Yacht Lec34 Hydrodynamics

Yacht Design & Technology

Hydrodynamics

Lecture Contents

• How is resistance determined?

• Components of resistance

• How can resistance be minimised?

Resistance

1) Model testing in a towing tank

Determining the Resistance of a Design


2) Calculation by Computational Fluid Dynamics (CFD)

Using numerical techniques to solve equations defining fluid flow

Equations solved are numerical approximations, hence inherent level of approximation in solution


3) Systematic Series

Calculation by empirical formulae - determined by regressional analysis of Systematic Series

• Series of towing tank test models all derived from one particular parent

• Change one parameter at a time and keep others constant

• Empirical formulation for determination of resistance of arbitrary shape

Components of Calm Water Resistance


Influence of Speed on Resistance

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

4 5 6 7 8 9 10 12 14 16 20 25

True Wind Speed (knots)

Dra

g B

ud

get induced drag

heel drag

appendage viscous drag

canoe body viscous drag

wave drag


Dependent on:• area of hull/keel/rudder in contact with water• forward speed• frictional coefficient

Frictional Resistance

SCV2

1R f

2friction


Total frictional resistance of yacht is

)CCC(2

1R rfrkfkcfc

2f SSSV

Subscripts: c = canoe body

k = keel

r = rudder


Note that Van Oossanen gives

Rn

1800

2) - (Log(Rn)

075.0C

2f

Cf determined from experiments with flat plates, now a standard equation, ITTC-57, is used

2f 2) - (Log(Rn)

075.0C

Dependent on:• length• forward speed• kinematic viscosity of fluid

Reynolds Number

vL

Rn

Remember that flow changes from laminar to turbulent flow at around Rn = 4.5x105

Reynolds Number – Canoe Body

WL

c

0.8L vRn

For ships L is taken as waterline length.

For yachts this is not a realistic representation. Therefore typically a value of L is taken between 70% & 90% of the waterline length.

This obviously leaves space for interpretation.

Reynolds Number - Foils

k

k

C vRn

r

r

C vRn

Average chord length used to determine RnIf taper ratio (difference between chord length at tip and root) greater than 0.6, then appendage divided into strips and total skin friction found by summing skin friction of all the strips.


The actual frictional resistance of the yacht will differ from plat plate frictional resistance due to shape of hull or ‘form’, i.e. flow is 3D rather than 2D.

Viscous Resistance - Form Drag

frictionviscous R)k1(R

))1(C)1(C)1(C(2

1R rrfrkkfkccfc

2viscous SkSkSkV

Form Factor, k, is determined from tank tests using Prohaska Plot. Obtain k from CT/Cf versus Fn4/Cf plot

k may also be calculated from Holtrop 1977.For sailing yacht k~0.1

Additional increase to viscous resistance caused by effects of hull surface, since ITTC-57 accounts for smooth surface only.



length chord aerofoil c

thicknessaerofoilt

digit-4NACA 60(t/c) 2(t/c) 1 k 1

65 & 64 63,NACA 70(t/c) 2(t/c) 1 k 14

4

Keel and rudder Form Factor may be determined from data available in literature e.g. Hoerner ‘Fluid Dynamics Drag’ & ‘Fluid Dynamics Lift’


Viscous Resistance - Transom

)(2

1with

5 0C

5 )2.01(2.0C

area transomimmersedA

CAV2

1

TR

TR

TR

TRTR2

TR

WL

WPWLT

T

T

T

TT

L

ABB

gB

VFn

Fn

FnFn

R

Pressure drag caused by immersed transom is a component of the viscous resistance

OK, we now know what Viscous Drag is - how do we minimise it?

Minimise Viscous Drag:

• Reduce wetted surface area

• Maintain laminar flow as far back as possible (use straight lines in forebody)

• Minimise form factor by ensuring that flow lines along hull are as straight as possible

• Straight flow obtained by adoptingslender waterlines in low BWL/Tc

slender/straight buttock lines in high BWL/Tc

avoid pronounced bilges in diagonal flow


Wave-making resistance is associated with the energy involved with generating the pattern of waves seen when a vessel travels along the surface.

Wave-Making Resistance

Flow along hull reduced (in relation to yacht speed) at bow and stern while increased at amidships.

This is responsible for: • increase pressure in bow region • decrease in pressure amidships• increase pressure at stern


The length of the wave is a function of the wave speed:

g

V2=

2


This means that as the speed of the yacht changes the interference between the waves generated by significant parts of yacht hull e.g. bow, shoulder, stern changes.

‘hull speed’ is when: = LWL

Influence of yacht speed on wave length



0

0.5

1

1.5

2

2.5

3

0.6 0.8 1 1.2 1.4 1.6 1.8 2

V/sqrt(L)

Ct

Humps and hollows of a yacht resistance curve(Ct = total resistance coefficient)

The volume of the keel produces wave-making resistance.

