Autonomous Sea Surface Vehicles 13.3 Naval Architecture of AUSV Design 327
Part B | 13.3
13.3 Naval Architecture of AUSV Design
This section will first define the general criteria used
to select a hull form as a function of operational speed
and size and then it will continue to describe in some
detail the hydrodynamic design and performance of
a new class of vehicles whose optimized design is
to become a reference for the next generation of autonomous unmanned surface vehicles for ocean and
coastal exploration.
13.3.1 Froude Number and Hull Typologies
Essential for selection of the hull form is the calculation of the relative speed of advance with respect to
a representative dimension (the length) and weight (displacement volume) of the hull.
In non-dimensional form these two parameters are
defined as the length Froude number Fr L and the volumetric Froude number Fr r
Fr L D
U
p
gL
; Fr r D
U
p gr 1=3 ;
(13.1)
where g is the acceleration of gravity, L is the submerged length of the hull, U, is the speed of the hull and
r is the hull displacement volume. The length Froude
number is often used to qualitatively discuss the speed
regime of a boat. From a purely physical point of view,
the Froude number is the ratio between inertial forces
due to the ship advancing at a certain speed U and the
gravitational force, which are responsible for the free
surface waves and the wave resistance. In fact, using
the dispersion relation valid for first-order plane progressive (airy) waves, it can be demonstrated that the
length-based Froude number is related to the ratio between the fundamental wavelength generated by the
hull and its own length.
If we approximate the length of a transverse wave
produced by a pressure region at the bow to that of
regular wave traveling with hull speed, we obtain the
following relation between the Froude number and the
relative wave length
2 D gT
2
! 2 D g
2
U 2 !
L
D 2Fr
2
L ; (13.2)
where in addition to the variables appearing in (13.1),
T is the period and is the length of the fundamental
transverse progressive wave.
Figure 13.5 compares the fundamental wavelengths
relative to the hull profile at four different Froude numbers representative of four different sailing regimes
and related hull types. In naval architecture, the length
Froude number is often used as an indication to select
the most suitable hull typology for the particular application, as it is graphically presented with the shaded
areas in Fig. 13.6. This is a preliminary distinction and
must correctly consider the volumetric Froude number,
especially to distinguish the regime of planing hulls
from that of semi-displacement hull forms. This will be
explained in more detail later on in this section. Slow
speed heavier displacement hull forms operate in the
lower Froude number range (Fig. 13.5a, upper panel),
at which the fundamental wave length is much lower
than the hull length and the resistance is dominated by
viscous effects (friction and form drag). The shape of
these types of hulls is optimized in order to reduce to
a minimum the frictional and form drag components.
Wavelength and wave resistance both increase with the
Froude number. Typically, at Fr D 0:25 the wave resistance and viscous resistance share the same relative
importance in the total resistance. For Fr D 0:4, the relative speed is representative of the limit speed for a fast
displacement hull. Most fast naval units (destroyers,
frigates) are at these Froude numbers. At this speed,
the hull is running on its own wave length (=L D 1).
Bulbous bows are very beneficial at these Froude numbers, since their generated waves can interfere directly
with the aft wave train (Fig. 13.5b, lower panel). At
Fr > 0:4, the fundamental wavelength is larger than the
hull length and the hull begins to severely squat and
trim down at the stern. The ship literally climbs up the
back of its own bow wave. At these speeds the flow
along the convex geometry of the hull bottom develops
large suction pressures that further increase the squat
and trim of the vessel. The hull resistance begins to
increase dramatically and becomes a practical barrier
to further increases in speed. The wave pattern generated by a displacement hull is, of course, more complex
as it derives from the continuously variable distribution
of dynamic pressure along the hull (which depends on
its shape), but to a first-order approximation, the final
transverse wave pattern can be thought as a superposition of a series of transverse wave trains, each one
generated at regions of the hull close to the free surface
with high pressure gradients.
A sketch of two transverse and divergent wave systems created at the bow and stern of a displacement hull
form (Fig. 13.7) is illustrative of the wave interference
effect. A solution to the complex free surface wave pattern was first attempted by Lord Kelvin and solved for
simple analytical hull shapes by Michell [13.17] and
later by Wigley [13.18]. These studies led the way to
the development of thin ship theory, which is the simplest theoretical or numerical method to predict ship
wave patterns, based on the assumption that the ship
Part B | 13.3
13.3 Naval Architecture of AUSV Design
This section will first define the general criteria used
to select a hull form as a function of operational speed
and size and then it will continue to describe in some
detail the hydrodynamic design and performance of
a new class of vehicles whose optimized design is
to become a reference for the next generation of autonomous unmanned surface vehicles for ocean and
coastal exploration.
