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Course Teacher: Dr. Md. Mashud Karim, Associate Professor, Dept. of NAME, BUET

Course #: NAME 324

Assignment # B.3: Approximate Calculation of Ship Resistance

Hotrop and Mennen’s Method

The total resistance of a ship can besubdivided into:

RT=RF(1+k1)+R APP+RW+RB+RTR+R A Where,

R F   Frictional resistance according tothe ITTC 1957 friction formula= 0.5. ρV 

2 SC F . 

C F   = 0.075/(Log 10 Re-2)2 

 

Re Reynold’s No.=  ρ VL /  µ  

1+k 1  Form factor describing the viscousresistance of the hull form in relation

to RF R  APP   Appendage resistanceR W   Wave-making and wave-breaking

resistanceR B  Additional pressure resistance due

to bulbous bow near the watersurface

R TR   Additional pressure resistance ofimmersed transom stern

R  A  Model-ship correlation resistance

The form factor of the hull can be predictedby:

})0225.01()95.0(

)/(93.0{1

6906.0521448.0

92497.0

12131

lcbC C 

 L Bcck 

 P  P 

 R

+−−

+=+

−

 

In this formula, C P  is the prismatic coefficientbased on the waterline length, L and lcb isthe longitudinal centre of buoyancy forwardof 0.5L as a percentage of L. Here, LR   is aparameter reflecting the length of the runaccording to:LR  /L=1-C P +0.06C P lcb(4C P -1)

C 12 =(T/L)0.2228446 

  if T/L > 0.05=48.20(T/L-0.02)

2.078 +0.479948 if

0.02<T/L<0.05=0.479948 if T/L<0.02

Where T  is the average moulded draught.

C 13=1+0.003C stern C stern will be -10, 0 and +10 if the afterbodyform is of V-shaped, Normal and U shapedsections respectively.

The wetted area of the hull can beapproximated by:

 B BT 

WP  M 

 B M 

C  A

C T  BC 

C C  BT  LS 

/38.2

)3696.0/003467.02862.0

4425.0453.0()2(

+

+−−

++=

 

where ABT  is the transverse sectional area ofthe bulb at the position where the still-watersurface intersects the stem.

The appendage resistance can bedetermined fromR  APP =0.5  ρV 

2 S APP (1+k 2  )eqC F  

Where S APP   the wetted area of theappendages, 1+k 2   the appendageresistance factor

 Approximate 1+k 2  values

Rudder behind skeg 1.5~2.0Rudder behind stern 1.3~1.5Twin-screw balance rudders 2.8Shaft brackets 3.0Skeg 1.5~2.0Strut bossings 3.0Hull bossings 2.0Shafts 2.0~4.0Stabilizer fins 2.8

Dome 2.7Bilge keels 1.4

The equivalent 1+k 2  value for a combinationof appendages is determined from:

(1+k2)eq =

∑∑   +

 APP 

 APP 

S 

S k   )1( 2 

The wave resistance is determined from:

{ })cos(exp   2

21521

−+∇= n

d 

nW   F m F m g ccc R   λ  ρ 

with37565.107961.178613.3

71   )90()/(2223105   −−=  E i BT cc

33333.0

7   )/(229577.0  L Bc   =   if B/L<0.11= B/L if 0.11<B/L<0.25= 0.5-0.0625 L/B if B/L>0.25  

32   89.1exp( cc   −=  

c 5  = 1-0.48AT  /(BTC M  )

 λ = 1.446C P -0.03 L/B if L/B < 12= 1.446C P -0.36 if L/B>12

8/19/2019 Metode Menghitung Hambatan Kapal

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Course Teacher: Dr. Md. Mashud Karim, Associate Professor, Dept. of NAME, BUET

16

3/1

1

/79323.4

/75254.1/0140407.0

c L B

 LT  Lm

−−

∇−= 

32

16   984388.68673.1307981.8  P  P  P  C C C c   +−=

  if C P <0.8

= 1.73014-0.7067C P if C P  > 0.8  

)1.0exp(   22

152

−−= n P   F C cm  

c 15  = -1.69385 for L3 / ▼<512

= 0 for L3 / ▼>1727

=-1.69385+(L/ ▼1/3

-8.0)/2.36if 512<L

3 / ▼<1727

d=-0.9

})/100(

)/()0225.01(

)1()/(exp{891

16302.03

34574.06367.0

30484.080856.0

 L

 B LlcbC 

C  B Li

 R P 

WP  E 

∇

−−

−−+=

 

)}31.0(/{56.0   5.1

3  B F  BT  BT  hT  A BT  Ac   −+=

 where hB is the position of the centre of thetransverse area ABT  above the keel line andT F  is the forward draught of the ship.

)1/()3exp(11.0   25.132

ni BT ni B B  F  g  A F  P  R   +−=  −  ρ   

)5.1/(56.0  B F  BT  B hT  A P    −=  

215.0)25.0(/ V  AhT  g V  F   BT  B F ni   +−−=

6

25.0 c AV  R T TR   ρ =  

)2.01(2.06 nT  F c  −=

  if F nT <5= 0 if F nT ≥5

)/(2/ WP T nT   BC  B gAV  F    +=  

 A A SC V  R   2

21  ρ =  

)04.0(5.7/003.0

00205.0)100(006.0

42

4

16.0

ccC  L

 LC 

 B

 A

−+

−+=  −

 

c 4= T F  /L when T F  /L ≤ 0.04c 4= 0.04 when T F  /L>0.04

Problem: The characteristics of a ship is asfollows:

L.O.W L=205.00 mL.B.P. LPP  = 200.00 mBreadth moulded B = 32.00 mDraught moulded on F.P, T F =10.00 mDraught moulded on A. P. T  A=10.00 mDisplacement volume moulded,▼=37500 m

3 

Longitudinal centre of buoyancy 2.02% aft of1/2LPP  Transverse bulb area ABT  = 20.0 m

2 

Centre of bulb area above keel line hB = 4.0 m

Midship section coefficient C M  = 0.98Waterplane area coefficient C WP  = 0.75Transom area  AT  = 16.0 m

2

Wetted area appendages S APP  = 50.0 m2 

Stern shape parameter, C stern = 10.0Propeller diameter, D = 8.0 mNumber of propeller blades Z  = 4Clearance of propeller with keel line 0.20 mShip speed V =25.0 knosDensity,  ρ = 1025.87Kinematic Viscosity, υ  = 1.18831e-006

Find RF, R  APP ,R W , R B, R TR , R  A, R total .

Reference: J. Holtrop and G.G. J. Mennen,1982:  An Approximate Power PredictionMethod, International Shipbuilding Progress,Vol. 29, No. 335.