Calculation of still-water resistance according to J. Holtrop and G.G.J. Mennen

(1)

Calculation of still-water resistance accotdting to

J.. Holtrop and G.G:. J. Mennen by

ing. A.P. de :Zwaan Report No. 777

(2)

INDEX.

Introduction.

General.

1.1 Program definitions. 1.2 Aim.

Organisation of the proram. 2.1 Formulas.

2.3 Explanation of used symbols,.

Program application. 3.1,. In-output parameters.. 3.2 Remarks. Bibliography.. page 1 1 1. 9 12 14 15

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Introduction.

In this report a. description is given of a computer program in Fortran 77 to calculate the still-water resstance of a ship according to (1], (2] and t3I.

The program can be used for the speed range 0 < F > 0.55 where

V

../ g*L

General.

1.1 Program definitions.

a). Language Fortran 77

b) a Calculation time 1 sec

c). Computer configuration : IBM compatible. Ms-Dos

1.2 Aim.

Calculating the still-water resistance of a ship;, the wake number, thrust deduction factor and the relative rotative efficiency.

Organisation of the program.

The program uses different formulas for the following speed ranges (3]:

0 0.40

0.40 < 0.55 a). 0.55 < F

2.1 Formulas.

The total resistance of a ship has been devided into:

Rrotai = RF (1+k1) + Rpp+

Rw +RB + R+RA

(3]

Where:

frictional resistance according to the ITTC-1957 formula

form factor of the hull. appendage resistance

wave resistance =

(4)

Frictional resistance. Sh 11

V*L

V where :

p - mass density of water

V

-. speed of the ship in knots B - moulded breadth

T - draught

L - length on the waterline

V - .mouIded displacement volume

C

- prismatic coefficient

lob - Longitudinal position of the

centre of, buoyancy

forward. of 0.5L as a percentage of: L

The wetted area of the hull is

be

approximated by _[21 : =

L(2T + BL/(0.453 + O.4425C8 - O.2862CM:

- O.003467

+

0.3696C) + 2.3.8_!!

where :

CM - midship section coefficient

CB - block coefficient on the basis of the waterline

length

C - waterplane area coefficient

ART - transverse sectional area of the bulb at the

po-sition where the still--water surface intersects

the stem.

1/2 p V2*O.075 0hull (1og(R-2)) 1 k1 = 0.93+0.487118C14(!)06806(-!)0.4606

(0.i2I563 ()

°36486(1-Ce) -0.604247 V L = L(1 _- + O.O6CP1Cb) Afterbody form

Pram with gondola

-25

V-shaped sections

-10

₀₁₄ ₌ 2. + 0.0I1C,, Normal section shape 0

U-shaped sections with

Rogner stern

10

- wetted area of

the hull

(5)

Appendage resistance.

R,

=1/2pV2S(1 +

_k2)

where :

0.075 (log R-2)2

p - mass density of water

V

- speed of the ship in knots - wetted area of the appendages

l+k2 - appendage resistance factor (2].

The equivalent 1+k2 value for a combination of appenda-ges is determined from (2]:

(1 +k2) -

E

(l+k2)s

The appendage resistance can be increased by the regis-tance of the bow thruster tunnel openings according to

(2]

.RBTO = pV2itd2C8

where:

d - tunnel diameter in rn

CB - ranges from 0.003 to 0.012

For openings in 'cylindrical part of the bulbous bow, the lower figures should be used.

