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TS 4001: Lecture Summary 4
Resistance
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20 February 2002 Resistance 2
Ship Resistance
• Very complex problem:
− Viscous effects.
− Free surface effects.
• Can only be solved by a combination of:
− Theoretical methods.
− Phenomenological methods.
− Experiments.
• Must predict resistance to select propulsion plant.
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20 February 2002 Resistance 3
Speed-Power Trends
• EHP = (Resistance) x (Speed)
• For the horizontal axis:V in knots, L in feet.
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20 February 2002 Resistance 4
Froude 1877
• Ships make waves.
• Waves require energy.
• Energy is spent from the ship’s propulsion plant.
• Therefore, waves = resistance.
• Test with models.
• But, that’s only half the problem – how about fluid friction?
• Unfortunately, viscous fluids were “unknown” to Froude.
• So, he tested with “waveless” models – wooden planks.
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20 February 2002 Resistance 5
Froude’s Early Sketch
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20 February 2002 Resistance 6
Sources of Resistance.
• Since ship resistance is such a complex problem, we have to break it down.
• To understand where it comes from, we have to understand the principal types of fluid flow.
• Look at a submerged body first, then bring in the free surface.
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20 February 2002 Resistance 7
Fluid Flow - Submerged
• Examples of fluid flow for a submerged body (no waves):
D’Alambert’s paradox
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20 February 2002 Resistance 8
Fluid Flow - Surface
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20 February 2002 Resistance 9
Types of Fluid Flow
• Potential flow.
• Viscous flow.
• Wavemaking.
• Flow separation.
• Circulation/Vortex motion.
• Cavitation.
• Hydrofoil flow.
• Elastic/Compressible flow.
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20 February 2002 Resistance 10
Potential Flow
• Ideal, non-viscous or frictionless, streamline flow.
• Unbroken streamlines whose journey is made with no friction.
• Many applications:
− Wave making.
− Bernoulli law.
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20 February 2002 Resistance 11
Viscous Flow
• Real, frictional flow.
• Attachment of innermost fluid particles to surface of body.
• Resistance to shear offered by moving particles in adjacent layers.
• Newtonian fluids.
• No-slip boundary condition.
• Boundary layer.
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20 February 2002 Resistance 12
Wavemaking
• Occurs at the interface of two non-mixing liquids.
• Free surface is disturbed by oscillatory movements giving rise in propagating waves.
• Energy carried away by the waves constitutes the wave making resistance.
• Not to be confused with resistance in waves.
• Gravity plays a very important role.
• Both surface and sub-surface waves.
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20 February 2002 Resistance 13
Flow Separation
• Occurs when streamlines are prevented from following contours of body.
• Vortices (or eddies) with circulatory motion and reverse flow are formed after separation.
• Important for resistance, but also for wake and propeller induced vibration.
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20 February 2002 Resistance 14
Circulation/Vortex Motion
• Circulatory motion of fluid about an axis, in planes perpendicular to that axis.
• Solid body may surround axis, or gas pocket may enter on it.
• Forming a core around which the coil of circulatory motion takesplace.
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20 February 2002 Resistance 15
Cavitation
• Formation of bubbles, voids, or cavities alongside or behind a body moving in a fluid.
• Occurs when fluid pressure at a point on the body is reduced to vapor pressure of fluid.
• Will study it in more detail in the next set.
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20 February 2002 Resistance 16
Hydrofoil Flow
• Combination of two or more flows.
• Relative motion of body and fluid develops drag and lift forces on the body at right angles to the direction of relative motion.
• Very important in special hull forms and in maneuvering and motion control (later).
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20 February 2002 Resistance 17
Elastic Flow
• Traveling pressure – Wave phenomenon.
• Arises from elasticity of fluid.
• Formation of shock pressure waves radiating at high speeds from exciting sources.
• Shock and vibration problem.
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20 February 2002 Resistance 18
Conclusions
• Ship resistance is caused by many different fluid flow phenomena.
• These interact and combine in complex ways.
• Theoretical methods have not yet been developed to the point where model tests are not needed.
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20 February 2002 Resistance 19
Resistance Source Summary
• Friction:− dominant at low speeds,− function of wetted surface area, speed, and roughness.