To avoid abrupt changes in lengthwise distribution of volume, keel volume may be faired into Curve of Cross Sectional Areas.

Work by Keuning & Binkhorst (Chesapeake 1997) measured forces on keel and rudder separately from hull forces. Results clearly showed residuary drag on the keel in upright condition (2 – 5% of overall resistance).

Wave-Making Appendage Resistance

OK, we now know what Wave-Making Drag is - how do we minimise it?

Minimise Wave-Making Drag:• Design hull to have long effective waterline length

• Carefully distribute displacement volume along length

• More volume towards bow and stern, decrease XSA of maximum section of hull - this increases prismatic coefficient, Cp

mWLAL=p

C

• Effective wave-making length of the hull is increased (distance between wave peak at bow & wave peak at stern increased)


Going to windward hull, keel and rudder develop side force.To generate side force flow requires angle of attack with respect to hull centreline.

Induced resistance is directly related to side force generated by hull and appendages. It is dependent on:

• wing geometry• flow around wing tip• aspect ratio of wing• presence of the free surface

Induced Resistance

Induced Resistance

Induced resistance minimised when wing has elliptical load distribution over span

Elliptical plan form is not strictly necessary for elliptical loading - taper ratio ct/cr=0.6 is effective (ct = tip chord & cr = root chord)

Induced Resistance – Wing Geometry

Induced resistance strongly related to strength and shape of tip vortex – changes to shape of wing tip may influence induced resistance.

Flow around tip, from high-pressure side to low-pressure side, must be restricted to minimise RI.

‘End plate’ may be used to minimise tip losses. Hull is one end plate. Wing tips or bulbs may be used at other end.

End plates & bulbs however have additional resistance e.g. large wetted area & form drag.

Induced Resistance – Wing Tip

Aspect ratio is ratio between wing span and the wing area. A long slender wing has a high aspect ratio.

For high AR wing, effect of wing tip on overall performance of wing is small.

Lift/RI increases with increasing AR

Induced Resistance – Aspect Ratio

‘Induced’ resistance effect due to pressure field around keel being close to free surface as yacht heels. This pressure field generates waves which manifests itself as resistance.

Induced Resistance – Free Surface Effect

When sweep angle increased pressure field is spread out over longer portion of free surface, hence reducing wave generation.

Has led to development of inverse taper keels and winglets.

Interaction between pressure field around keel and free surface may not be neglected during keel design.

Induced Resistance – Free Surface Effect

Forces on sails produce heeling and trimming moments in addition to drive force for yacht.

Running trim will lead to a bow down attitude, unless counteracted by crew movement.

This will change both the viscous and residuary resistance

Heeled Resistance

When yacht heels underwater part of hull will become asymmetrical and there will most likely be a change in the wetted surface area.

New wetted area may be found from hydrostatic calculations.

Change of Viscous Res. due to Heel

This is more significant than change in viscous resistance due to heel.

When yacht heels there will be a change in the distribution of of the cross sectional areas over the length of the yacht.

Depending on hull geometry this will lead to change in hull shape parameters:• waterline length• waterline beam• canoe body depth• LCB – may lead to change in trim (bow down as LCB moves aft)

Change of Residuary Res. due to Heel

Most influential are B/T ratio and LCB.

• Hullform with increased B/T ratio tends to have greater increase in residuary resistance when heeled.

• Trimming effect can significantly increase resistance – by 10-15% at high speeds.

Change of Residuary Res. due to Heel

Ability of yacht to sail close to wind and achieve good VMG is mainly dependent on ability of hull, keel and rudder to develop substantial side force without significant resistance.

Side force produced when hull has yaw or leeway angle relative to track of yacht through water.

Yachts with good windward performance can generate high side force at small leeway angle, whereby leeway is reduced.

Hydrodynamic Side Force

Keel & rudder must be symmetrical – this limits lift to drag ratio to the order of 10. (Non-symmetrical cambered wing sections can have lift to drag ratios of 30 for small angles of attack).Flaps may be used on trailing edge to increase lift, though drag penalty also present.

Canoe body is inefficient producer of side force with max L/D ratio about 5 – 6 at low speed and 2 – 3 at high speed.

Large Keel

• high sideforce, large wetted area, VB low, bTW small

• Sails high and slow

Small Keel

• low sideforce, small wetted area, VB high, bTW large

• Sails low and fast

Hydrodynamic Side Force

Side Force:Aspect Ratio

Lift increases with angle of attack until flow separates from foil and it stalls.

High AR wing more effective at producing lift.

High AR wing generate high lift at small angles of attack stall very soon.

High Aspect Ratio:• High lift production• Small leeway angles • Minimal induced drag• Reduction in WSA lowers frictional resistance

Drawbacks:• After tack large angle of attack and wing may stall• Water depth• Structural implications• In waves angle of attack varies considerably due to motions, also lower speed, hence wing may stall.

