Transcript How fast can Dumbo Fly?

How
Fastfast
Cancan
Dumbo
Fly
How
Dumbo
Fly?
By
Randy Rogers
Physiologists have determined that a
small percent of the general population
will barf if subjected to 1.5 G’s 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 G’s. This is considered
the safe limit of G forces in a spinning
mode.
Should we subject an average patron to 1.5 G’s 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!
We want this
Not this!
So how can we determine the
maximum speed to spin the
Dumbo ride without causing any
of the aforementioned
phenomena?
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
If gravity is one G and the maximum force we want is
1.414 G’s 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 G’s
Therefore how fast can we spin Dumbo before we
exceed one G of centrifugal force?
We know that the formula for centrifugal force is:
F=m v2/r
Since force of gravity = 9.8m
9.8m= m v2/r
or
9.8 = v2/r
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
v2=3.46
v=1.86m/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!
On the real Dumbo ride we would have a radius of 10 meters
9.8 = v2/r
9.8 = v2/10
v2=98
v=9.9 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
Is it proportional?
• If you calculate
max speed for a
model, will the
max speed be the
same for the full
sized ride?
velocity
RPM
er
et
m
10 ter
e
5 m eter
m r
.7 ete
m
.35
No, while velocity goes up
RPM goes down
70
60
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40
30
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10
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