• Wavemaking:− dominant at higher speeds,− function of hull form and speed,− part of “residual resistance”.
• Eddy/Form:− result of pressure difference,− part of “residual resistance”.
• Air/Appendage:− not always designed for,− can be significant.
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20 February 2002 Resistance 20
Resistance Breakdown
• Different fluid flows generate different resistance components.
• This decomposition has some physical grounds and is used simply because it is convenient.
• Study the major resistance components separately.
• Then find a way to put them together.
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20 February 2002 Resistance 21
Frictional Resistance
• Also known as viscous resistance.
• Aft acting force to set fluid within the boundary layer in motion.
• Depends on wetted surface of body, not its geometry.
• Zero for an ideal fluid.
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20 February 2002 Resistance 22
Wavemaking Resistance
• Part of residuary resistance.
• Energy expended to produce waves is a measure of the work done by the ship on water.
• Nonzero even for an ideal fluid.
• Directly related to wavemaking by the body.
• Related to hull geometry.
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20 February 2002 Resistance 23
Separation Resistance
• Also known as Form Drag.
• Part of residuary resistance.
• Occurs when fluid flow separates from hull, especially near the stern.
• (Residuary) = (Wavemaking) + (Separation)
• (Residuary) = (Total) - (Frictional)
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20 February 2002 Resistance 24
Appendage Resistance
• Very difficult to predict and scale up: Vastly different scale from ship.
• Many causes:
− Eddy making resistance: Inability of water to flow in smooth streamlines around abrupt discontinuities; flow breaks clear and reverses; eddies fill in the void.
− Frictional resistance.
− Cavitation.
• Usually dealt with as a single number, either a total for all appendages, or each individual appendage.
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20 February 2002 Resistance 25
Typical Appendage Resistance
-2-5%2-5%All single propeller ships
-8-14%8-14%Large, medium speed, 2 propellers
-10-23%12-30%Small, medium speed, 2 propellers
10-15%17-25%20-30%Small, fast, 2 propellers
-10-16%10-16%Large, fast, 4 propellers
1.61.000.7
TYPE OF SHIP LV
: i n k n o t s , i n f e e t .V L V L
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20 February 2002 Resistance 26
Air Resistance
• Consists of both frictional and eddy-making resistances caused by relative flow of air around above water part of the ship.
• Usually not designed for, but can be a major component in certain cases.
• Depends on air density, relative wind speed, projected area of above water part of the ship, and some resistance coefficient.
• Wind tunnel tests can be used to evaluate the air resistance coefficient.
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20 February 2002 Resistance 27
Total
(Total Resistance) =
(Frictional Resistance) +
(Residuary Resistance) +
(Appendage Resistance)(1) +
(Air Resistance)(1) +
(Correlation Allowance)(2)
(1): If available.(2): To patch things up.
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20 February 2002 Resistance 28
Correlation Allowance
• All extrapolation methods require an adjustment to achieve correct correlation between model and ship.
• Determined by comparing full scale ship trials to previous modeltest results.
• Must be known in advance.
• Decreases with increasing ship length.
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20 February 2002 Resistance 29
Typical Speed Profile
Ship is “climbing” its own bow wave
Typical ResistanceCharacteristics of
Displacement Vessels
Res
ista
nce
(lbs)
/ D
ispl
acem
ent (
tons
)
Wavemaking resistancedominates at high speeds
Speed/Length Ratio
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20 February 2002 Resistance 30
Summary: Resistance Components
• Frictional− Equivalent to resistance of flat plate being towed
• Form (Eddy/Separation)− Energy lost in the formation of eddies caused by flow separation
• Wave− Energy lost in the making and breaking of waves
• Appendage− Added resistance of bilge keels, struts, shafts, rudders, and propellers
• Air− Drag associated with superstructure and hull above the waterline
• Correlation Allowance− Accounts for hull roughness and scaling differences between model and ship
(Typically runs from 0.0004 to 0.0005)
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20 February 2002 Resistance 31
Sources of Information
• Theoretical Calculations:− Solution of the complete problem (Navier-Stokes with a free surface
at high fluid speeds) is not yet practical.
