Chap 7 Resistance and Powering of Ship
• Recall Static Equilibrium!
• What are the forces in the xaxis of the ship?
– Resistance or Drag
– Thrust (Propulsion)
– We will first look at propulsion,
then drag in this chapter.
41 knots!
Ship Drive Train and Power
7.2 Ship Drive Train System
Engine
Reduction
Gear
Strut Screw
Bearing
Seals
THP
BHP
Shaft
SHP
DHP
Ship Drive Train and Power
Horse Power in Drive Train
Brake Horse Power (BHP)
- Power output at the shaft coming out of the engine before
the reduction gears
Shaft Horse Power (SHP)
- Power output after the reduction gears (at shaft)
- SHP=BHP - losses in reduction gear
Ship Drive Train and Power
Delivered Horse Power (DHP)
- Power delivered to the propeller
- DHP=SHP – losses in shafting, shaft bearings and seals
Thrust Horse Power (THP)
- Power created by the screw/propeller (ie prop thrust)
- THP=DHP – Propeller losses
E/G
BHP
R/G
SHP
Relative Magnitudes?
BHP>SHP>DHP>THP
Shaft
Bearing
DHP
Prop.
THP
Hull
EHP
7.3 Effective Horse Power (EHP)
• EHP : The power required to move the ship hull at a given
speed in the absence of propeller action (related to resistance)
(EHP is not related with Power Train System)
• EHP can be determined from the towing tank experiments at
the various speeds of the model ship.
• EHP of the model ship is converted into EHP of the full scale
ship by the Froude’s Law.
EHP is approximately equal to THP (usually slightly less)
V
Towing Tank
Measured EHP
Towing carriage
E f f e c t iv e H o r s e p o w e r , E H P ( H P )
Effective Horse Power (EHP)
POWER CURVE
YARD PATROL CRAFT
1000
800
600
400
200
0
0
2
4
6
8
10
12
14
16
Ship Speed, Vs (Knots)
Typical EHP Curve of YP
What EHP is required for the 12 knot YP cruise?
Effective Horse Power (EHP)
Efficiencies
• Hull Efficiency
EHP
H 
THP
- Hull efficiency changes due to hull-propeller interactions.
- Well-designed ship :
H  1
- Poorly-designed ship :
H  1
Well-designed
Poorly-designed
- Flow is not smooth.
- THP is reduced.
- High THP is needed
to get designed speed.
Effective Horse Power (EHP)
Efficiencies (cont’d)
EHP
• Propeller Efficiency
 propeller
Screw
THP

DHP
DHP
THP
SHP
• Propulsive Coefficient (PC) ~ An overall measure of drive train
efficiency
EHP
p 
SHP
p  0.6 for well designed propeller
7.5 Total Hull Resistance
• Total Hull Resistance (RT)
The force that the ship experiences opposite to the motion of
the ship as it moves.
• EHP Calculation
 ft 
RT (lb)  VS  
s
EHP(H P ) 
 ft lb 

550
 s HP 
RT  total hull resistance
VS  speed of ship
 ft  lb  ft J
RT V S  lb     
  Watts : Power
s
s
 s 
1 Watts  1 / 550 H P
Total Hull Resistance (cont)
• Coefficient of Total Hull Resistance
- Non-dimensional value of total resistance
lb
RT

