An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

2/10/2016

Waves 2005 Conference 1

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AN EMPIRICAL MODEL FOR SHIP-GENERATED WAVES

David Kriebel1 and William Seelig2

1 Professor of Ocean Engineering, US Naval Academy, Annapolis, Maryland 2 Senior Engineer, Naval Facilities Engineering Services Center, Washington, DC

2

ObjectivesShip-Generated Wave Heights

• Develop empirical equation to predict maximum wave heights generated by conventional ships

• Improve upon existing predictive equations:– Sorensen and Weggel (1984) & Weggel and Sorensen (1986)– PIANC (1987)

• Use existing data published in the literature

• Run new lab tests to supplement existing data

• Run field trials to verify empirical model– Tests conducted in Chesapeake Bay April 2005

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

2/10/2016

Waves 2005 Conference 2

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Definitions

• Two wave systems:– Diverging Waves– Transverse Waves

• Maximum wave heights– Form along “Cusp Line” – Vary with distance from

sailing line, y

19.47o

V

0

DIVERGING WAVETRANSVERSE

CUSP LOCUS LINE

Cd

y

SAILING LINE

WAVE

SAMPLE SHIP-GENERATED WAVE PATTERN

FOR DEEP WATER

(after Sorensen, 1997)

4Sample Wave Records

from LiteratureDeep Water

from Das (1969)

Shallow Water

from Das (1969)

Hmax

Separate “draw down” from diverging waves

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

2/10/2016

Waves 2005 Conference 3

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1 0 1 2 1 4 1 6 1 8 2 0

-0 .5

0

0 .5G

ag

e

1 (

in)

T im e (s e c )1 0 1 2 1 4 1 6 1 8 2 0

-0 .5

0

0 .5

Ga

ge

2

(in

)

T im e (s e c )

1 0 1 2 1 4 1 6 1 8 2 0

-0 .5

0

0 .5

Ga

ge

3

(in

)

T im e (s e c )1 0 1 2 1 4 1 6 1 8 2 0

-0 .5

0

0 .5

Ga

ge

4

(in

)

T im e (s e c )

1 0 1 2 1 4 1 6 1 8 2 0

-0 .5

0

0 .5

Ga

ge

5

(in

)

T im e (s e c )1 0 1 2 1 4 1 6 1 8 2 0

-0 .5

0

0 .5

Ga

ge

6

(in

)

T im e (s e c )

Examples from Naval Academy TestsWaves measured at 6 distances y off sailing line

6

Ship Wave Database

( )47 Carruthers (1966) 73.54 Cape Breton Miner Bulk Carrier No Bulb 1:96 75.952 7.083 6.72 0.75 0.270848 Carruthers (1966) 44.28 Cape Breton Miner Bulk Carrier No Bulb 1:57.8 347.992 11.763 11.16058 1.2456 0.44974549 Carruthers (1966) 44.28 Cape Breton Miner Bulk Carrier No Bulb SHORT 1:57.8 191.718 7.092146 6.489276 1.2456 0.44974550 Helwig (1966) 71.56 Cape Breton Miner Bulk Carrier Bulb 1:96 81 7.0833 6.72 0.75 0.28651 Helwig (1966) 71.56 Cape Breton Miner Bulk Carrier No Bulb 1:96 81 7.0833 6.72 0.75 0.28652 V M th (1962) 87 87 USCG 30 Foot Utilit Boat 1 10 91 7 13 2 8 2 52 0 804 0 24083

Ship Investigator Scale for Vessel Scale Displacement Length Lwl Beam DraftNumber Rx=10 m (lbs) (feet) (feet) (feet) (feet)

