SD2706 Sailing for Performance Objective: Learn to calculate the performance of sailing boats
Predict Performance - Velocity Prediction Program Wind: -speed -angle Boat data Performance: - Speed - Heel - Leeway -...
Literature You need the book! 300:- from Jakob (or e.g. on Bokus...) We will use better notation than the book. Follow our notation. Teachers: Jakob Kuttenkeuler jakob@kth.se (Examiner) Mikael Razola, razola@kth.se First time we run the course...
Course Format: Code and use your own VPP! Cycle: 1. Reading (Fossati mostly) 2. Lecture 3. Homework 4. Peer review of printed reports 5. In-class discussions Components for your VPP Chapter in your VPP reference graded by teachers Cycles: Keel/Stability/Sails/Hull resistance/vpp solver/design optimization Guest lecture Hands on sailing lab :-) J92 VPP-optimize your boat within a rule Oral exam on theory Competition
Mikael
Jakob
The boat mast Port = Left side of boat Starboard = Right side of boat Boat = Rig + Hull Spinnacker IMSYC-66 Rig Mast & boom + Sails Hull Canoe body + appendages Appendages Keel + rudder Keel Blade (or fin) + bulb (weight) Head sail genoa Jib Main sail boom Canoe body Stern Bow keel blade Fin rudder Bulb
The boat - As we define it IMSYC-66 P I CEA J E LPG D BAD z LWL DWL x TC CEH T TK C LOA
VPP Program structure User input: Rig dimensions P,E,J,I,LPG,BAD Hull offset file Example.bri Loading condition WK,LCG Keel geometry TK,C Lines Processing Program, LPP: LPP_for_VPP.m Hydrostatic calculations GZdata,V,LOA,BMAX,KG,LCB, LCF,AWP,BWL,TC,CM,D,CP,LW, T,LCBfpp,LCFfpp hulldata rigdata Solve equilibrium solve_netwon.m 2-dim Netwon-Raphson iterative method State variables: VS,HEEL Homework 1 Hydrodynamics calc_hydro.m Canoe body viscous drag RFC Residuary drag RR + drrh Keel fin drag RF Residuals calc_residuals_newton.m df = FAX + FHX (FORCE) dm = MH + MR (MOMENT) FH,CEH FA,CEA Aerodynamics calc_aero.m Lift CL Viscous drag CD Induced drag CDi Centre of effort CEH Centre of effort CEA
The boat The Force Balance 3 forces- Aero+hydro+gravity, how hard can it be?! Aero Hydro Static forces: Gravity & buoyancy Dynamic forces: Due to relative motion Gravity
What equations to solve In this course: Only static conditions considered z Basically: Find maximal boat speed (VS) for which all equations can be solved 6 DOF and 6 Equations: Fx Surge (Thrust vs Resistance) Fy Sway (Side forces) Fz Heave (gravity vs buoyancy vs...) Mx Roll (Heeling vs rightening moment) My Pitch (Pitching-rightening moment ) Mz Yaw (Yawing moment) x y
Types of Sailing Craft: Let us look at some eye-candy Keel Boats Windsurfers Kitesurfers Dinghies Cruising Yachts Racing Yachts Multihulls catamarans, trimarans Superyachts Sail-Assisted Vessels etc...
Not much new under the sun The earliest known depictions of sails are from ancient Egypt around 3200 BCE where reed boats sailed upstream against the River Nile's current. Malaysia today reed boats
Windsurfers & Kitesurfers
Dinghies
Land and Snow sailing 16
Keelboats J92
Cruising Yachts
Racing Yachts
Multihulls Often for performance
Superyachts
Moth Balancing on foils
Speed monsters Windjet Hydroptère Yellow pages Sailrocket Swedish speed sailing challenge
Sail Assisted Vessels
Ice sailing with very low resistance
Oops!
