Part B | 12.4
312 Part B Autonomous Ocean Vehicles, Subsystems and Control
10
–6
10
–2
10
–4
Profiling gliders
b = M
1/3
Hang
gliders
General
aviation
Transports
Sailplanes
MPA
Birds
Pferanodon
Insects
Huming birds
Bats
Zinonia
1
1 0
2
10
4
10
6
a) Wing span S (m)
10
2
10
1
10
0
10
–1
10
–2
10
–3
10
–6
10
–2
10
–4
Profiling gliders
A = M
2/3
Hang gliders
General
aviation
Transports
Sailplanes
MPA
M = 15 S
3/2
Birds
Pferanodon
Insects
Huming birds
Bats
Zinonia
1
1 0
2
10
4
10
6
b) Wing area A (m
2
)
Loaded mass M (kg)
Loaded mass M (kg)
10
3
10
2
10
1
10
0
10
–1
10
–2
10
–3
10
–4
Fig. 12.10a,b Characteristic wing dimensions as a function of loaded mass. (a) Scaling of wingspan as a function of
loaded mass; (b) wing area as a function of loaded mass for natural and man-made fliers (after [12.12, 18])
in horizontal transport economy. As a benchmark in underwater gliders, Seaglider has an N A D 21:1 [12.3].
However, the smallest N A values are associated with flying wing and blended wing/body geometries, such as
utilized by birds, for which typically N A 2:2 to 2:4.
The other benefit derived from concentrating the vehicle volume in the wing itself is a large wing area that
reduces the magnitudes of C L and the associated induced
drag (the largest component of the drag at minimum
E e ). Equation (12.13) indicates that specific energy consumption grows as C
=4
L . However, increasing wing area
indefinitely to achieve a low C L becomes mutually exclusive with high aspect ratio, N R . In (12.13), the factor
C
=2
L =N
1=2
R
indicates that a large N R exerts a greater
reduction in E e than does a proportionally smaller C L ,
subject to the structural limits mentioned above.
Another issue with concentrating vehicle volume
in the wing is the effect on the profile drag shape
factor K 0 . Shape efficiency comparisons based on K 0
between a 2-D flying wing and a three-dimensional
(3-D) winged body of revolution should be based on the
same vehicle volume, V 0 . Considering both shapes are
streamlined bodies, K 0 scales in proportion to the wetted surface area relative to volume as A t =V
2=3
0 . Taking
an ellipse as the canonical cross section for both 2-D
and 3-D shapes, and following the assumption taken
in [12.23] and [12.24] that the skin friction per unit area
is the same for each shape, the shape factor ratio at con-
312 Part B Autonomous Ocean Vehicles, Subsystems and Control
10
–6
10
–2
10
–4
Profiling gliders
b = M
1/3
Hang
gliders
General
aviation
Transports
Sailplanes
MPA
Birds
Pferanodon
Insects
Huming birds
Bats
Zinonia
1
1 0
2
10
4
10
6
a) Wing span S (m)
10
2
10
1
10
0
10
–1
10
–2
10
–3
10
–6
10
–2
10
–4
Profiling gliders
A = M
2/3
Hang gliders
General
aviation
Transports
Sailplanes
MPA
M = 15 S
3/2
Birds
Pferanodon
Insects
Huming birds
Bats
Zinonia
1
1 0
2
10
4
10
6
b) Wing area A (m
2
)
Loaded mass M (kg)
Loaded mass M (kg)
10
3
10
2
10
1
10
0
10
–1
10
–2
10
–3
10
–4
Fig. 12.10a,b Characteristic wing dimensions as a function of loaded mass. (a) Scaling of wingspan as a function of
loaded mass; (b) wing area as a function of loaded mass for natural and man-made fliers (after [12.12, 18])
in horizontal transport economy. As a benchmark in underwater gliders, Seaglider has an N A D 21:1 [12.3].
However, the smallest N A values are associated with flying wing and blended wing/body geometries, such as
utilized by birds, for which typically N A 2:2 to 2:4.
The other benefit derived from concentrating the vehicle volume in the wing itself is a large wing area that
reduces the magnitudes of C L and the associated induced
drag (the largest component of the drag at minimum
E e ). Equation (12.13) indicates that specific energy consumption grows as C
=4
L . However, increasing wing area
indefinitely to achieve a low C L becomes mutually exclusive with high aspect ratio, N R . In (12.13), the factor
C
=2
L =N
1=2
R
indicates that a large N R exerts a greater
reduction in E e than does a proportionally smaller C L ,
subject to the structural limits mentioned above.
Another issue with concentrating vehicle volume
in the wing is the effect on the profile drag shape
factor K 0 . Shape efficiency comparisons based on K 0
between a 2-D flying wing and a three-dimensional
(3-D) winged body of revolution should be based on the
same vehicle volume, V 0 . Considering both shapes are
streamlined bodies, K 0 scales in proportion to the wetted surface area relative to volume as A t =V
2=3
0 . Taking
an ellipse as the canonical cross section for both 2-D
and 3-D shapes, and following the assumption taken
in [12.23] and [12.24] that the skin friction per unit area
is the same for each shape, the shape factor ratio at con-