− Wavemaking can be predicted relatively well, frictional not so.
• Tests:− Full scale would be best but is of course not practical.
− Have to do model scale and then “extrapolate”.
• Preliminary:− Regression analyses of earlier ship data.
− Standard series.
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20 February 2002 Resistance 32
The Main Problem
• How do we extrapolate from model scale to full scale.
• How to “scale up” dimensions, velocities, and forces from model to full scale ship?
• In other words, how do we go …
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20 February 2002 Resistance 33
… from this …
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20 February 2002 Resistance 34
… to this.
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20 February 2002 Resistance 35
Dynamic Similarity
• Consider two geometrically similar ships.
• How do we scale their resistance properties?
• Flows must be similar.
• Resistance depends on:
− Length,
− Water density,
− Kinematic viscosity,
− Ship speed,
− Acceleration of gravity,
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20 February 2002 Resistance 36
Dimensional Analysis
• Assume:
• For this to be dimensionally correct:
• Solving:
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20 February 2002 Resistance 37
The Resistance Equation
• Therefore:
• Since we have geometrically similar bodies:
• Therefore, we can write:
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20 February 2002 Resistance 38
Resistance Coefficient
• The resistance coefficient
is a function of the Reynolds number
and the Froude number
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20 February 2002 Resistance 39
Conclusions
• The two important parameters in ship resistance are:
− The Reynolds number, which physically represents viscous effects, and
− The Froude number, which represents wavemaking.
• Two geometrically similar hull forms (geosims) will have the same wave resistance coefficient if and only if they have the same Reynolds number and Froude number.
• How do we achieve this?
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20 February 2002 Resistance 40
Resistance Calculations
1/ 2 1/ 2
Want to find: (Re, Fn)If subscript corresponds to ship and to model we must have:( ) ( )For that we need:
(Re) (Re) or
and
(Fn) (Fn) or
R
R s R m
m s sm s
s m m
m m mm s
s s s
Cs m
C C
V LV L
V g LV g L
νν
=
= =
= =
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20 February 2002 Resistance 41
Is this possible?
1/ 2
Pick a reasonable model/ship ratio / 1/100Then the previous requirements are:
1100 and 10
In order to satisfy both we must either:(a) perform the experiments on a
m s
m s m m
s m s s
L L
V V gV V g
νν
=
= =
space station with adjustableorbit and adjustable g, or(b) invent an exotic fluid with kinematic viscosity one thousandththat of seawater.Unfortunately, none of these options is feasible.
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20 February 2002 Resistance 42
So which one to choose?
So we can't satisfy both both Re and Fn scaling simultaneously.Which one to choose?Call the ship/model ratio / ( 1).Then we either satisfy
s mL L λ=
This is for the same fluid for ship and model. Since ( 1), Re scaling is highly impractical.Fn scaling is all we can do.
λ
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20 February 2002 Resistance 43
Froude’s Hypothesis
So the problem is how to get (CR)s from measurements of (CR)m assuming Fn scaling only. Strictly speaking, since CR is a function of both Re and Fn, this is not possible.
Froude’s hypothesis is:
CF is the frictional resistance coefficient and this is a function of Re only (assuming that the extra friction due to the waves generated by the ship is small).
CW is the wavemaking resistance coefficient and this is a function of Fn only.
CFORM is the form drag (separation resistance) and we assume that it is a function of hull geometry only.
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20 February 2002 Resistance 44
Froude’s Method
Froude was able to verify this experimentally by pulling wooden planks down Thames and in his basement!
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20 February 2002 Resistance 45
Froude’s Calculations
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20 February 2002 Resistance 46
Total Resistance Coefficient
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20 February 2002 Resistance 47
Frictional Resistance
• Characterized by the Reynolds number, Re.
• From 50% of the overall resistance (high speed streamlined ships) to over 85% (slow speed tankers).
• Flow is laminar for low Re and turbulent for high Re (more typical in full scale ships).
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20 February 2002 Resistance 48
Skin Friction Lines
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20 February 2002 Resistance 49
I.T.T.C. Friction Line
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20 February 2002 Resistance 50
Correlation Allowance
• I.T.T.C. friction line
• Correlation allowance:
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20 February 2002 Resistance 51
Wavemaking Resistance
• Froude’s pattern was explained by Lord Kelvin using the method of stationary phase.
