SD2706 Sailing for Performance

Objective: Learn to calculate the performance of sailing boats

Today: Sailplan aerodynamics Recap

User input: Rig dimensions ‣ P,E,J,I,LPG,BAD Hull offset file Lines Processing Program, LPP: ‣ Example.bri LPP_for_VPP.m rigdata Hydrostatic calculations Loading condition ‣ GZdata,V,LOA,BMAX,KG,LCB, hulldata ‣ WK,LCG LCF,AWP,BWL,TC,CM,D,CP,LW, T,LCBfpp,LCFfpp Keel geometry ‣ TK,C

Solve equilibrium State variables: Environmental variables: solve_Netwon.m iterative ‣ VS,HEEL ‣ TWS,TWA ‣ 2-dim Netwon-Raphson iterative method

Hydrodynamics Aerodynamics calc_hydro.m calc_aero.m VS,HEEL dF,dM Canoe body viscous drag Lift ‣ RFC ‣ CL Residuals Viscous drag Residuary drag calc_residuals_Newton.m ‣ RR + dRRH ‣ CD ‣ dF = FAX + FHX (FORCE) Keel fin drag ‣ dM = MH + MR (MOMENT) Induced drag ‣ RF ‣ CDi

Centre of effort Centre of effort ‣ CEH ‣ CEA FH,CEH FA,CEA The rig As we see it

Sail plan ≈ Mainsail + Jib (or genoa) + Spinnaker

The sail plan is defined by: IMSYC-66 P Mainsail hoist [m] P E Boom leech length [m] BAD Boom above deck [m] I I Height of fore triangle [m] J Base of fore triangle [m] LPG Perpendicular of jib [m] CEA CEA Centre of effort [m]

R Reef factor [-] J

E LPG

BAD

D Sailplan modelling

What is the purpose of the sails on our yacht?

To maximize boat speed on a given course in a given wind strength ‣ Max driving force, within our available righting moment

Since: We seek:

Fx (Thrust vs Resistance) ‣ Driving force, FAx Fy (Side forces, Sails vs. Keel) ‣ Heeling force, FAy (Mx (Heeling-righting moment)) ‣ Heeling arm, CAE Aerodynamics of sails

A sail is: ‣ a foil with very small thickness and large camber, ‣ with flexible geometry, ‣ usually operating together with another sail ‣ and operating at a large variety of angles of attack ‣ Environment L

D V

Each vertical section is a differently cambered thin foil Aerodynamics of sails

TWIST due to e.g. ‣ Spanwise loading ≈ elliptical ‣ Wind shear Altitude ‣ Heel

Wind speed

Each vertical section is a differently cambered thin foil, with an individual angle of attack!

Messy! Need simplified rational approximative approach! Aerodynamic forces In the VPP calculations we are interested in the total THRUST and SIDEFORCE generated by the sailplan since Windtriangle Fx (Thrust vs Resistance) Fy (Side forces, Sails vs. Keel) (Mx (Heeling-righting moment)) TWS AWS TWA

AWA VS Lift, L, perpendicular to apparent wind Drag, D, parallell to Total sailplan force apparent wind REMINDER: 3 coordinate systems - Upright: follows the un-heeled boat - heeled: heels with the boat - Wind fixed: follows the AW Aerodynamic forces The aerodynamic force vector In the upright coordinate system FA = [FAx,FAy,FAz]

FAz

FAx, total thrust D FAy L

FAx W FAy, total side force Aerodynamic forces The lift and drag can then be transformed and expressed in the upright boat-fixed force vector

Lift & Drag expressed in force vector

⎡ FAx ⎤ ⎡ cos AWA sin AWA 0 ⎤ ⎡ −D ⎤ ⎢ ⎥ FAy = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ −sin AWA ?cos AWA 0 ⎥ ⎢ L ⎥ ⎣⎢ FAz ⎦⎥ ⎣⎢ 0 0 0 ⎦⎥ ⎣⎢ 0 ⎦⎥