1 Sorensen (1973) 8.73 Cabin Cruiser full 6,000 23 8.3 1.702 8.58 Coast Guard Cutter (40-FOOT) full 19,730 40 37 10.7 1.913 3.71 Tugboat full 58,000 45 13 6.004 5.29 Air-Sea Rescue Vessel full 70,000 64 12.8 3.005 1.87 Fireboat full 686,000 100 28 11.006 1.18 Barge full 10,840,000 263 55 14.007 0.77 Moore Dry Dock Tanker full 37,600,000 504 482.496 66 28.008 Sorensen (1966) 185.59 Model A unspecified 2.625 1.5 1.5 0.250 0.1259 139.12 Model B unspecified 6.222 2 2 0.333 0.16710 111.40 Model C unspecified 12.153 2.5 2.5 0.417 0.20811 92.80 Model D unspecified 21 3 3 0.500 0.25012 69.61 Model E unspecified 49.778 4 4 0.667 0.33313 77.83 Weinblum hull unspecified 39.5 5.333 5.333 0.667 0.33314 Hay (1967) 76.11 Mariner Class Cargo Ship 1:96 37.32 5.896 5.39 0.771 0.25015 81.58 SERIES 60 Cb=0.6 1:96 30.45 5.260 5.050 0.667 0.25016 74.05 Moore Dry Dock Tanker 1:96 45.48 5.25 5.026 0.688 0.29217 58.20 Auxiliary Supply Vessel 1:32 61 4.885 4.767 1.132 0.28118 57.02 Barge 1:48 97.8 5.49 5.313 1.135 0.29219 47.88 Tug 1:32 66.5 4.771 4.26 1.073 0.43820 Bidde (1968) 76.11 Mariner Class Cargo Ship (A) 1:96 37.32 5.896 5.39 0.771 0.25021 Barge (E) 1:96 11.24 2.75 0.563 0.14622 Das (1969) 76.11 Mariner Class Cargo Ship 1:96 37.32 5.896 5.39 0.771 0.25023 Cruiser 1:16 24.913 4.063 0.5 0.16724 Zabawa & Ostroa (1980) Uniflight Cruiser full ? 28.17 10.83 2.83325 Boston Whaler full ? 16 ? ?26 Kurata & Oda (1984) 64.76 Ferryboat 1:60 36.911 4.485 0.797 0.32227 Tugboat 1:60 2.027 1.532 0.469 0.14128 USNA (2000) 78.58 SERIES 60 Cb=0.6 MID 1:96 33.28 5 5.083 0.667 0.269429 USNA (2000) 75.40 SERIES 60 Cb=0.6HEAVY 1:96 36.608 5 5.083 0.667 0.2917530 USNA (2000) 83.10 SERIES 60 Cb=0.6 LIGHT 1:96 29.25 5 5.083 0.667 0.24167

Ship wave data used in present analysis: 2100 data points for 12 ships

41 Helwig (1966) Empress of Canada (Ocean Liner) 1:96 69.9 6.25 0.914 0.30842 Helwig (1966) M.S. Wearfield (Ocean Freighter) 1:96 78 6.04 0.75 0.34

4 9 C A P E B R E T O N M IN E R

4 7 ,4 8 ,5 0 ,5 1 C A P E B R E T O N M IN E R

7 , 1 6 M O O R E D R Y D O C K T A N K E R

1 5 , 2 8 to 3 1 , 3 2 S E R IE S 6 0 C b = 0 .6

1 4 , 2 2 M A R IN E R

1 9 H A Y T U G

1 8 H A Y B A R G E

1 7 H A Y A U X

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

2/10/2016

Waves 2005 Conference 4

7Sample Wave Data

from Literature

• Wave heights for a given ship hull form characterized by:– Length, L– Beam, B– Draft, D– Hull Form

• Wave Heights vary with:– Ship speed, V– Distance from

sailing line, y– Water depth, d

(FROM HELWIG, 1966)

8

Normalizing Wave Measurements

• Wave height normalized by velocity head gH/V2

• Distance from sailing line can be normalized in many ways (with various length scales L, B, etc) ...we use:

y/L

• Data in shallow water organized by depth-to-draft ratioD/d

• Velocities normalized as Froude NumberFd = V/(gd)1/2 or FL = V/(gL)1/2

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

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Empirical ModelVariation of H with Distance from Sailing Line

• Havelock (1908) theory for deep water:H ~ y-1/3 for diverging wavesH ~ y-1/2 for transverse waves

• Empirical evidence in literature shows a range from

H ~ y-0.25 to H ~ y-0.6

• Present study:– Least–squares fit of both -1/3 and -1/2

models to data– Model using -1/3 power gave best fit

• C varies with ship hull form, T/D, Fd or FL

gH

VC

y

L2

1 3

/

10

Examples of Fit

gH/V2 versus (y/L)-1/3

Value of gH/V2 at y/L=1 used as a characteristic value for further analysis

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

2/10/2016

Waves 2005 Conference 6

11gH/V2 (at y/L=1)