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20 February 2002 Resistance 52
Typical Ship Wave Pattern
• Calculation of wave pattern allows calculation of wave making resistance.
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20 February 2002 Resistance 53
Typical Plots
• Typical wavemaking resistance coefficient plots exhibit multiple peaks and valleys.
• This has led to many optimization studies.
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20 February 2002 Resistance 54
Other Components of Resistance
• Wind resistance.
• Added resistance due to waves.
• Added resistance due to turning.
• Appendage resistance.
• Effects of trim.
• Shallow water effects.
• Subsurface waves.
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20 February 2002 Resistance 55
Operational Factors
• Displacement and Still-water Trim− Resistance sensitive to changes in displacement and trim
• Sinkage and Squat− Caused by bow and stern wave systems− Ship sinks down without trimming at low to moderate speed− Stern begins to “squat” as speed increases
• Shallow Water− Generally increased resistance in shallow water
• Sea Conditions− The heavier the seas, the higher the resistance
• High Winds− Increase ship resistance, especially if rudder is used to maintain course
• Fouling− Can significantly increase resistance if not controlled
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20 February 2002 Resistance 56
Shallow Water Effects
• As the wave pattern changes, the wavemaking resistance also changes.
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20 February 2002 Resistance 57
Shallow Water Effects (cont.)
• Water depth: h
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20 February 2002 Resistance 58
Speed Reduction in Shallow Water
Contours show percent speed loss.
Ax = max cross sectional area of the hull.
h = water depth
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20 February 2002 Resistance 59
Speed in Restricted Channels
For a rectangular channel of width b and depth h:
If a ship with cross sectional area Axand wetted girth p is in the channel:
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20 February 2002 Resistance 60
Resistance Prediction
• If model tests are not available:
− ITTC for frictional resistance.
− Resistance standard series for wavemaking and form drag (residuary resistance).
− Pick the right standard series:
• Taylor series
• Holtrop
• Many, many others.
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20 February 2002 Resistance 61
Standard Series
• Start with a parent hull.
• Build several models by systematically varying key hull geometric parameters.
• Test, measure, and curve fit.
Parent hull form for Taylor standard series.
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20 February 2002 Resistance 62
Taylor Series – Typical Contours
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20 February 2002 Resistance 63
Holtrop’s Method
• See the UM notes and software implementation on the class web notes.
• AUTOHYDRO module of AUTOSHIP implements a number of standard series.
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20 February 2002 Resistance 64
Definition of Standard Speeds
• Maximum− Trial speed measured in calm water with maximum power output from the engines,
with a clean and freshly painted hull− Max speed declines with engine degradation, hull fouling, and sea state− Max power output from engines cannot be sustained for long periods without
suffering engine damage (redlining)• Sustained
− Speed with engines at 80% power and clean hull in calm water− Requirements usually state sustained vs. maximum speed− Can be maintained for long periods as necessary
• Cruise− Speed at which ship is expected to meet range requirement
• Most Economical− Speed and engine combination where fuel usage is least
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20 February 2002 Resistance 65
Effect of Length on Powering
• Hull Speed (Why does a longer ship need less power to make speed?)− Speed at which the ship overtakes its bow wave and “climbs the hill”− If vship is the ship velocity in fps, cwave is the celerity of the transverse wave train in
fps, and Lw is the length of the transverse wave in feet, then:
− By equating the wave length to the ship length (LS), and converting fps to knots, we have the equation for hull speed (VS):
• Since they have higher hull speeds, longer ships have lower wave resistance at the required speed, and thus need less power than their shorter counterparts
v cgL
Lship wavew
w= = =2
2 26π
.
V L LS w S= =2 261 688
1 34..
.
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20 February 2002 Resistance 66
Additional Reading
• 1.4.1 Ship Resistance and Propulsion Notes
• 1.4.2 Reliable Performance Prediction (D. M. MacPherson)
• 1.4.3 Practical Hydrodynamic Optimization of a Monohull(D. Hendrix et al)