AWA

NOTE: Zero heel is assumed! What FAx happens to AWA and AWS as HEEL≠0

L D

FAy Aerodynamic forces Effects of heel 1 L = ρV 2C A 2 L W is not CL = f (angle of attack) z V to mast perpendicular to =⊥ } mast! W_RED Introduce wind vector, W, as ⎡ ⎤ −AWS cos AWA W W = ⎢ ⎥ D ⎢ AWSsin AWA ⎥ ⎣⎢ 0 ⎦⎥

L

Transform W to heeled CSYS y W W_RED

x Aerodynamic forces

Transformation from upright to heeled CSYS ⎡ W _ REDx ⎤ ⎢ ⎥ -1 W _ RED = ⎢ W _ REDy ⎥ = C W ⎢ W _ REDz ⎥ ⎣ ⎦ W_RED

⎡ 1 0 0 ⎤ W D C = ⎢ ⎥ ⎢ 0 cos HEEL −sin HEEL ⎥ ⎣⎢ 0 sin HEEL cos HEEL ⎦⎥ L

NOTE: Download SailView from the course homepage. Use this program to understand what goes on in this transformation and why it is important! Aerodynamic forces

Flow velocity in heeled CSYS

2 2 AWS _ red = W _ REDx + W _ REDy Lift and Drag in the heeled wind-fixed coordinate system Reduced apparent wind angle, in MATLAB AWA _ red=π-atan2(W _ REDx, W _ REDy) }

”In the VPP calculations we are interested in the total THRUST and SIDEFORCE generated by the sailplan”, in the upright coordinate system

Transform lift and drag into upright force vector FA Aerodynamic forces Assume that L & D are Lift & Drag in heeled boat fixed CSYS know as functions of AWS_RED & AWA_RED ⎡ FA _ HEELx ⎤ ⎡ -D ⎤ ⎢ ⎥ FA _ HEEL = FA _ HEELy = A ⎢ ⎥ ⎢ ⎥ ⎢ L ⎥ ⎢ ⎥ 0 ⎣ F A _ H E E L z ⎦ ⎣⎢ ⎦⎥     Heeled FA_WIND, wind- AWS_RED fixed vector

Transformation matrix, remember? AWA_RED ⎡ cos AWA _ red sin AWA _ red 0 ⎤ ⎢ ⎥ FA_HEELx A = ⎢ −sin AWA _ red cos AWA _ red 0 ⎥ ⎣⎢ 0 0 1 ⎦⎥

L D

FA_HEELy Aerodynamic forces

CALCULATE AWA & AWS IN From heeled CSYS to upright CSYS UPRIGHT CSYS

⎡ FAx ⎤ FORMULATE WIND VECTOR ⎢ ⎥ W FA = ⎢ FAy ⎥ = C ⋅ FA _ HEEL ⎣⎢ FAz ⎦⎥ TRANSFORM W TO HEELED CSYS

FAx = Thrust CALCULATE AWS_RED & AWA_RED FAy = Sideforce, induces heeling moment CALCULATE L & D IN FAz = Non-zero! Assumed to be HEELED WIND-FIXED CSYS counteracted by the lift produced by the keel TRANSFORM L & D TO HEELED CSYS (FA_HEEL)

TRANSFORM TO UPRIGHT How do we determine L & D? CSYS (FA) Lift and Drag of sails

For sails, there are principally 2 methods to derive the lift and drag coefficients ‣ Model or full-scale experiment So how do we do? ‣ Numerical methods (CFD or PF) } Lift and Drag of sails

As with foils in general

1 2 1 2 L = ρC V A D = ρCDV A 2 L 2 and Apparent wind angle

CL ,CD = f (geometry,angle of attack) L D which are controlled by trimming: ‣ Luffing or bearing away ‣ Adjusting any number of trim controls ‣ or a combination of the two Angle of attack

Apparent wind speed

UPWIND - Large lift/drag OFFWIND - large drag, ratio, operates below stall stalled state Lift and Drag of sails

Note: Thrust and Sideforce are indirectly related to the angle of attack, but directly related to the apperent wind angle D L

