How Fast Can Dumbo Fly

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How Fast Can Dumbo Fly
How fast can Dumbo Fly?
By Randy Rogers
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(No Transcript)
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Physiologists have determined that a small
percent of the general population will barf if
subjected to 1.5 Gs in a spinning mode. Yet, to
make the ride at Disneyland more fun for the
younger crowd we want to spin the ride as fast as
possible without subjecting the riders to more
than 1.414 Gs. This is considered the safe
limit of G forces in a spinning mode.
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Should we subject an average patron to 1.5 Gs or
more he/she will do one of the following
BARF PUKE BLOW LUNCH TOSS HIS COOKIES DRIVE THE
PORCELIN BUS DO THE TECHNICOLOR YAWN HAIL TO KING
RALPH REVISIT HIS BREAKFAST SET FREE HIS
INTESTINES
All of the above is not good!
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We want this
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Not this!
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So how can we determine the maximum speed to spin
the Dumbo ride without causing any of the
aforementioned phenomena?
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First Let us determine what forces would be
acting upon the Dumbo adventurer when riding our
famous elephant.
Why is this diagram correct?
Centrifugal force is horizontal while gravity is
vertical. They must be equal for resultant force
to be 1.414 Gs
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If gravity is one G and the maximum force we want
is 1.414 Gs then we must limit centrifugal force
to one G. Note It is amazing that our
physiologists stated the safe G force to be 1.414
Gs
Therefore how fast can we spin Dumbo before we
exceed one G of centrifugal force? We know that
the formula for centrifugal force is
Fm v2/r Since force of gravity 9.8m 9.8m m
v2/r or 9.8 v2/r
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Since we also know that the force of gravity on
one kilogram is 9.8 Newtons then all we need to
do is solve for V if we know r. Using our model
we will set r at .3535 meters.  9.8 v2/.3535
v23.46 v1.86m/sec  With a radius of .35
meter, circumference 2.22meters and a speed of
1.86m/sec  1.86m/sec / 2.22 m/rev .84
rev/sec or 11.9 sec/10 rev or approx 50 rpm!
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On the real Dumbo ride we would have a radius of
10 meters  9.8 v2/r 9.8 v2/10 v298 v9.9
m/sec  With a radius of 10 meter, circumference
62.8 meters and a speed of 9.9 m/sec  9.9 m/sec /
62.8 m/rev .16 rev/sec or approx 9.5 rpm! And
that is as fast as Dumbo can fly!
Click to repeat calculations
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Is it proportional?

• If you calculate max speed for a model, will the
  max speed be the same for the full sized ride?

No, while velocity goes up RPM goes down
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Information on the real Dumbo ride
http//www.anycities.com/user1/disneyworld/disney-
world-orlando-magic-kingdom-fantasyland-4.html