Sailing for PerformanceObjective: Learn to calculate the performance of sailing boats

SD2706

Today: Sailplan aerodynamics

User input:Rig dimensions‣ P,E,J,I,LPG,BAD

Hull offset file‣ Example.bri

Keel geometry‣ TK,C

Loading condition‣ WK,LCG

rigdata

hulldata

Lines Processing Program, LPP:

Hydrostatic calculations‣ GZdata,V,LOA,BMAX,KG,LCB, LCF,AWP,BWL,TC,CM,D,CP,LW, T,LCBfpp,LCFfpp

FA,CEAFH,CEH

Aerodynamics

Lift‣ CL

Viscous drag‣ CD

Induced drag‣ CDi

Centre of effort‣ CEA

calc_aero.mHydrodynamics

Canoe body viscous drag‣ RFC

Residuary drag‣ RR + dRRH

Keel fin drag‣ RF

Centre of effort‣ CEH

calc_hydro.m

State variables:‣ VS,HEEL

Residualscalc_residuals_Newton.m

‣ dF = FAX + FHX (FORCE)‣ dM = MH + MR (MOMENT)

Solve equilibriumsolve_Netwon.m‣ 2-dim Netwon-Raphson iterative method

LPP_for_VPP.m

Environmental variables:‣ TWS,TWA

dF,dMVS,HEEL

iterative

Recap

IMSYC-66

E

BAD

LPG

I

P

J

CEA

D

The rigAs we see it

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

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

Sailplan modellingWhat 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

Fx (Thrust vs Resistance)

Fy (Side forces, Sails vs. Keel)

(Mx (Heeling-righting moment))

Since:

‣ Driving force, FAx

‣ Heeling force, FAy

‣ Heeling arm, CAE

We seek:

Aerodynamics of sailsA 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

Each vertical section is a differently cambered thin foil

V

L

D

Aerodynamics of sails

‣ Spanwise loading ≈ elliptical ‣ Wind shear‣ Heel

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

Altitude

Wind speed

TWIST due to e.g.

Messy! Need simplified rational approximative approach!

Aerodynamic forces

AWA

TWAAWS

Lift, L, perpendicular to apparent wind

Drag, D, parallell to apparent windTotal sailplan force

In the VPP calculations we are interested in the total THRUST and SIDEFORCE generated by the sailplan since

Fx (Thrust vs Resistance)

Fy (Side forces, Sails vs. Keel)

(Mx (Heeling-righting moment)) TWS

VS

Windtriangle

3 coordinate systems- Upright: follows the un-heeled boat- heeled: heels with the boat- Wind fixed: follows the AW

REMINDER:

FAy, total side force

FAx, total thrust

In the upright coordinate system FA = FAx,FAy,FAz[ ]

Aerodynamic forcesThe aerodynamic force vector

FAy

FAx

FAz

W

L

D

FAxFAyFAz

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥=

cosAWA sinAWA 0− sinAWA cosAWA 0

0 0 0

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

−DL0

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

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

Aerodynamic forces

FAy

FAx

LD

AWA

?

Lift & Drag expressed in force vector

The lift and drag can then be transformed and expressed in the upright boat-fixed force vector

Introduce wind vector, W, as

W =−AWS cosAWAAWS sinAWA

0

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

Aerodynamic forces

z

y

x

W

W_RED

D

L

W is not perpendicular to mast!

L =12ρV 2CLA

Effects of heel

CL = f (angle of attack)V =⊥ to mast }

W W_RED

Transform W to heeled CSYS

Transformation from upright to heeled CSYS

W _ RED =W _ REDxW _ REDyW _ REDz

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥= C -1W

C =1 0 00 cosHEEL − sinHEEL0 sinHEEL cosHEEL

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

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

W

W_RED

D

L

Flow velocity in heeled CSYS

AWS _ red = W _ REDx2 +W _ REDy2

AWA_ red=π -atan2 W _ REDx, W _ REDy( )Reduced apparent wind angle, in MATLAB

Lift and Drag in the heeled wind-fixed coordinate system

Aerodynamic forces

}”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

FA_HEEL =

FA_HEELxFA_HEELyFA_HEELz

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥= A

-DL0

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

Heeled FA_WIND, wind-fixed vector

A =cosAWA_ red sinAWA_ red 0− sinAWA_ red cosAWA_ red 0

0 0 1

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

Aerodynamic forcesLift & Drag in heeled boat fixed CSYS

Transformation matrix, remember?

