a Free Surface. 1. Martn, M., The Stablty Dervatves of a Hydrofol Boat, n Hydronautcs Incorporated, Techncal Report 001-10. 1963. 13. Hoerner, S., Flud-dynamc drag. 1958: Hoerner.