1. Chap 7 Resistance and Powering of Ship
Recall Static Equilibrium!
What are the forces in the x-axis of the ship?
Resistance or Drag
Thrust (Propulsion)
We will first look at propulsion, then drag in this chapter.
41 knots!

2. Ship Drive Train and Power
7.2 Ship Drive Train System
Engine
Reduction
Gear
Screw
Strut
Bearing
Seals
THP
Shaft
BHP
SHP
DHP

3. 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

4. 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
BHP
SHP
DHP
THP
EHP
E/G
R/G
Shaft
Bearing
Prop.
Hull
Relative Magnitudes?
BHP>SHP>DHP>THP

5. 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)
Measured EHP V
Towing Tank
Towing carriage

6. Effective Horse Power (EHP)
Typical EHP Curve of YP
What EHP is required for the 12 knot YP cruise?

7. Effective Horse Power (EHP)
Efficiencies
Hull Efficiency
Hull efficiency changes due to hull-propeller interactions.
Well-designed ship :
Poorly-designed ship :
Well-designed
Poorly-designed
Flow is not smooth.
THP is reduced.
- High THP is needed
to get designed speed.

8. Effective Horse Power (EHP)
Efficiencies (cont’d)
EHP
Propeller Efficiency
Screw
THP
DHP
SHP
Propulsive Coefficient (PC) ~ An overall measure of drive train efficiency

9. 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

10. Total Hull Resistance (cont)
Coefficient of Total Hull Resistance
- Non-dimensional value of total resistance

11. Total Hull Resistance (cont)
Coefficient of Total Hull Resistance (cont’d)
Total Resistance of full scale ship can be determined using

12. Total Hull Resistance (cont)
Relation of Total Resistance Coefficient and Speed

13. 7.6 Components of Total 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

14. 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

15. Components of Total Hull Resistance
Total Resistance and Relative Magnitude of Components
Air Resistance
Hollow
Hump
Wave-making
Resistance (lb)
Viscous
Speed (kts)
Low speed : Viscous R dominates
Higher speed : Wave-making R dominates
Hump (Hollow) : location is function of ship length and speed.

16. 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.

17. Coefficient of Viscous Resistance (cont)
Coefficients of Viscous Resistance
- Non-dimensional quantity of viscous resistance
- It consists of tangential and normal components.
normal
tangential
flow
ship
stern
bow
Tangential Component :
- Tangential stress is parallel to ship’s hull and causes
a net force opposing the motion ; Skin Friction
- It is assumed can be obtained from data of flat plates.

18. Coefficient of Viscous Resistance (cont)
Semi-empirical
equation

19. 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.
Laminar Flow
Turbulent Flow
Flow over
flat plate

20. 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

21. Coefficient of Viscous Resistance (cont)
Normal Component (cont’d)
- It is calculated by the product of Skin Friction with Form Factor.

22. 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 

23. Wave-Making Resistance
Definition : refer to the previous note
Typical Wave Pattern
Stern divergent wave
Bow divergent wave
Bow divergent wave L
Transverse wave
Wave Length

25. 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.

26. Wave-Making Resistance (cont)
Transverse wave System
Vs < Hull Speed
Wave Length
Wave
Length
Slow
Speed
“Hull”
Vs  Hull Speed
Hull Speed : speed at which the transverse wave length equals
the ship length.
(Wavemaking resistance drastically increases above hull speed)

27. 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.

28. 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.

29. 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.

30. 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!

31. Wave-Making Resistance (cont)
Bulbous Bow

32. Coefficient of Total Resistance
Coefficient of total hull resistance: the C’s added
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,
For ship, empirical formulas can be used.

33. 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).

34. 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

35. ? 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. ?
Dimension
Speed
Force
prototype
Model
prototype ship
model ship

36. 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.

37. 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

38. 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?

39. 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.

40. Basic Theory behind Ship Modeling
Corresponding Speeds
Example :
Ship length = 200 ft, Model length : 10 ft
Ship speed = 20 kts, Model speed towed ?
1kts=1.688 ft/s

41. Chap 7.7 Basic Theory Behind Ship Modeling
Modeling Summary 1)
Measured in tank
Froude
Expansion 2) 3)

42. 7.9 The Screw Propeller

43. 7.9 Screw Propeller
Diameter
Hub
Blade Tip
Blade Root

44. Pitch Distance
Pitch Angle
Fixed Pitch
Variable Pitch
Controllable Pitch
(Constant Speed)

45. 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

46. Right and Left Hand Props
Right Hand

47. Suction Face
Leading Edge
Trailing Edge
Pressure Face

48. 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.

49. Prop Walk Solutions Twin Screws
Counter rotating propellers (one shaft)
Tunnels/shrouds (nozzle)

50. Shrouded (nozzle) prop

51. 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

52. 7.9. Propeller Theory Propeller Theory Speed of Advance P Wake RegionQ P
Wake Region
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,
Speed of Advance

53. 7.9 Propeller Theory Propeller Efficiency Maximum
~70 % for well-designed prop
Maximum
- For a given T (Thrust), Ao
(Diameter ) ; CT ; Prop Eff
The larger the diameter of propeller, the better the propeller efficiency

54. 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.

55. 1 atm=101kpa
=14.7psi

57. 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.

58. 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

59. 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.

60. 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.

61. Other forms of propulsion
A one horsepower cable-drawn ferry!