AW

Hence: Cl and Cd are usually expressed as functions of apparent AWA instead of AoA. This implies that the coefficients represent optimum trim at a certain AWA, i.e. max(THRUST)! Lift and Drag Upwind sailset = 1 Downwind sailset = 2 Kerwin model (MIT 1976) The aerodynamic model is based on a sailsets. Characterized by: ‣ Total sail area, SA_i ‣ Total aerodynamic centre of effort, CE_i ‣ Total aerodynamic lift and drag coefficients as functions of AWA, cl_i, cd_i

where i, is the sail type (e.g. main, jib or spinnaker)

During extensive work on the development of VPP programs starting in the 1970’s. (Hazen, Poor, Fossati) Experimental activities have been performed to derive generic sail coefficients for different types of sails. The rig As we see it

The individual sail areas are calculated as SA _ main = 0.5 ⋅ P ⋅ E ⋅1.1 2 2 SA _ jib = 0.5 J + I ⋅ LPG IMSYC-66 SA _ spinn = 1.8 ⋅ J ⋅ I P Sailsets I Upwind sailset = 1 ⇒ SA _ spinn = 0 Downwind sailset = 2 ⇒ SA _ jib = 0 CEA The reference sail area is defined as SA _ ref = ∑SA _i J E LPG

BAD

D The rig As we see it Total aerodynamic centre of effort R=1.0 CE _ main ⋅ SA _ main + CE _ jib ⋅ SA _ jib + CE _ spinn ⋅ SA _ spinn CEA = ⋅ R SA _ main + SA _ jib + SA _ spinn

Reef factor, varies between 0.3-1.0

Vertical centre of effort from baseline (keel line of canoe body) CE _ main = 0.39 ⋅ P + BAD + D R=0.6 CE _ jib = 0.39 ⋅ I + D CE _ spinn = 0.565 ⋅ I + D

NOTE: We only consider the vertical position of the centre of effort! Lift and Drag Defined for each individual sail and derived with trim corresponding to maximum thrust

2 (CL _ main ⋅ SA _ main + CL _ jib ⋅ SA _ jib + CL _ spinn ⋅ SA _ spinn) CL = R SA _ ref

2 (CD _ main ⋅ SA _ main + CD _ jib ⋅ SA _ jib + CD _ spinn ⋅ SA _ spinn) CD = R SA _ ref CD _TOT = CD + CD _i

1.8

1.6 CL main CL jib 1.4 CL spinnaker CD main 1.2 CD jib CD spinnaker

] 1 ï

0.8

CL, CD [ 0.6

0.4

0.2

0

ï0.2 0 20 40 60 80 100 120 140 160 180 Apparent wind angle [deg] Lift and Drag Induced drag and aspect ratio Dependent on planform geometry which changes depending on apparent wind angle

2 ⎛ 1 ⎞ CD _i = CL ⎜ + 0.005⎟ ⎝ π AR ⎠

2 IMSYC-66 (I (1+ 0.1⋅ BE)) AR = where SA _ ref

BE = 1 AWA _ red < 30° BE = 0 AWA _ red > 90° 30° < AWA _ red < 90° linear interpolation

z

x Lift and Drag

Finally lift and drag are determined as 1 L = AWS _ red 2 ⋅CL ⋅ SA _ ref 2 1 We’re done, puh.....! D = AWS _ red 2 ⋅CD _TOT ⋅ SA _ ref 2 Homework 3 Finish the implementation of the aerodynamic model in calc_aero.m calc_Sail_CLCD.m You do NOT need to add any new lines of code! Verify your results against ours in the exercises! 29 april 2011 Reminder kl. 10.00 Plats: meddelas via mail Center for O.S.A senast 20/4 via mail till: Naval Architecture Prepare 2 questions or points of [email protected], OBS ange ämnesrad: mangeolsson Magnus ‘Mange’ Olsson discussion each Skeppare, Ericsson 3 VOR 08/09 Tekniskt ansvarig, Ericsson VOR 05/06 Vinnare, EF language VOR 97/98 6 varv runt jorden, m.m.

[email protected] Föreläsning, Sailing for Performance SD2706 Mange Olsson No later then 21/4!!