4.3.1 The scaling factors necessary for Froude
scaling were developed in the previous section. These scaling factors
are summarized in table 4.2. The magnitude of prototype parameters
are obtained by multiplying the magnitude of the model parameter by
the appropriate scale factor. Or inversely, the magnitude of model
parameters can be obtained by dividing the magnitude of the prototype
parameter by the scale factor.
Table 4.2 Scaling Factors for
Free-Fall Lifeboats
|
Symbol
|
Parameter
|
Units
|
| S
|
General Length Terms
|
λ
|
| m
|
Mass of the Lifeboat
|
λ3
|
| ρ
|
Fluid Mass Density
|
l
|
|
υ
|
Fluid Kinematic Viscosity
|
l
|
| ν
|
Velocity of the Lifeboat CG
|
λ1/2
|
| a
|
Acceleration of the Lifeboat
CG
|
l
|
| ω
|
Angular Velocity of Lifeboat
|
λ1/2
|
| α
|
Angular Acceleration of
Lifeboat
|
l
|
| g
|
Gravitational
Acceleration
|
l
|
| I
|
Lifeboat Second Moment
of Mass
|
λ5
|
| t
|
Time
|
λ1/2
|
4.3.2 To demonstrate the use of the scaling factors,
consider the design of a lifeboat that is 10 meters in length and
weighs 11.5 tonnes. These and other pertinent parameters of this lifeboat
are summarized in the second column of Table 4.3. The parameters shown
do not relate to any current lifeboat design. They are being used
here only for demonstration of scaling principles. Let us also assume
the naval architect wants to build a 1:5 scale model of this lifeboat
to evaluate its performance.
The scaling factors used to convert the full-scale parameters
to equivalent model parameters are presented in the third column of
the table. The resulting scaled characteristics of the model are presented
in the fourth column of table 4.3.
Table 4.3 Scale Model Equivalent
Dimensions and Launch Characteristics
|
Lifeboat or Launch Parameter
|
Full-Scale Characteristics
|
Scaling Factors (Full to Model)
|
Model Characteristics
|
| Boat Length
|
10.0 m
|
0.2
|
2.00 m
|
| Beam
|
3.5 m
|
0.2
|
0.70 m
|
| Boat Height
|
3.4 m
|
0.2
|
0.68 m
|
| Boat Weight
|
11.5 t
|
0.008
|
92.00 kg
|
| LCG
|
4.8 m
|
0.2
|
0.96 m
|
| VCG
|
1.7 m
|
0.2
|
0.34 m
|
| Second Moment of Mass
|
42,000 kg-m2
|
0.00032
|
13.44 kg-m2
|
| Launch Height
|
22 m
|
0.2
|
4.40 m
|
| Launch Angle
|
35°
|
1.0
|
35°
|
| Ramp Length
|
12.0 m
|
0.2
|
2.40 m
|
4.3.3 Normally the location of the CG and the
second moment of mass are calculated when the lifeboat is being designed.
The launch height is the design free-fall height and the launch angle
is the intended angle of the launch ramp. After the model has been
built, the designer should verify that the important characteristics
are scaled properly and that geometric similarity of the hull has
been maintained. The second moment of mass of the model can be measured
using the procedure presented in the following section. If necessary,
the second moment of mass of the full-scale lifeboat can be measured
using this same procedure after it has been constructed.
Table 4.4 Full-Scale Equivalent of
Model Data
|
Lifeboat or Launch Parameter
|
Measured Model Data
|
Scaling Factors (Model to Full)
|
Full-Scale Equivalent
|
| Maximum Acceleration
|
11.0 g's
|
1.0
|
11.0 g's
|
| Water Entry Velocity
|
7.5 m/s
|
2.236
|
16.77 m/s
|
| Horizontal Position
|
3.3 m
|
5.0
|
16.50 m
|
| Water Entry Angle
|
55°
|
1.0
|
55°
|
| Time of Free-Fall
|
0.95 s
|
2.236
|
2.12 s
|
4.3.4 Suppose that during the tests with this
lifeboat model the data shown in the second column of table 4.4 were
obtained. To find the full-scale equivalent of these data, the scaling
factors shown in the third column are used. The resulting full-scale
equivalent of these data are presented in the last column of table
4.4. If the model was properly scaled, and the tests were carefully
conducted, these are the data that would have been obtained if the
same tests had been conducted using the full-scale lifeboat. If the
performance is not acceptable, adjustments and modifications can be
made before the full-scale lifeboat is constructed.