2.016 HW #4
Out: October 4, 2005
Due: October 18, 2005
1)
A sphere of volume
V
in a fluid of density
ρ
is located at a point (0,
L
, 0) with respect
to a certain coordinate system.
In terms of this coordinate system
, identify whether
each of the 6x6 added mass coefficients are zero (0), or nonzero (x) (do not work out
).
x
y
z
(
)
any values
0, L, 0
2) A positively buoyant cone with length L, and maximum radius R
o
is placed with the
apex at the origin of a coordinate system as shown below.
z
y
a) Calculate the center of buoyancy for the cone.
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View Full Documentb) Determine which added mass coefficients are zero or nonzero. You can fill out a
6x6 matrix with X for nonzero and 0 for zero.
c)
Use Strip Theory to calculate M
55
, M
11
, M
44
, M
66
, M
51
, and M
22
. Hint: first
consider any symmetry that might make these calculations easier.
d)
Write the equation of motion of the cone in roll, and calculate the natural
frequency.
3)
A new class of submarine can be modeled by a cylinder of length
L
and radius
R
, with
a vertical sail and horizontal elliptical wings of major and minor axis radii
a
and
b
and length
h
, as shown.
Assuming that these main members are slender so that their longitudinal added mass may
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 Fall '05
 AlexandraTechet
 #, Fundamental physics concepts, 2.5ft, 6 degree

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