1 3. Resistance of a Ship 3.1 Model testing • Resistance of a ship: – Total resistance • V Speed of the ship • L Length of the ship • Density of the fluid • Kinematic viscosity of the fluid • g Acceleration of gravity ) , , , , ( g L V f R T ν ρ = ρ ν
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1
3. Resistance of a Ship3.1 Model testing
• Resistance of a ship:
– Total resistance
• V Speed of the ship
• L Length of the ship
• Density of the fluid
• Kinematic viscosity of the fluid
• g Acceleration of gravity
),,,,( gLVfRT νρ=
ρ
ν
2
3. Resistance of a Ship3.1 Model testing
• Dimensional analysis
– Total resistance coefficient
• Total resistance coefficient
(S = Wetted surface)
• Reynolds number
• Froude number
),( nnTT FRCC =
SV
RC T
T 22/1 ρ=
ν
VLRn =
gL
VFn =
3
• Equal non-dimensional numbers.
- Reynolds number: (same fluid)
- Froude number:
• Conclusion: it is impossible to satisfy simultaneously the
equality of Reynolds and Froude numbers.
• The model dimensions do not allow the equality of the
Reynolds number for model testing.
sm
smnn V
L
LVRR
ms=⇒=
ss
mmnn V
L
LVFF
ms=⇒=
3. Resistance of a Ship3.1 Model testing
Flow similarity
4
• Resistance force is measured at model scale (model) and
extrapolated for full scale (ship).
• Measurements are performed with the equality of the
Froude number at model and full scale (Froude scaling):
• is the scale factor.
• Model’s length is determined by the geometrical
properties of the towing tank.
sm VV 2/1−= α
ms LL /=α
3. Resistance of a Ship3.1 Model testing
Resistance tests
mL
5
• The length of the model should try to minimize the
difference in Reynolds number (maximum length) within
the limits imposed by the towing tank dimensions.
– The precision of the measurements increases with the
growth of the model.
– Model dimensions are limited by the depth (h) and
width (b) of the towing tank section to avoid a
significant influence of the bottom and side walls.
3. Resistance of a Ship3.1 Model testing
Resistance tests
6
• Typical model dimensions:
h: depth
b: width
Area of the model’s midsection < 1/200 bh
– With the reduction of the ship’s length it becomes
difficult to avoid a significant region of laminar flow.
• At full scale, the flow is nearly “fully-turbulent” (region of
laminar flow at the bow is negligible). Therefore, model
testing should avoid laminar flow.
hLm <
2/bLm <
3. Resistance of a Ship3.1 Model testing
Resistance tests
7
• For the typical Reynolds number of model testing (106 to
107), transition to turbulence must be stimulated:
– Trip wires, studs or roughness strips applied at the bow.
These devices introduce an added resistance that has to
be estimated to correct the measured resistance.
– Turbulence of the outer flow may be increased with the