 non - dimension
2
CT 
2
 lb  s 2  ft  2
0.5 Vs S
 4 
 ft
 ft  s 
CT  Coefficien t of total hull resistance in calm water
RT  Total hull resistance
  Fluid density
VS  Speed of ship
S  wetted surface area on the submerged hull
Total Hull Resistance (cont)
• Coefficient of Total Hull Resistance (cont’d)
-Total Resistance of full scale ship can be determined using
CT ,  , S and VS
RT (lb )  0.5SVS  CT
2
CT : determined by the model test
 : available from water property table
S : obtained from Curves of form
VS : Full scale ship speed
Total Hull Resistance (cont)
T o t a l R e s is t a n c e , R t (lb )
• Relation of Total Resistance Coefficient and Speed
TOTAL RESISTANCE CURVE
YARD PAT ROL CRAFT
20000
15000
10000
5000
0
0
2
4
6
8
10
12
14
16
Ship Speed, Vs (knots)
RT  CT  VS
 VS
2
n
n  from 2 at low speed
to 5 at high speed
EHP  RTVS  CT  VS  VS
2
 VS
n
n  from 3 at low speed
to 6 at high speed
7.6 Components of Total Resistance
• Total Resistance
RT  RV  RW  RA
RV : Viscous Resistance
RW : Wave Making Resistance
RA : Air Resistance
• Viscous Resistance
- Resistance due to the viscous stresses that the fluid exerts
on the hull.
( i.e. due to friction of the water against the surface of the ship)
- Water viscosity, ship’s velocity, wetted surface area and roughness
of the ship generally affect the viscous resistance.
Characterized by the non-dimensional Reynold’s Number, Rn
Components of Total Resistance
• Wave-Making Resistance
- Resistance caused by waves generated by the motion of the ship
- Wave-making resistance is affected by beam to length ratio,
displacement, shape of hull, (ship length & speed)
Characterized by the non-dimensional Froude Number, Fn
• Air Resistance
- Resistance caused by the flow of air over the ship with no
wind present
- Air resistance is affected by projected area, shape of the ship
above the water line, wind velocity and direction
- Typically 4 ~ 8 % of the total resistance
Components of Total Hull Resistance
• Total Resistance and Relative Magnitude of Components
Air Resistance
Hollow
Hump
Wave-making
Viscous
Speed (kts)
- Low speed : Viscous R dominates
- Higher speed : Wave-making R dominates
- Hump (Hollow) : location is function of ship length and speed.
Coefficient of Viscous Resistance
• Viscous Flow around a ship
Real ship : Turbulent flow exists from near the bow.
Model ship : Studs or sand strips are attached at the bow
to create the turbulent flow.
Coefficient of Viscous Resistance
(cont)
• Coefficients of Viscous Resistance
- Non-dimensional quantity of viscous resistance
- It consists of tangential and normal components.
CV  Ctangential  Cnormal  CF  KCF
flow
bow
ship
stern
• Tangential Component : CF
- Tangential stress is parallel to ship’s hull and causes
a net force opposing the motion ; Skin Friction
- It is assumed
CF can be obtained from data of flat plates.
Coefficient of Viscous Resistance (cont)
Tangential Component of CV  CF
0.075
CF 
(log 10 Rn  2) 2
Rn 
Semi-empirical
equation
LVS

Rn  Reynolds Number
L  L pp (ft)
VS  Ship Speed(ft/s )
  Kinematic Viscosity (ft 2 /s)
 1.2260  10-5 ft 2 /s for fresh water
 1.2791  10-5 ft 2 /s for salt water
Coefficient of Viscous Resistance
(cont)
• Tangential Component (cont’d)
- Relation between viscous flow and Reynolds number
· Laminar flow : In laminar flow, the fluid flows in layers
in an orderly fashion. The layers do not mix transversely
but slide over one another.
· Turbulent flow : In turbulent flow, the flow is chaotic and
mixed transversely.
Flow over
flat plate
Laminar Flow
Turbulent Flow
Rn  about 5 10
5
Rn  about 5  10
5
Coefficient of Viscous Resistance
(cont)
• Normal Component
- Normal component causes a pressure distribution along the
underwater hull form of ship
- A high pressure is formed in the forward direction opposing
the motion and a lower pressure is formed aft.
- Normal component generates the eddy behind the hull.
- It is affected by hull shape.
Fuller shape ship has larger normal component than slender
ship.
large eddy
Full ship
Slender ship
small eddy
Coefficient of Viscous Resistance
(cont)
• Normal Component (cont’d)
- It is calculated by the product of Skin Friction with Form Factor.
Normal Component of Cv  K CF
CF  Skin Friction Coeff.
K  Form Factor

(ft )
B ( ft) 