FA_HEELy

FA_HEELx

AWA_RED

DL

AWS_RED

Assume that L & D are know as functions of AWS_RED & AWA_RED

CALCULATE AWA & AWS IN UPRIGHT CSYS

FORMULATE WIND VECTOR W

TRANSFORM W TO HEELED CSYS

CALCULATE AWS_RED & AWA_RED

CALCULATE L & D IN HEELED WIND-FIXED CSYS

TRANSFORM L & D TO HEELED CSYS (FA_HEEL)

TRANSFORM TO UPRIGHT CSYS (FA)

From heeled CSYS to upright CSYS

FA =FAxFAyFAz

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥= C ⋅FA_HEEL

FAx = Thrust

FAy = Sideforce, induces heeling moment

FAz = Non-zero! Assumed to be counteracted by the lift produced by the keel

Aerodynamic forces

How do we determine L & D?

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

As with foils in general

Apparent wind speed

L =12ρCLV

2A D =12ρCDV

2A

Apparent wind angle

Angle of attack

LD

CL ,CD = f geometry,angle of attack( )

and

which are controlled by trimming:‣ Luffing or bearing away‣ Adjusting any number of trim controls‣ or a combination of the two

UPWIND - Large lift/drag ratio, operates below stall

OFFWIND - large drag, 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

AW

LD

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 of sails

Lift and Drag

Kerwin model (MIT 1976)The aerodynamic model is based on a sailsets. Characterized by:

sailset = 1sailset = 2

Upwind

Downwind

‣ 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 rigAs we see it

The individual sail areas are calculated asSA_main = 0.5 ⋅P ⋅E ⋅1.1

The reference sail area is defined as

SA_ ref = SA_ i∑

IMSYC-66

E

BAD

LPG

I

P

J

CEA

D

SA_ jib = 0.5 J 2 + I 2 ⋅ LPGSA_ spinn = 1.8 ⋅ J ⋅ I

Sailsets

sailset = 1⇒ SA_ spinn = 0sailset = 2⇒ SA_ jib = 0

Upwind

Downwind

The rigAs we see it

Vertical centre of effort from baseline (keel line of canoe body)

Total aerodynamic centre of effort

CE _ spinn = 0.565 ⋅ I + D

NOTE: We only consider the vertical position of the centre of effort!

CE _main = 0.39 ⋅P + BAD + D

CE _ jib = 0.39 ⋅ I + D

CEA =CE _main ⋅SA_main + CE _ jib ⋅SA_ jib + CE _ spinn ⋅SA_ spinn

SA_main + SA_ jib + SA_ spinn⋅ R

Reef factor, varies between 0.3-1.0

R=1.0

R=0.6

0 20 40 60 80 100 120 140 160 1800.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Apparent wind angle [deg]

CL,

CD

[]

CL mainCL jibCL spinnakerCD mainCD jibCD spinnaker

Lift and DragDefined for each individual sail and derived with trim corresponding to maximum thrust

CL = R2CL _main ⋅SA_main + CL _ jib ⋅SA_ jib + CL _ spinn ⋅SA_ spinn( )

SA_ ref

CD = R2CD _main ⋅SA_main + CD _ jib ⋅SA_ jib + CD _ spinn ⋅SA_ spinn( )

SA_ ref

CD _TOT = CD + CD _ i

z

x

IMSYC-66

Lift and DragInduced drag and aspect ratioDependent on planform geometry which changes depending on apparent wind angle

AR =I 1+ 0.1 ⋅ BE( )( )2

SA_ ref

BE = 1 AWA_ red < 30°BE = 0 AWA_ red > 90°

30° < AWA_ red < 90° linear interpolation

where

CD _ i = CL2 1πAR

+ 0.005⎛⎝⎜

⎞⎠⎟

Lift and Drag

Finally lift and drag are determined as

L =12AWS _ red 2 ⋅CL ⋅SA_ ref

D =12AWS _ red 2 ⋅CD _TOT ⋅SA_ ref

We’re done, puh.....!

Homework 3

calc_aero.mcalc_Sail_CLCD.m

Finish the implementation of the aerodynamic model in

You do NOT need to add any new lines of code!

Verify your results against ours in the exercises!

Föreläsning, Sailing for Performance SD2706

Mange Olsson

Magnus ‘Mange’ OlssonSkeppare, Ericsson 3 VOR 08/09Tekniskt ansvarig, Ericsson VOR 05/06Vinnare, EF language VOR 97/986 varv runt jorden, m.m.

29 april 2011kl. 10.00Plats: meddelas via mail

Center for Naval ArchitectureO.S.A senast 20/4 via mail till:

razola@kth.se, OBS ange ämnesrad: mangeolsson

ReminderPrepare 2 questions or points of discussion each

razola@kth.se

No later then 21/4!!