1. Resistance and Powering of Ships

2. Considerations Required Power Select Power Plant
Determine amount of FO storage
KG Calculation

3. 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

4. Complete Physical Equation
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

5. 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

6. 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

7. Wave Patterns & Eddy Making

8. Resistance Equation Rewritten:
Froude Number – associated with wave making resistance
Reynolds Number – frictional resistance
Resistance coefficient uses wetted surface instead of length

9. 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

10. 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

11. 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

12. 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 = / (log10Rn-2)2 (ITTC 1957)

13. Correlation Allowance
Not exact
Additive to water resistance coefficients
Accounts for air, hull roughness, missing hull appendages
Use ITTC 1957 equation

14. Coefficients Dimensionless Divide each term by ½ ρSV2
CT = CF + CR + CA

15. Expanding Model Resistance to the Ship
Tow model at the corresponding speed VM = VS / √λ and measure model towing force or total model resistance (RTM)
Calculate the model’s total resistance coefficient CTM = RTM/1/2ρMSMVM2
Calculate model’s Reynold’s number RnM = VMLM / νM and model’s frictional resistance coefficient CFM = f(RnM) (ITTC equation)
Calculate model’s residuary resistance coefficient CRM by subtraction
According to law of comparison, CR of the ship equals that of the model CRS = CRM
Calculate ship’s Reynold’s number (RnS) and ship frictional resistance coefficient (CFS), using ITTC equation
Calculate ship total resistance CTS = CFS + CRS + CA
Calculate ship total resistance RTS = CTS(1/2 ρS SS VS2)

16. 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”

17. 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