K  19 
 L( ft) B ( ft)T ( ft) L( ft) 
3
2
Summary of Viscous Resistance Coefficient
• Reducing the Viscous Resistance Coefficient
- Method : Increasing L with constant submerged volume
1) Form Factor K   Normal component KCF 
 Slender hull is favorable. ( Slender hull form will create
a smaller pressure difference between bow and stern.)
2) Reynolds No. Rn   CF   KCF 
Wave-Making Resistance
• Definition : refer to the previous note
•Typical Wave Pattern
Stern divergent wave
Bow divergent wave
L
Transverse wave
Wave Length
Wave-Making Resistance
Transverse wave system : Waves perpendicular to wake
• It travels at approximately the same speed as the ship.
• At slow speed, several crests exist along the ship length
because the wave lengths are smaller than the ship length.
• As the ship speeds up, the length of the transverse wave
increases.
• When the transverse wave length approaches the ship length,
the wave making resistance increases very rapidly.
This is the main reason for the dramatic increase in
Total Resistance as speed increases.
Wave-Making Resistance (cont)
Transverse wave System
Vs < Hull Speed
Slow
Speed
Wave
Length
Vs  Hull Speed
“Hull”
Speed
Wave Length
Hull Speed : speed at which the transverse wave length equals
the ship length.
(Wavemaking resistance drastically increases above hull speed)
Wave-Making Resistance (cont)
Divergent Wave System: waves that angle out
• It consists of Bow and Stern Waves.
• Interaction of the bow and stern waves create the Hollow or
Hump on the resistance curve.
• Hump : When the bow and stern waves are in phase,
the crests are added up so that larger divergent wave systems
are generated.
• Hollow : When the bow and stern waves are out of phase,
the crests match the troughs so that smaller divergent wave
systems are generated.
Wave-Making Resistance (cont)
Calculation of Wave-Making Resistance Coeff.
• Wave-making resistance is influenced by:
- beam to length ratio
- displacement
- hull shape
- Froude number
• The calculation of the coefficient is too complex for a simple
theoretical or empirical equation.
(Because mathematical modeling of the flow around ship
is very complex since there exists fluid-air boundary,
wave-body interaction)
• Therefore model test in the towing tank and Froude expansion
are the best way to calculate the Cw of the real ship.
Wave-Making Resistance (cont)
Reducing Wave Making Resistance
1) Increasing ship length to reduce the transverse wave
- Hull speed will increase.
- Therefore increment of wave-making resistance of longer
ship will be small until the ship reaches to the hull speed.
Wave-Making Resistance (cont)
Reducing Wave Making Resistance (cont’d)
2) Attaching Bulbous Bow to reduce the bow divergent wave
- Bulbous bow generates the second bow waves .
- Then the waves interact with the bow wave resulting in
ideally no waves, practically smaller bow divergent waves.
- EX :
DDG 51 : 7 % reduction in fuel consumption at cruise speed
3% reduction at max speed.
design &retrofit cost : less than $30 million
life cycle fuel cost saving for all the ship : $250 mil.
Tankers & Containers : adopting the Bulbous bow
3) Stern flaps - helps with launching small boats, too!
Wave-Making Resistance (cont)
Bulbous Bow
Coefficient of Total Resistance
Coefficient of total hull resistance: the C’s added
CT  C V  C W  C A
 C F(1  K)  C W  C A
C A: Correlatio n Allowance
Correlation Allowance
• It accounts for hull resistance due to surface roughness,
paint roughness, corrosion, and fouling of the hull surface.
• It is only used when a full-scale ship prediction of EHP is made
from model test results.
• For model, CA  0 Since model surface is smooth.
• For ship, empirical formulas can be used.
Other Type of Resistances
• Appendage Resistance
- Frictional resistance caused by the underwater appendages
such as rudder, propeller shaft, bilge keels and struts
- 224% of the total resistance in naval ship.
• Steering Resistance
- Resistance caused by the rudder motion.
- Small in warships but troublesome in sail boats
•Added Resistance
- Resistance due to sea waves which will cause the ship
motions (pitching, rolling, heaving, yawing).
Other Resistances
• Increased Resistance in Shallow Water
- Resistance caused by shallow water effect
- Flow velocities under the hull increases in shallow water.
: Increment of frictional resistance due to the velocities
: Pressure drop, suction, increment of wetted surface area
 Increases frictional resistance
- The waves created in shallow water take more energy from
the ship than they do in deep water for the same speed.
 Increases wave making resistance
7.7 Basic Theory Behind Ship Modeling
• Modeling a ship
- Not possible to measure the resistance of the prototype ship
- The ship needs to be scaled down to test in the tank but
the scaled ship (model) must behave in exactly same way
as the real ship.
- How to scale the prototype ship ?
How to make relationships between the prototype and model
data?
- Geometric and Dynamic similarity must be achieved.
prototype
ship
prototype
?
model ship
Dimension
Speed
Force
Model
Basic Theory behind Ship Modeling
• Geometric Similarity
- Geometric similarity exists between model and
prototype if the ratios of all characteristic dimensions
in model and prototype are equal.
- The ratio of the ship length to the model length is typically
used to define the scale factor.
Scale Factor  λ
LS (ft)

