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Planing vessel lecture

O.M.FaltinsenCeSOS,NTNU

Content

• Steady performance• Stepped planing hulls• Dynamic stability• Porpoising• Wave-induced motions• Maneuvering

Planing craftSteamer duckReady for planing !Froude number up to 3Distance up to 1km

Typical planing hull Double-chine hull

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Hard-chine planing hull

Interceptors

2.5D analysis of steady verticalforces = The water entry problem

Drop test of wedge 2D+t representation

Water entry of a wedge Water entry of wedgeTheory and experiments

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Simplified lift (L) calculations

( )3 33df a Vdt

=

( )3 33df U a Udx

τ=

( )233 TL U a xτ=

Consequences of simplified lift formula

• The vessel must have a transom stern and a trim angle to get hydrodynamic lift

• Flow separation from the chines is importantfor trim

( )3 33df U a Udx

τ=

( )233 TL U a xτ=

Design to avoid cavitation,i.edynamic instabilities

• Avoid negative pressuresrelative to atmosphericpressure

• Simplified vertical loadformula gives:

• Avoid convex keel and buttock lines aft of thebow sections

• Careful with how theplaning surface is warped

3 33( )df U a Udx

dzdx

τ

τ

=

= −

Warped planing surface

Savitsky’s formula

0.60 00.0065L L LC C Cβ β= −

1.1 0.5 2.5 20 deg (0.012 0.0055 / )L W W BC Fnτ λ λ= +

2 2

10.755.21 / 2.39

p

W B W

lB Fnλ λ= −

+

Prismatic planing hull

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Planing hulls (Ikeda et al.)Lift force on prismatic planing hull

β = 20ºτ = 4ºλ = 3

1/FnB2

Lift force on prismatic planing hull

β = 20ºτ = 4ºλ = 3

1/FnB2

Hydrostatic force calculations

Lift force and moment on planing vessels

• 2.5D Analysis with flow separation and zero gravity

• 3D Correction in the bow area• Hydrostatic pressure• Suction pressure at the stern

Lift Force on Prismatic Planing Hull

FnB ∞

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Lift Force on Prismatic Planing Hull

FnB ∞

Stepped planing hull

Separation aft ofchine separation

VentilatingRudder

Free-surface-piercing propeller

Flow separation at transom Free-surface profile at the transom

3

2

/ 2 cos(3 / 2)

2S

SU g

Ar

U

X

D

U θ

=

Φ

+

= +

Local analysis offree-surface profile

3/ 2Z AX=

Pressure distribution on the hull

• Infinite pressure gradient at the transomstern

• The local transom stern flow does not match the 2.5D theory

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Savitsky’s empirical formula2 2.44

1 2 3Z X X XC C CB B B B

⎛ ⎞ ⎛ ⎞ ⎛ ⎞= − +⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

20.7deg

1 0.6

2.440.7deg

2 0.6

0.341 deg

0.02064

0.00448

0.0108

B

B

W

CFn

CFn

C

τ

τ

λ τ

⎛ ⎞= ⎜ ⎟⎜ ⎟

⎝ ⎠

⎛ ⎞= ⎜ ⎟⎜ ⎟

⎝ ⎠=

Center-line free-surface profile

2D flat planing surfaceLift force and moment on2D flat planing surface.

2D flat planing surface. Nonlinearities Running attitude and resistance

M=27,000 kglcg=8.84mB=4.27 mDeadrise=10degU=20.58m/s

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Keel and chine wetted lengths

Monohull.Ref.:Per Werenskiold

Heel Angle

Steady roll stability as a function ofspeed

Steady heel instability and chine walking

Φ

0 20

–0.01

0

0.01

0.02

φ(deg)

GZ(m)GZ curve at Fn=0

W=5.31kgmeasured

Fn=1.6

Heel Angle Φ (deg)

Water entry ofheeled section

Simplified water entry analysis ofheeled section

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Porpoising in nature and of planing vessels

Porpoising stability criterion

Porpoising analysis Porpoising

• Equilibrium position for given speed• Stability analysis of coupled linearized

heave and pitch equations withoutexcitation

Porpoising analysis

( )2 2

3 3 5 533 33 33 3 35 35 35 52 2 0d d d dM A B C A B C

dt dt dt dtη η η ηη η+ + + + + + =

tj jae

βη η=

0α >Instability:

iβ α ω= +

( )2 2

3 3 5 553 53 53 3 55 55 55 55 52 2 0d d d dA B C I A B C

dt dt dt dtη η η ηη η+ + + + + + =

Instantaneous position of COG and keel

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Restoring CoefficientsSavitsky´s Formula

Heave force

Restoring CoefficientsSavitsky´s Formula

Pitch moment

Added Mass

• High-frequency strip theory• No forward speed effect

2D infinite frequency heave addedmass

Damping

• No wave radiation• Hull lift damping. Use lift part of Savitsky’s

formula in a quasi-steady analysis

Example heave

Effect of lcg on porpoising

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Porpoising.Sensitivity to hydrodynamic coefficients

Stability parameter <0 Porpoising

Planing boat in waves

Vertical accelerations of 57-foot boat in sea state 5 Generalized Froude Kriloff loads

sin( )a et kxζ ζ ω= −

sin cos cos sin sin cosa e a e a e a et kx t kx t xk tζ ζ ω ζ ω ζ ω ζ ω= − ≈ −

3 33 35sin cosFKa e a eF C t C k tζ ω ζ ω= +

5 53 55sin cosFKa e a eF C t C k tζ ω ζ ω= +

Long wave length approximation ofwave excitation

Resonant wave length condition

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Strong nonlinearities in shipmotions of a planing craft

Heave/Wave amplitude

Wave length/L

Maneuvering

Steady turning motion GZ during turning