Today, we watch boats rocking. The University of
Houston's College of Engineering presents this
series about the machines that make our
civilization run, and the people whose ingenuity
created them.
A listener wrote me with a
question about the movement of his WW-II troopship
at anchor. I didn't manage to answer his question,
but it set me to thinking about something we call a
metacenter. I was diverted into thinking
about how ships or boats rock back and forth. (So
I'm distractable.) Let's think about rocking.
Any floating body has a center of gravity through
which its weight acts. This is in the middle of the
hull, if the load is balanced. If the boat heels to
one side, then the force of gravity will tend to
keep it tipping, further and further.
But the boat does not normally capsize because
hulls are designed so buoyancy will oppose
tipping. Buoyancy acts through the center of
gravity, not of the ship, but of the displaced
water. We call that point the center of
buoyancy. Normally, buoyancy restores the boat
to vertical. But there's a catch.
Both gravity and buoyancy act vertically. If a boat
lists to one side, then the point where the
buoyancy force meets the centerline of the tipped
ship had better be above the ship's center of
gravity. That point is the metacenter.
And, if the metacenter should fall below
the ship's center of gravity, it'll capsize. And
that's were rocking comes in.
A well designed ship bobs back and forth. The
larger it is, the slower it rocks. However, we need
to watch the metacenter. The center of gravity
should be as low as possible and the center of
buoyancy should be high. A racing sailboat manages
that by having a fairly shallow hull with a deep,
heavy keel. It's very hard to tip over; it can heel
until its sails almost touch the water.
After a rich haul of crabs, Alaskan crab boats
sometimes stack too many heavy crab pots on their
decks. That raises the center of gravity without
significantly changing the center of buoyancy. The
result? The metacenter is now below the center of
gravity, and many such boats have abruptly capsized
without giving time for the crew to get out or even
to send a distress signal.
These same instabilities would be a problem for
dirigibles and hot air balloons. However, they
normally have very low centers of gravity. Still,
just imagine a balloon with the gondola on top. In
an airplane, these problems evaporate since
buoyancy is negligible in comparison with forces of
lift, drag, and thrust.
When we swim, our lungs are high in our bodies, so
our center of gravity is relatively low. But a
surfer's center of gravity is far above the
metacenter. He's unstable, and constantly has to
re-position his center of gravity by leaning right
or left.
I suppose these aren't things we incline to think
about on our summer vacations. And yet, I find
metacentric stability is no less a part of nature's
rich texture than the blue sky above, or cool water
about us. Now if I can only figure out why that
troopship moved the way it did ...
I'm John Lienhard, at the University of Houston,
where we're interested in the way inventive minds
work.
(Theme music)
H. W. King, C. O. Wisler, and J. G. Woodburn,
Hydraulics. New York: John Wiley & Sons,
Inc. 1948. Section 36.
I am grateful to Mechanical Engineering colleague
Ralph Metcalfe, and to Edward Morrison for their
counsel on this episode. William L. Howard posed
the still-unresolved question of the motion of his
old troopship. And Edward Morrison adds a
fascinating codicil. When the Battleship
Texas was modified in 1925-27 its
metacentric height (the distance between G
and M was increased fom 4.5 feet to 10 feet. The
unexpected result of the increased stability was
difficulty in maneuvering.