Side Force – Aspect Ratio

Thickness Ratio (max. section thickness/chord):• Greater thickness increase max lift.• Slightly higher resistance.• Thicker foils less sensitive to stall than thinner foils.

Longitudinal position along chord length of max. thickness:• Determines extent of laminar flow on foil.• Move position aft & laminar flow may be promoted.• Too far aft and boundary layer will separate at low lift coefficients.

Good reference: ‘Theory of Wing Sections’ Abbott & von Doenhoff

Side Force – Section Profile

It is recommended that every Naval Architect draws a lines plan ‘by hand’ at some stage in their career.

Slow work but gives excellent appreciation of the process of simultaneously drawing 3 fair orthogonal views.

Possible Technique:• Work with parameters: length, displacement, beam waterline, Cp and LCB.• Draw profile • Draw maximum section shape• Examine Sectional Area curve• Adjust for displacement – using selected Cp

Hull Form – Lines Development

Hull Form Influences:

Class Exercise - Try and define a possible influence of the following conditions or hull form parameters:

• Heel• Bow type• Flared topsides• Displacement• Cp• LCB

Boats spend large sailing time at heel.

Tend to trim bow down as they heel - aft shift in LCB & sail force trimming moment.

Need to consider heeled lines as much as upright lines.

Hull Form – Design for Heel

Cruising yachts: styling, flare forward, shape of deck edge in plan view, sea conditions.

Racing yachts: Rating rule• IMS system gives fine forward waterlines & vertical stem profile.• IACC rule measurement at waterline – overhanging bow encouraged (‘Meter bows’).

Hull Form – Bow Type

Greater asymmetry results in greater drag at heel.

Flared topsides (high B to Bwl ratio) create asymmetry.

Deck beam important for crew-righting moment & water ballast.

Hull Form – Flared Topsides

Determines general character of boat.

High L/disp tends to give increased beam-draft ratio since will derive stability from form rather than ballast.

Hull Form – Displacement

Typically Cp optimised for Fn = 0.33-0.35 (upwind sailing for racing yacht in medium winds)

Cp typically vary from 0.52 to 0.56

Hull Form – Prismatic Coefficient

LCB typically range between 3 – 6% aft of amidships.

LCB towards gives fine bow = less added resistance & may be appropriate for planing at higher speeds.

However may nose dive in large waves trim bow down with heel.

Hull Form – LCB

Series established in 1974 by Gerritsma et al. at Delft university of Technology in order to derive empirical expressions for hydrodynamic forces on sailing yachts.

Over 50 systematically varied models tested upright, heeled and yawed at various speeds.

Parent hullforms have evolved as yacht design has developed:

Delft Systematic Yacht Hull Series

Parent Hull Form Year IntroducedStandfast 43 1974Van de Stadt 40 1980S&S IMS-40 1995


Length displacement Ratio 5.0 to 8.0Length to Beam Rat io 5.0 to 2.8Beam to Draft ratio 2.5 to 19LCB (%LW L) 0.0 to 8.0 (aft midship)Prismatic Coefficient 0.52 to 0.60Cross Sectional Area Coefficient 0.646 to 0.777

The following hull parameters were chosen:

The total resistance is calculated from the addition of the residuary resistance and frictional resistance (ITTC-57):

The residuary resistance is determined analytically from the individual contributions made by the hull and the keel.

Using the polynomial equation with hull form geometry coefficients as variables the hull residuary resistance may be determined from:


frt RRR

rkrhr RRR

LWLCA

LWL

LCBA

LCF

LCBA

SA

LWLLWL

BWLA

AACA

LWL

LCBAA

g

R

cp

fp

fp

fp

c

c

c

w

cp

fp

c

rh

3/12

8

2

76

3/2

5

3/1

4

3/2

3210


0

0 0.2 0.4 0.6 0.8

Fn

Res

ista

nce

004 experiment

theory, Kuening (1999)/Gerritsma (1992)

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Fn

Res

ista

nce

008 experiment

theory, Kuening (1999)/Gerritsma (1992)

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Fn

Re

sist

an

ce

017 experiment

theory, Kuening(1999)/Gerritsma(1992)

0

0 0.2 0.4 0.6 0.8

Fn

Res

ista

nce

018 experiment

theory, Kuening(1999)/Gerritsma(1992)

A similar procedure is utilised for determining:

• Appendage resistance

• Induced resistance

• Hydrodynamic side force


Good Reference for Delft Series:

Keuning, J.A. & Sonnenberg, U.B. Approximation of the Calm Water Resistance on a Sailing Yacht Based on the ‘Delft Systematic Yacht Hull Series’ 14th Chesapeake Sailing Yacht Symposium, January 1999.


Recap/reflect

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Yacht Lec34 Hydrodynamics