Points of Sailing Static equilibrium at various True Wind Angles, TWA True wind, VT Hydro The rudder is the yaw moment control Reaching (öppen bog) Aero. Beating (Bidevind) Running (Undanvind) Running (Undanvind) upright (rudder needed) heeled
Boat performance Polar diagram True wind, VT True wind angle TWA Velocty Made Good (VMG) 4.5kn 9kn Boat speed VS [knots]
You do know what a knot is?! 1 Nautical mile (NM) = 1852 m 1 knot = 1 NM/hour 1 knot = 1.852 km/h 1 knot = 1852 m/s 3600
Velocity triangle Our Notation: AWA : Apparent Wind Angle AWS : Apparent Wind Speed TWA : True Wind Angle TWA : True Wind Angle Angles are relative to boat, not relative earth True wind TWS TWA Apparent wind, AWS Typically: TWA, TWS and VS, are given AWA and AWS are calculated by you Hint: Law of Cosines (Cosinussatsen) AWA Ship speed, VS
Equilibrium In the horizontal plane LEEWAY x Apparent wind VA FHY=FAY Hydrodynamic force FH Boat speed VS FAX FHX=FAX FH: VS, Leeway, Geometry of hull & fin, Rudder, Keel, etc. Aerodynamic force FA FA: VT, AWA, Sheet, Heel, Sail area, Sail trim, Types of sails, Type of rig, etc. FAY So roughly (in reality & in VPP): 1. Wind+rig generates FA 2. LEEWAY ajusted to achieve FHY=FAY 3. We pay the prize FHX 4. if FAX FHX then adjust VS
Generate side force Approximations: 1) All side force generated by fin, ignore the hull 2) Use full depth T=TK+TC Canoe body (or Hull) T TK Fin C CEH x z TC Bulb Now we must learn how lifting surfaces work!
Fluid dynamics of lifting surfaces!! The force is simply... the surface integral of the pressure field F= df = Pn ds S! Newtons laws of motion Fluid is redirected (like the Archimedes integral) S but the problem is the difficulty in calculating the pressure... We need a more hands on, rational, simplistic although approximative approach :-)!
2D lifting profile (no span-wise flow) Drag // flow Lift flow L = qac l Size Flow speed force = qac Shape & angle Low pressure A: Projected Area of wing D = qac d q = 1 2 ρv 2 Dynamic pressure High pressure!
Lift (Side force) Drag // flow Lift flow z T TK CEH x TC C 2D: (No 3D effects) L = qac l A: Fin area (c*t) c: chord 3D: (Looses efficiency) L = qac L C L = C l 1 + 2 ear!
Drag/Resistance 2 components with different origin 1)Friction & turbulence 2)Tip vortex= pressure leakage!! 1 2D, Viscous drag: (friction & turbulence) D visc = RF visc = qac d Resistance Fin A: Fin area (c*t) c: chord 2 3D: Induced drag: (due to lift) Where: D i = RF i = qac Di Aspect ratio: AR = T 2 A Span efficiency factor e 0.8 C Di = C 2 L πear Thus, for the fin i total: RF = RF visc + RF i
Lifting sections Nice tool: www.javafoil.com We know l = qcc l d = qcc d Cl NACA0012 Cl C l = C l α α = C l α α α C d k 0 + k 1 C l + k 2 C l 2 Cd From the linear region of the figure: 0.85 180 7.5 π 6.5 C lα 2π
Sections design If you like www..com Reynolds number ratio of inertial forces to viscous forces 1. Choose profile family (Geometry tab) 2. Adjust thickness etc (Geometry tab) 3. Choose Reynolds number (Polar tab) 4. Plot Cl -α and Cd-Cl curves (Polar tab) R e = VC ν v: kinematic viscosity Water: v = 1*10-6 m 2 /s Air: v = 15*10-6 m 2 /s C Keel
Homework: Keel blade (or fin) Center of Effort Hydro CEH=-T/2 z FHY =FAY T TK CEH x TC Heel & FAY given Calculate hydro forces on the fin Write code for RF & CEH Do not forget the 3D effects! Verify your code Study the keel blade/fin, 3-12kn Verify against my results Follow the rules Bring results on paper to next lecture C FAX FAY Assumed given This homework FHX= RFin +RCanoe
My results on H1 Constant side force at 3-12 knots!! Low speed vs high speed? What happens at another heel? What happens at another AR? Keep an eye on LEEWAY What happens at low speed? What happens with smaller/bigger area?