40
METACENTRIC
HEIGHT
OF
A
CATAMARAN
164
40
Metacentric
Height
of
a
Catamaran
Consider
the
roll
stability
of
a
catamaran
described
as
follows:
total
beam
is
6
b
, where
b
is
the
beam
of
each
hull,
the
draft
is
T
,
and
each
hull
is
rectangular
in
crosssection.
1.
What
is
the
distance
KM
for
this
section,
at
small
roll
angles?
You
may
approximate
the
area
of
the
”buoyancy
wedges”
as
the
mean
height
times
the
width.
The
differential
moment
is
as
follows:
5
5
b
2
θ
×
dM
= 2
×
b
×
ρg
dx,
2
2
where
the
terms
separated
by
the
×
symbol
are
for:
two
wedges,
the
area
enclosed
in
each
wedge
(approximation),
the
moment
arm
of
each
wedge,
density
and
gravity
and
the
differential
length.
We
know
that
ρgd
∇
(
KM
)
θ
=
dM
,
which
leads
directly
to
25
b
2
KM
=
.
4
T
There
is
an
additional
term
T/
2
(as
in
the
case
of
monohulls)
but
this
is
very
small
by
comparison
for
a
catamaran.
2.
What
is
KM
for
a
single
block
of
draft
T
and
beam
2
b
?
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 Spring '05
 GeorgeKocur
 Buoyancy, Ship construction, Metacentric height, righting moment, Inclining test

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