: Length
LM (ft)
S S (ft 2 )
 
S M (ft 2 )
: Area
 S (ft 3 )
 
 M (ft 3 )
: Volume
2
3
S : full scale ship
M : Model
Basic Theory behind Ship Modeling
• Dynamic Similarity
- Dynamic Similarity exists between model and prototype
if the ratios of all forces in model and prototype are the
same.
- Total Resistance : Frictional Resistance+ Wave Making+Others
CV  f ( Rn ),
CW  f ( Fn )
RnS  RnM ,
FnS  FnM
LSVS LMVM

,
vS
vM
vM LS
VM  VS
,
vS LM
VS
VM

gLS
gLM
VM  VS
LM
LS
Basic Theory behind Ship Modeling
• Dynamic Similarity (cont’d)
- Both Geometric and Dynamic similarity cannot be achieved
at same time in the model test because making both Rn and
Fn the same for the model and ship is not physically possible.
Example
Ship Length=100ft, Ship Speed=10kts, Model Length=10ft
Model speed to satisfy both geometric and dynamic similitude?
VM  VS
LM
LS
10ft
 10(kts )
100ft
 3.16(kts )
vM LS
VM  VS
vS LM
100 ft
 10(kts)
(assume vM  vS )
10 ft
 100( kts)
Basic Theory behind Ship Modeling
• Dynamic Similarity (cont’d)
- Choice ?
· Make Fn the same for the model.
· Have Rn different
 Incomplete dynamic similarity
- However partial dynamic similarity can be achieved by
towing the model at the “corresponding speed”
- Due to the partial dynamic similarity, the following
relations in forces are established.
CW M  CW S
CVM  CVS
Basic Theory behind Ship Modeling
• Corresponding Speeds
VS
V
 M
gLS
gLM
FnS  FnM ,
VS (ft/s) VM (ft/s)

LS (ft)
LM (ft)
- Example :
Ship length = 200 ft, Model length : 10 ft
Ship speed = 20 kts, Model speed towed ?
VM  VS
 VS
LM
1
 VS
LS
LS / LM
1
1
 20kts
 4.47 kts