Approximate 1+k2 values

rudder behind .skeg 1.5' - 2.0

rudder behind stern 1.3 - 1.5 twin-screw balance rudders 2.8

shaft brackets 3.0 skeg '1.5 -strut bossings 3.0 hull bossings 2.0 shafts 2.0 - 4.0' stabilizer fins 2.8 dome 2.7 bilge keels 1.4

(6)

Wave resistance. P

> 0.55

: = _017c2c5.vpge (m3F' +m4coa(AF2)) where,: = 6919. 3C3346 (_._!_)2.00977 _2),1.40692 L3 B rn3=-7.2035 (!.)0.326869(L L 0.605375 C2=

-i.89.J)

C' =1-0.8

₅ BTCM = 1.446C - 0.03- for - <.12 = i.446C, -

0.36

for. -= -0.9 C3= 0.56

BT (0. 31/

+ _TF

_{- hB)}

-3.29 m4- c150.4e' .0 4F

05

-1.69385 when <

512

L

c

₁₅,= -1.69385 + 2.36 L3 when 512 1726.91 V 15= 0 when -- >

1726.91

kr - iersed transom area at .res.t m2

AliT - transverse area. of the. bulbous bow. m2

- vertical positIon of the centre of AliT above the keel 0.6 TF (rnoulded draught on F.P.)

(7)

o < F

0.4

RW_AT.. C1C2cvpge (mFm4cou(AF1))

with

c1=

2223105c.78613(..!.) 1.07961(90

_{- 1B)}

iE=is9exP [- (-k)

°80856(i.-C,,)

o.3o4e4

(i_C-o.o225icb)0.6367(.)034574

( iOOV)0.16302] c7=

when

0.11

c7= -

When 0.1i<- 0.25

c7= 0.5 -

0.0625-i when

-

>0.25

L B m1= 0.0140407--1.75254 L -4.79323--cj6 c6=' 8. 07981C-i3 .8673C6 ..984388C:' when C 0.8 c16=1.73014 - O.7067C when C > 0.8

rn4 as in the _R formula for the high speed

range.

0.40 <

0.55:

-

i10E-4) (Rw8-RwA0)

R1, _R,,A0

1.5 with

fa the wave resistance for .F 0.4' R.,_-B059 is the wave resistance f or .F_n =

0 55

(8)

Additional pressure resistance of bulbous bow.

0. 11exp(-3P)FjA5pg

Where the coefficient P11 is a measure for the emergence

of the bow and F i.g the Froude number based on the immersion: O.56/ABT

T-1.5h8

and

V /g(T_h11_0.25fA) ₊ _{0 .i5V}

Additinal pressure resistance of immersed transom

stern

R=0 i.5pV2ATC6.

with

COr2(i0.2FflT) when F < 5

or

C6=O when FflT

nT

has

been defined as:

V

2gA

N B+BC

in this definition C

is

the waterplane area coeff:i-cient.

Model -ship corxeiation. resiStance.

RA=

1/2 PV2SOcA

where:

CA= 0.O06(L+100)06_0...0O2O50.003J

₇₅

Cc2(O.O4-c4)

with

04= -

when TF

O.04

c4= 0.04 when

TF> 0.04

(9)

Pro sulsion

data

for a). Wake fraction

w

₌ _{cgc2oCv*(0.050776} +

O.934O5c11

00= S

B

L D(--3)

TA 09,= C when

0 < 28

or

09 32

_Cr24

_{when c}

28

TA T

-- when-<2

or

When!

TA T T

o.oa333aa(-)

+

.3333 when

-_-0.12997 0.11056

whenC <0.7

.O.95-CB

0.95-C

P

or

c19-l.S.-CM

- 0.71267

+ 0.38648C

when C

0.7.

c3= 1

+ 0 015 CBtern

C1= 1.45C -

0.315 -

O.02251b

3: +

_{0. 279i5c2o}

L(I -

20

The coefficient

c9 depends

on the coefficient c8, def

i-ned as:

BS

_tot

_B

when -

_<5

LDTA

TA or a.

.e screw

shi 7B 25 TA

(10)

The coefficient C, is the viscous resistance coeffi,-cient with

C=

(14k)

CF + CA where

1 + k =

1+k1

+ ((1 + k2) -

(1 + k1)) tot b). Thrust deduction,. B 0.28956

,,

0.2624

0 .25014 (-)

(VJ)

L D

(1 - C + 0.0225 lcb)

0.01762

C).

