Hydromechanics 7.1 Dimensional Analysis, Basic Estimation, and Model Testing 141
Part A | 7.1
Course
x Heading
y
F net
θ
α
F L
F D
V A
Apparent wind
a)
Course
x Heading
y
F net
θ
δ
β
β
ψ
90°– β
λ
F L
F AR
F AS
V S
V A
V t
Apparent wind
c)
b)
Fig. 7.15a–c Sailboat aerodynamic free body diagrams in the boat fixed frame. (a) The airfoil profile represents the wing
and ˛ is the angle of attack of the sail with respect to the apparent wind angle. (b) is the true wind direction, ˇ is the
apparent wind angle. (c) The x- and y-axes are the boat-fixed maneuvering coordinate system, the x-axis gives the heading
while the angle between course and heading is the leeway angle ; ı D .ˇ Â/ is the angle between the net aerodynamic
force F net and the side force F AS (after [7.25], courtesy of the Institute of Electrical and Electronics Engineers (IEEE))
–20
–10
0
10
20
C L
α
3
2
1
0
–1
–2
–3
–10
–15
–5 0
5 10 15
C D
α
0.02
0.015
0.01
0.005
0
Fig. 7.16 Sailboat wing aerodynamic
characteristics
3. The keel:
Here, the keel will be a thin flat plate with a span
of S k D 1:2 m and a chord of l k D 1:5 m. In order
to keep the lateral (transverse) component of the
aerodynamic forces F AS from pushing the yacht off
course, the keel must have a small leeway angle
(angle of attack) with respect to the boat’s course
(Fig. 7.17). Assuming F AS is balanced entirely by
the lift on the keel F HS – calculate .
Solution 7.6
1. The hullform:
a) The model and prototype sailboats are geometrically similar:
i. The missing prototype values have been included in Table 7.4.
ii. The prototype will be operated at Fr D
0:375, where the relevant length scale is
taken as the length on the waterline, LWL
(Table 7.2). What is the design speed V S of
the prototype?
V S D F
p
gLWL p D 3:51 m s
1
Table 7.4 Model and prototype dimensions
Quantity
Model Prototype
Length overall (LOA) [m]
2:47
11
Length on waterline (LWL) [m]
2:00
LWL p D 8:91
Wetted surface area [m 2 ]
0:965
Sw p D 19:1
Part A | 7.1
Course
x Heading
y
F net
θ
α
F L
F D
V A
Apparent wind
a)
Course
x Heading
y
F net
θ
δ
β
β
ψ
90°– β
λ
F L
F AR
F AS
V S
V A
V t
Apparent wind
c)
b)
Fig. 7.15a–c Sailboat aerodynamic free body diagrams in the boat fixed frame. (a) The airfoil profile represents the wing
and ˛ is the angle of attack of the sail with respect to the apparent wind angle. (b) is the true wind direction, ˇ is the
apparent wind angle. (c) The x- and y-axes are the boat-fixed maneuvering coordinate system, the x-axis gives the heading
while the angle between course and heading is the leeway angle ; ı D .ˇ Â/ is the angle between the net aerodynamic
force F net and the side force F AS (after [7.25], courtesy of the Institute of Electrical and Electronics Engineers (IEEE))
–20
–10
0
10
20
C L
α
3
2
1
0
–1
–2
–3
–10
–15
–5 0
5 10 15
C D
α
0.02
0.015
0.01
0.005
0
Fig. 7.16 Sailboat wing aerodynamic
characteristics
3. The keel:
Here, the keel will be a thin flat plate with a span
of S k D 1:2 m and a chord of l k D 1:5 m. In order
to keep the lateral (transverse) component of the
aerodynamic forces F AS from pushing the yacht off
course, the keel must have a small leeway angle
(angle of attack) with respect to the boat’s course
(Fig. 7.17). Assuming F AS is balanced entirely by
the lift on the keel F HS – calculate .
Solution 7.6
1. The hullform:
a) The model and prototype sailboats are geometrically similar:
i. The missing prototype values have been included in Table 7.4.
ii. The prototype will be operated at Fr D
0:375, where the relevant length scale is
taken as the length on the waterline, LWL
(Table 7.2). What is the design speed V S of
the prototype?
V S D F
p
gLWL p D 3:51 m s
1
Table 7.4 Model and prototype dimensions
Quantity
Model Prototype
Length overall (LOA) [m]
2:47
11
Length on waterline (LWL) [m]
2:00
LWL p D 8:91
Wetted surface area [m 2 ]
0:965
Sw p D 19:1