20
1kts=1.688 ft/s
Chap 7.7 Basic Theory Behind Ship Modeling
• Modeling Summary
CT  CV  CW  C A  CF (1  K )  CW  C A
1) CTM  CFM (1  K M )  CWM  C AM
Froude
Expansion
Measured in tank
CWM  CTM CFM (1  K )  C AM
2) CTS  CFS (1  K S )  CWS  C AS
RTS VS
3)
EHP (hp ) 
550
( RTS  CTS * 0.5 S S SVs 2 )
CWS  CWM ( FnS  FnM , VS / gLS  VM / gLM )
CFM , CFS
(calculate d)
KS  KM
(due to scale factor  . Calculated or given )
C AM  0
( Model is smooth)
C AS  0
(given, or calculated )
7.9 The Screw Propeller
7.9 Screw Propeller
Diameter
Hub
Blade Tip
Blade Root
Pitch Distance
Pitch Angle
Fixed Pitch
Variable Pitch
Controllable Pitch
(Constant Speed)
7.9 Screw Propeller
• Variable Pitch (the standard prop):
- The pitch varies at the radial distance from the hub.
- Improves the propeller efficiency.
- Blade may be designed to be adjusted to a different
pitch setting when propeller is stopped.
• Controllable Pitch :
- The position of the blades relative to the hub can be
changed while the propeller is rotating.
- This will improve the control and ship handling.
- Expensive and difficult to design and build
Right and Left Hand Props
Left Hand
Right Hand
Suction Face
Leading Edge
Trailing Edge
Pressure Face
Propeller Walk
• Due to a difference in the pressure at
the top and bottom of the prop (due to
boundary layer), the lower part of the
prop works harder.
• This leads to a slight turning moment.
• Right hand props cause turns to port
when moving ahead.
Prop Walk Solutions
• Twin Screws
• Counter rotating propellers (one shaft)
• Tunnels/shrouds (nozzle)
Shrouded (nozzle) prop
7.9 Skewed Screw Propeller
Highly Skewed Propeller
Advantages
- Reduce interaction between
propeller and rudder wake.
- Reduce vibration and noise
Disadvantages
- Expensive
- Less efficient operating in
reverse
DDG51
7.9. Propeller Theory
Propeller Theory
• Speed of Advance
P
Vwater  0
Wake Region
VS
Q
VW
Vwater  VS
• The ship drags the surrounding water so that the wake to
follow the ship with a wake speed (Vw) is generated in the
stern.
• The flow speed at the propeller is,
VA  VS  VW
Speed of Advance
7.9 Propeller Theory
Propeller Efficiency
 propeller 
2
1  1  Ct
T
CT 
2
0.5 VA Ao
 propeller
THP

DHP
~70 % for well-designed prop
CT : Thrust loading coefficien t
T : Propelle r thrust
A o : Area of the projected propeller disc
- For a given T (Thrust),
Ao (Diameter ) ; CT
Maximum
; Prop Eff
The larger the diameter of propeller, the better the propeller efficiency
Chap 7.9.3 Propeller Cavitation
• Cavitation : Definition
- The formation and subsequent collapse of vapor bubbles
on propeller blades where pressure has fallen below the
vapor pressure of water.
- Bernoulli’s Equation can be used to predict pressure.
- Cavitation occurs on propellers (or rudders) that are
heavily loaded, or are experiencing a high thrust loading
coefficient.
1 atm=101kpa
=14.7psi
Blade Tip Cavitation
Navy Model Propeller 5236
Flow velocities at the tip
are fastest so that
pressure drop occurs at
the tip first.
Sheet Cavitation
Large and stable region
of cavitation covering the
suction face of propeller.
Propeller Cavitation
Consequences of Cavitation
1) Low propeller efficiency (Thrust reduction)
2) Propeller erosion (mechanical erosion as bubbles
collapse, up to 180 ton/in² pressure)
3) Vibration due to uneven loading
4) Cavitation noise due to impulsion by the bubble
collapse
Propeller Cavitation
• Preventing Cavitation
- Remove fouling, nicks and scratch.
- Increase or decrease the engine RPM smoothly to avoid
an abrupt change in thrust.
rapid change of rpm  high propeller thrust but small
change in VA  larger CT  cavitation &
low propeller efficiency
- Keep appropriate pitch setting for controllable pitch
propeller
- For submarines, diving to deeper depths will delay or
prevent cavitation as hydrostatic pressure increases.
Propeller Cavitation
• Ventilation
- If a propeller or rudder operates too close to the water
surface, surface air or exhaust gases are drawn into the
propeller blade due to the localized low pressure around
propeller. The prop “digs a hole” in the water.
- The load on the propeller is reduced by the mixing of
air or exhaust gases into the water causing effects
similar to those for cavitation.
-Ventilation often occurs in ships in a very light
condition(small draft), in rough seas, or during hard
turns.
Other forms of propulsion
A one horsepower cable-drawn ferry!