'Relative-rotative efficiency.

i= 0.9922 - 0.05908! + 0.07424(C - 0;.02251Cb)

Propulsion data for multiple-screw ships [2].

Wake fraction

V =

O.3O9SCB + 1OCVCB -

0.23

D

Thrust deduction.

t = 0.325C - 0.1885

D

Relative- rotative efficiency.

1h

=0.9737 + 0.1i1(C-0.0225lcb) - 0.06325-!

(11)

2..3 Explanation of used symbols.

Symbol Program Dimension Description

ABT ABULB m2 Transverse sectional area of the bulb at

the position where the still water surface

intersects the stem.

AE/AO

___

- Expanded blade area

ratio of the propeller

Ar AT m2

Xersed transom area.

B BR

m

Moulded breadth.

CA CA - Model-ship correlation

allowance coefficient.

Cli CB - Blockcoefficient on

basis.

of the waterline length. CB CBTH - Coefficient bowthrus-ter openings. 0.003

CYJ

0.012

CF - Frictional resistance coefficient.

CM cM - Midship section

coef-ficient.

C CP - Prismatic coefficient.

CAPT - Stern shape parameter. CWP - Waterplane area

coef-ficient. c, cv - Viscous resistance coefficient. D DP

m

Propeller diameter. d DBTT

m

Tunnel diameter. F FN - Froude number.

FNI - Froude number based on

the immersion of the bow.

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Explanation of used symbols (continued).

10

Symbol Program Dimension Description ALFA

H

degrees 'angie of the waterline at the bow with

refe-rence to the centre plane but neglecting

the local shape of the stem.

L SLWL

m

Length on waterline.

lab SLCB Longitudinal, position

of the centre of buo-yancy forward of 0.5L as a percentage of, .L.

SLR

m

Length of the run.

PB PB - A measure for the

emergence of. the bow.

RA R.A N. Model- ship correlation

resistance.

R.APP N Appendage resistance.

RB RB . N. Additional pressure

resistance of bulbous bow near the water

surfaced

RBT(J RBTH N Resistance of bow

thruster tunnel ope-nings.

RF RF1KI N Frictional resistance

'according to iTTC19!57 formula. RN - Reynoldsnumber. RTR N Additional presSure resistance due to

transom iersion.

Rw RW' N. Wave resistance.

SAPP m2 Wetted area appendages SHULL m2 Wetted area of the

hull.

STOT m2 Total 'wetted area.

T DRAFT

m

Moulded draugth.

T - Thrust deduction,.

TA TA

m

Draught moulded on A.P

(13)

Explanation of: used. srnibolS (continued).

Sy]nbol Program Dimension Description

V

ITK VM: knots rn/sec Ship Speed.

w

w - Wake fraction.

RRE - Relative-rotative

ef-ficiency.

p RHO kg/rn3 Mass density of water.

V RN rn2/sec Coefficient of

kinema-tic viscosity.

V VOL rn3 Displacement volume

(14)

3. Proqrarn application.

3.1 In-and output parameters.

i = input, 0

= output

12

SLPP

i:

- Length between perpendiculars

(m)

SLWL

i:

Length on the waterline (rn)

BR

i:

Moulded breadth (rn)

DRAFT

i:

Midship draft (m)

TRIM

i:

Trim (m)

VOL

i:

Moulded volume of displacernent (m3)

SLCB

ii

0:

C.O.B. forward of SLPP/2 in % of SLPP

C.O.B. forward of SLWL/2 in % of SLWL

CWP

i:

Waterplane area coefficient (-)

i:

Midship section coefficient (-)

SHULL

i:

Wetted area hull (m2)

If unknown : SHULL=0

CAPT

i:

Shape coefficient aft (-)

U-form with Hogner stern : CAFT=+10.0

Normalform.

. . .

.:CAPT=

0.0 V-form

. .

. ...:CAFT=-10.0

Pram with gondola .

. .

.: CAPT=-25.0

SRUD

i:

Wetted area rudder (rn2)

CRUD

i:

'Rudder

Rudder coefficient C-')

Rudder behind skeg

. . .

