How Fast Can Dumbo FlyHow fast can 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?

010203040506070

.35 meter

.7 meter

5 meter

10 meter

velocityRPM

No, while velocity goes up RPM goes down

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