Resistance and Powering of
Ships
Considerations
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Required Power
Select Power Plant
Determine amount of FO storage
KG Calculation
Power = Resistance * Speed
• RT = RF + RR
• RT = Total Resistance
• RF = Frictional Resistance
– Boundary Layer
• RR = Residuary Resistance
– Wave Making Resistance
– Eddy Making Resistance
– Air Resistance
Complete Physical Equation
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R = f( L, V, ρ, ν, g )
L – Length on waterline
V – Velocity
ρ – mass density of water
ν – viscosity of water
g – gravitational acceleration
Froude
• Model testing (1867)
• 3’, 6’ 12’ models towed in open water
• Observed that wave patterns related to
ship resistance
• Similar regardless of model size
• Similar to full size ship at corresponding
speed
• Speed length ratio V/√L
Laws of Comparison
• Model Test Conducted
• Measured resistances must be expanded to
their corresponding resistances of the full scale
ship corresponding to chosen model speeds
• Large # of variables, extensive testing
• Need to reduce the number of quantities to be
examined by use of “dimensional analysis,”
regrouping of variables
Wave Patterns & Eddy Making
Resistance Equation
Rewritten:
 VL V 
R
CT  1
 f ,
  f  Re,Fr 
2

Lg 
2  SV

Froude Number – associated with wave making resistance
Reynolds Number – frictional resistance
Resistance coefficient uses wetted surface instead of length
Geometric Similarity
λ = Ls/LM, BS/BM, Ts/ TM, …
FnS = FnM
( V / √gL)S = (V / √gL)M
VS/VM = √gSLS / √gMLM = √LS / √LM = √λ
Therefore the corresponding model speed is:
VM = VS / √λ
What about Reynold’s Number?
RnS = RnM
( VL / ν )S = ( VL / ν )M
VS/VM = (LM/Ls)(νS/νM)
If we assume the viscosities of the liquids are nearly
equal…
Vs / VM = LM / LS = 1 / λ
Or
VM = VS λ
This requires model speed to be greater than the ship
speed, test at Froude Speed
Example
20’ model of 720’ ship
λ = 720 / 20 = 36
If model is tested at Reynold’s Speed,
assume ship speed to be 24 kts
VM = (24)(36) = 864 kts
What about Froude speed?
VM = 24 / √36 = 4 kts
How can both equations be satisfied?
2 components – RF = frictional resistance, RR =
residuary resistance
Model testing measures RT
Froude Number is used to scale RR
Reynolds Number is used to predict RF
Studies done towing flat plates, equating surface
areas
CF = 0.075 / (log10Rn-2)2 (ITTC 1957)
Correlation Allowance
• Not exact
• Additive to water resistance coefficients
• Accounts for air, hull roughness, missing
hull appendages
• Use ITTC 1957 equation
Coefficients
Dimensionless
Divide each term by ½ ρSV2
CT = CF + CR + CA
Expanding Model Resistance to the Ship
1. Tow model at the corresponding speed VM = VS / √λ and measure model
towing force or total model resistance (RTM)
2. Calculate the model’s total resistance coefficient CTM = RTM/1/2ρMSMVM2
3. Calculate model’s Reynold’s number RnM = VMLM / νM and model’s
frictional resistance coefficient CFM = f(RnM) (ITTC equation)
4. Calculate model’s residuary resistance coefficient CRM by subtraction
5. According to law of comparison, CR of the ship equals that of the model
CRS = CRM
6. Calculate ship’s Reynold’s number (RnS) and ship frictional resistance
coefficient (CFS), using ITTC equation
7. Calculate ship total resistance CTS = CFS + CRS + CA
8. Calculate ship total resistance RTS = CTS(1/2 ρS SS VS2)
Speed Length Ratio
• Wave making resistance
limits ship speed
• Amplitude of waves is
function of energy
expended to generate
them
• Critical speed length ratio
VS/√LS = 1.34
• When a surface ship
attempts to exceed this
speed, “climbing a hill of
water”
Bulbous Bows
• D.W. Taylor experiments with bulbous bows at
higher V/√L range from 0.9 to 1.9 and showed
reduced resistance due to a newly created
pressure pattern in area of bow wave (1907)
• T. Inui’s (1962) research showed reduction in
resistance due to wave cancellation and speed
augmentation at lower Froude numbers
• Other research indicated an alteration in flow
characteristics around bow and along the bottom
of the bulbous form is the source of the
reduction