.:CRUD=1.5-2.0

behind stern

. .

.:CRtJD=1.3-1.5

'Twin-screw balance rudders:CRUD=

2.8

SAPP

i:

Wetted area appendages (rn2)

SAPP=SUM[sapp(i)]

CAPP

i:

Equivalent appendage factor C-)

CAPP=SUM[capp(i)*sapp(i)] /SuMisapp(i)i

Shaft brackets

:

capp(i)=

'

3.0 Skeg

. . .

.: capp(i)=1.5-2.0

Strut bossings

: cappU)=

3.0 'Hull bossings

.: capp'(i)=

2.0 Shafts .

. . .

.: capp(i)=2..0-4.0

Stabilizer fins

:

capp(i)=

2.8 Dcme .

. . . .

.: capp(i)=

2.7 Bilge keels

.

.: capp(i)=

1.4

ABULB

i:

Cross section area bulbous bow (rn2)

No bow correction : ABULB=0

HBULB

i:

Centroid of bulbous bow cross section

to keel (rn). If ABULB=0 HBULB can have

(15)

Inand output

ararneters (continued). i = input, o = output

DBTT i: Diameter of bow thruster tunnel (rn)

If no bow thruster DBTT=O

If N bow thusters DBTT=DBTT*sqrt(N)

CBT.T i,: Resistance coefficient of bow thruster

tunnel '(-).

IF no bow thruster CBTT=O Thruster in cylindrical part CBTT=O.003 Thruster at the worst location CBTT=O.012

AT

1: Area of iersed transom (rn2)

SLR i: Length of the run (rn) if unknown SLR=O

ALFA i: Half angle of entrance of the waterline (degrees). If unknown ALFA=O

NPROP : Number of propellers (-)

NPROP=O : No calculation of W,T and RRE NPROP=i : Calculation .of W,T and RR NPROP=2 : Calculation of W,T and RRE NPROP=1 or 2 DP i: AAE i: PPD 1: Diameter of propeller (rn) Expanded blade area (-)

Pitch diameter ratio (-)

NV

i: Number of ship speeds (-) max 25

VK (NV) i: Array with ship speeds (knots)

RSW(NV)

0:

Array with still water resistances (kN) W(NV)

0:

Array with wake fractions (-)

T(NV)

0:

Array with thrust. deduction fractions (-) RRE(NV)

0:

Array with relative-rotative efficiences

IERR

0:

In case of an error the program returns with IERR=- 1

(16)

3.1 Remarks.

There are three posibilities if the error message XERR=- 1 occurs:

Prismatic coefficient CP=CB/( > 1.0 with

CB=VOL/SLWL/ BR/DRAFT is given by input.

Action : Correct. the input value CB or Length of the run SLR c 0.01

Action : If the value SLR is calculated in the pro-gram, (SLR=0 in the input file) give the value for SLR by .input.

1.0 - CP 0.025*SLCB < 0 : see formula for half angle of entrance iR on page 5 or formula for the thrust deduction fraction t on page 8.

Action : CP or/and SLCB has to be corrected.

The input value for the center of buoyancy SLCB is gi-ven in a percentage of the length between.

perpendcu.-lars. The foulas in the program needs the value in a percentage of the length on the waterline.

The value of SLCB is recalculated fOr this value: SLCB=SLCB*SLPP/1 00

SLCB=SLCB+(SLWL-SLPP) /2 SLCB=SLCB* 10 0/SLWL

(17)

Bibiioqraphy.

Holtrop,J. and Mennen,G.G.J.

A statistical power prediction method, International Shipbuiding Progress, Vol. 25, October 1978

Holtrop,J., and Mennen,G.G.J.

An approximate power prediction method, International Shipbuilding Progress,, Vol. 29, July 19.82

Hoi,trop,J.

A statistical re-analysis of resistance ad propulsion data,

international Shipbuiding Progress, VOlume 31, November 1984