13.3.1 Froude Number and Hull Typologies
Essential for selection of the hull form is the calculation of the relative speed of advance with respect to
a representative dimension (the length) and weight (displacement volume) of the hull.
In non-dimensional form these two parameters are
defined as the length Froude number Fr L and the volumetric Froude number Fr r
Fr L D
U
p
gL
; Fr r D
U
p gr 1=3 ;
(13.1)
where g is the acceleration of gravity, L is the submerged length of the hull, U, is the speed of the hull and
r is the hull displacement volume. The length Froude
number is often used to qualitatively discuss the speed
regime of a boat. From a purely physical point of view,
the Froude number is the ratio between inertial forces
due to the ship advancing at a certain speed U and the
gravitational force, which are responsible for the free
surface waves and the wave resistance. In fact, using
the dispersion relation valid for first-order plane progressive (airy) waves, it can be demonstrated that the
length-based Froude number is related to the ratio between the fundamental wavelength generated by the
hull and its own length.
If we approximate the length of a transverse wave
produced by a pressure region at the bow to that of
regular wave traveling with hull speed, we obtain the
following relation between the Froude number and the
relative wave length
2 D gT
2
! 2 D g
2
U 2 !
L
D 2Fr
2
L ; (13.2)
where in addition to the variables appearing in (13.1),
T is the period and is the length of the fundamental
transverse progressive wave.
Figure 13.5 compares the fundamental wavelengths
relative to the hull profile at four different Froude numbers representative of four different sailing regimes
and related hull types. In naval architecture, the length
Froude number is often used as an indication to select
the most suitable hull typology for the particular application, as it is graphically presented with the shaded
areas in Fig. 13.6. This is a preliminary distinction and
must correctly consider the volumetric Froude number,
especially to distinguish the regime of planing hulls
from that of semi-displacement hull forms. This will be
explained in more detail later on in this section. Slow
speed heavier displacement hull forms operate in the
lower Froude number range (Fig. 13.5a, upper panel),
at which the fundamental wave length is much lower
than the hull length and the resistance is dominated by
viscous effects (friction and form drag). The shape of
these types of hulls is optimized in order to reduce to
a minimum the frictional and form drag components.
Wavelength and wave resistance both increase with the
Froude number. Typically, at Fr D 0:25 the wave resistance and viscous resistance share the same relative
importance in the total resistance. For Fr D 0:4, the relative speed is representative of the limit speed for a fast
displacement hull. Most fast naval units (destroyers,
frigates) are at these Froude numbers. At this speed,
the hull is running on its own wave length (=L D 1).
Bulbous bows are very beneficial at these Froude numbers, since their generated waves can interfere directly
with the aft wave train (Fig. 13.5b, lower panel). At
Fr > 0:4, the fundamental wavelength is larger than the
hull length and the hull begins to severely squat and
trim down at the stern. The ship literally climbs up the
back of its own bow wave. At these speeds the flow
along the convex geometry of the hull bottom develops
large suction pressures that further increase the squat
and trim of the vessel. The hull resistance begins to
increase dramatically and becomes a practical barrier
to further increases in speed. The wave pattern generated by a displacement hull is, of course, more complex
as it derives from the continuously variable distribution
of dynamic pressure along the hull (which depends on
its shape), but to a first-order approximation, the final
transverse wave pattern can be thought as a superposition of a series of transverse wave trains, each one
generated at regions of the hull close to the free surface
with high pressure gradients.
A sketch of two transverse and divergent wave systems created at the bow and stern of a displacement hull
form (Fig. 13.7) is illustrative of the wave interference
effect. A solution to the complex free surface wave pattern was first attempted by Lord Kelvin and solved for
simple analytical hull shapes by Michell [13.17] and
later by Wigley [13.18]. These studies led the way to
the development of thin ship theory, which is the simplest theoretical or numerical method to predict ship
wave patterns, based on the assumption that the ship