Plotted vs Length Froude Number FL

M.S. Warefield

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4

FL

gH

/V2 a

t y

/L=

1

Ship42 ,d/T=1.47

Ship42 ,d/T=2.33

Ship42 ,d/T=5.53

Cape Breton Miner

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4

Ship 50 ,d /T=1.75

Ship 50 ,d /T=2 .77

Ship 50 ,d /T=4 .2 2

Ship 50 ,d /T=6 .56

Aux Supply Vessel

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4

Ship17,d /T=1.37

Ship17,d /T=2.5

Ship17,d /T=3.0

Mariner and Series 60

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4

Ship14,d/T=1.60

Ship14,d/T=1.83

Ship14,d/T=2.0

Ship14,d/T=2.5

Ship14,d/T=3.0

Ship29,d/T=54.8

12gH/V2 (at y/L=1)

Plotted vs Depth Froude Number Fd

Mariner and Series 60

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.2 0.4 0.6 0.8 1.0

Ship14,d/T=1.60

Ship14,d/T=1.83

Ship14,d/T=2.0

Ship14,d/T=2.5

Ship14,d/T=3.0

Ship29,d/T=54.8

Aux Supply Vessel

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.2 0.4 0.6 0.8 1.0

Ship17,d/T=1.37

Ship17,d/T=2.5

Ship17,d/T=3.0

Cape Breton Miner

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.2 0.4 0.6 0.8 1.0

Ship50,d/T=1.75

Ship50,d/T=4.22

Ship50,d/T=6.56

M.S. Warefield

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.2 0.4 0.6 0.8 1.0

Fd

gH

/V2 a

t y/

L=

1

Ship42 ,d /T=1.47Ship42 ,d /T=2 .33Ship42 ,d /T=5.5

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

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Define Modified Froude Number F*

An empirical “Froude number” seems to collapse data from a

given ship:

Single empirical coefficient is dependent on ship hull form

large for slender hulls small for blocky hulls

F FD

dL* exp

Aux Supply Vessel

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.2 0.4 0.6

Ship17,d/T=1.37

Ship17,d/T=2.5

Ship17,d/T=3.0

M.S. Wearfield

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Ship42,d /T=1.47

Ship42,d /T=2.33

Ship42,d /T=5.53

Mariner and Series 60

0.00

0.10

0.20

0.30

0.40

0.50

0.0 0.1 0.2 0.3 0.4 0.5 0.6

F*

gH

/V2

at

y/L

=1

S hip 15,d / T=1.3 8

S hip 14 ,d / T=1.6 0

S hip 14 ,d / T=1.8 3

S hip 14 ,d / T=2 .0

S hip 15,d / T=2 .0

S hip 14 ,d / T=2 .5

S hip 15,d / T=2 .5

S hip 14 ,d / T=3 .0

S hip 15,d / T=3 .0

14

Variation of with Hull Form

• Investigated dependence of on hull form

• Seems to depend mainly on Block Coefficient

• General trends:– Streamlined hulls have

of 1 or more– Blunt hulls have

of 0.2 to 0.4

F FD

d

C

L

b

* exp

.

with

2 35 1

= 2.35 (1-Cb)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.5 0.6 0.7 0.8 0.9 1.0

Block Coefficient Cb

alp

ha

CL B D

b

* *

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

2/10/2016

Waves 2005 Conference 8

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Search for Functional Relationshipbetween gH/V2 and F*

• Data for a given ship shows gH/V2 increases with F*– No waves measured for F* below 0.1– Data shows quadratic or higher order relationship– Distinct variations observed as function of hull form

• No simple mathematical function seems to ideally describe data

• Preliminary work uses quadratic expression in the form

varies with hull form and found by best fit of data for each ship

gH

VF2

201 * .

16

Results of gH/V2 (at y/L=1)Plotted vs Modified Froude Number F* with empirical curve fit

Mariner and Series 60

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Moore Dry Dock tanker

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6

M.S. Warefield

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6

F*

gH

/V2

Empress of Canada

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6

gH

VF2

201 * .

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

2/10/2016

Waves 2005 Conference 9

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Results of gH/V2 (at y/L=1)Plotted vs Modified Froude Number F* with empirical curve fit

Aux Supply Vessel

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Cape Breton Minershortened

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Cape Breton Miner

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Barges

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6

F*

gH

/V2

gH

VF2

201 * .

18

47,48,50,51 CAPE BRETON MINER

7, 16 MOORE DRYDOCK TANKER

15, 28 to 31, 32 SERIES 60 Cb=0.6

Coefficient seems to Vary with Entrance Length, Le

• Defined as length from bow to start of parallel middle-body

• Importance noted by Saunders (1957)

• Used in some other predictive models (Gates and Herbich, 1975)

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

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Waves 2005 Conference 10

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Variation of with Hull Form

correlated to entrance length

– Best correlation was based on L/Le ratio

• Streamlined ships have of 1 to 2

• Blunt hulls have up to 9

– Tentative relationship:

1 8 3 0 45 2*tanh .

L

Le

0.0

2.0

4.0

6.0

8.0

10.0

2.0 4.0 6.0 8.0 10.0 12.0

L/Le

be

ta

20

Evaluation of Wave Height Models

Model developed in present study

compared to 1200+ data points

gH

VF

y

L

F FT

d

C

L

Le

L

b

2

21 3

3

01

2 5 1

1 8 0 45 2

*

/

*

.

exp

. ( )

tanh .

where

Preliminary Model

0.0

0.2

0.4

0.6

0.0 0.2 0.4 0.6

gH/V^2 - predicted

gH

/V^

2 -

mea

sure

d

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

2/10/2016

Waves 2005 Conference 11

21

Evaluation of Wave Height Models• Sorensen & Weggel (1984) and Weggel & Sorensen (1986)

H Y

a b d c d

a F b F c F

n d

F

F

F

F

and

HH

YY

n

d d d

d

d

d

d

* *

* *

.

*

*.

*.

log log (log )

. . . .

. .

. . .

. .

. . .

where

with

and

with

=- 0.225 F for

for

=- 0.118 F for

for

d-0.699

d-0.356

2

1 0 125

0 33 0 33

0 6 0 75 2 653 195

0 2 055

0 342 05 080

0 2 055

0146 05 080

dd*

. 0 33

Sorensen and Weggel

0.0

0.2

0.4

0.6

0.0 0.2 0.4 0.6

gH/V^2 - predicted

gH

/V^

2 -

me

as

ure

d• A little complicated and

removed from the physics• Not dependent on hull form

22

Evaluation of Wave Height Models

• PIANC (1987)– Based on work at Delft

by Blaauw et al (1984) for ships in shallow confined canals

gH

VF

y

dd

B2

2

1 32

//

PIANC

0.0

0.2

0.4

0.6

0.0 0.2 0.4 0.6

gH/V^2 - predicted

gH

/V^

2 -

me

as

ure

d

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

2/10/2016

Waves 2005 Conference 12

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Ship Waves Trials19 April 2005

Severn River (Chesapeake Bay)

24

Wave gage frame being deployed from

YP686

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

2/10/2016

Waves 2005 Conference 13

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Wave gage deployed

26

YP686 at 10 knots

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

2/10/2016

Waves 2005 Conference 14

27YP686 approaching wave gage(gage located 100 ft off sailing line)

28YP686 passing wave gage(gage located 50 ft off sailing line)

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

2/10/2016

Waves 2005 Conference 15

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30Sample data showing background wind waves and ship-generated waves

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

2/10/2016

Waves 2005 Conference 16

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3470 3480 3490 3500 3510 35200.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

time (sec)

elev

(m

)

32

Measured vs PredictedNew Empirical Model

0.00

0.05

0.10

0.15

0.20

0.25

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

y/L

gH

/V^

2

10 knots pred

10 knots

9 knots pred

9 knots

8 knots pred

8 knots

7 knots pred

7 knots

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

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Waves 2005 Conference 17

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Measured vs PredictedSorensen and Weggel Model

0.00

0.05

0.10

0.15

0.20

0.25

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

y/L

gH

/V^2

10 knots S&W

10 knots

9 knots S&W

9 knots

8 knots S&W

8 knots

7 knots S&W

7 knots

34

Measured vs PredictedPIANC Model

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

y/L

gH

/V^

2

10 knots pred

10 knots

9 knots pred

9 knots

8 knots pred

8 knots

7 knots pred

7 knots

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

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Waves 2005 Conference 18

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0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4 0.5

H predicted (m)

H m

easu

red

(m

)

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.1 0.2 0.3 0.4 0.5

H predicted (m)

H m

easu

red

(m

)

36Summary and Conclusions

Ship-Generated waves

• New model gives improved predictions– exp(T/d) term “unifies” data collected in

various water depths

• Model can be further improved – (y/L)-1/3 can be optimized

• Exponent may depend on hull form– (F*-0.1)2 can be optimized

• Higher power needed for some hull forms – Coefficients and can be improved with

data from more ships

• Need data in shallow water– Lab data for very shallow water T/d <1.3– Field data

gH

VF

y

L

F FT

d

C

L

Le

L

b

2

21 3

3

01

2 35 1

1 8 0 45 2

*

/

*

.

exp

. ( )

tanh .

where

An Empirical Model for Ship-generated Waves – Kriebel & Seelig 2005

2/10/2016

Waves 2005 Conference 19

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