






Basic Roller
Coaster Physics
Roller coasters
work on the basic principle of energy conservation and conversion.
What this means is that, technically, a roller coaster train has the
exact same amount of energy throughout its cycle, but just in
different forms.
The two main forms
of energy are potential and kinetic. Potential energy is dependent on
the mass of the train, its height above the ground, and the
acceleration of gravity. This relationship means that the higher
Superman's train is, the more potential energy it has. It also means
that the more mass it has (more people!), the more potential energy
it has, as well.
Kinetic energy is
energy in motion and depends on the mass of the train and its velocity.
Using these
concepts, Superman's train can then be described by gaining potential
energy as it ascends the lift hill. Because, as stated, the amount of
energy is conserved, this potential energy must be coming from
somewhere. The answer lies in the lift motor. The power (and thus,
work) delivered by the motor is converted to potential energy in the
train. (Note: Because the train is moving up the lift, too, it has a
small amount of kinetic energy as well.)
So once Superman's
train reaches the 208foot apex, it has a great amount of potential
energy and a little bit of kinetic energy. As it rounds the top and
begins to descend, the potential energy begins to convert to kinetic
energy (because the height decreases), causing the increase in
velocity. When the train reaches the bottom of the first drop, its
kinetic energy is at its maximum and there is little or no potential
energy (actually, getting more complicated, there would be a negative
amount of potential energy due to the underground tunnel  the height
would be negative).
This conversion
between kinetic and potential energy continues throughout the cycle
and is what allows Superman to complete the course.
But if the amount
of energy in Superman's train is supposed to be constant throughout
the cycle, then why is the train obviously slower and can only go
over only small hills by the end? The answer is simple: Some of the
energy is also converted into energy lost by friction and drag. Every
joint that moves and every wheel that touches the track causes a loss
of energy through friction. And because Superman isn't 100%
aerodynamically sound (especially with 36 riders with hands up), some
energy is lost through wind resistance (drag). This explains why each
hill is successively smaller and Superman's average speed slowly decreases.
Kinetic
Energy / Potential Energy
/ Energy lost
from Friction & Drag
This explanation
of energy provides answers as to how a 27,000pound train can so
easily climb a hill, but it does not explain why. This answer lies in
the principle of intertia. Inertia is the tendancy of every object in
space to continue in a straightline path unless acted upon by a
force. In the case of Superman, these forces include gravity and the
track "pushing" on the wheels to force the train in a
certain direction. 









More Technically
E_{TOTAL}
= E_{KINETIC}
+ E_{POTENTIAL}
+ E_{FRICTION}
E = ^{1}/_{2}mv^{2}
+ mgh + umg x
cos(a) x d at any point along the circuit
where
m = mass of
the train, v = velocity of the train, g = acceleration
of gravity,
h = height
above the ground, u = coefficient of friction, a =
angle of the train,
d = change
in distance
m = 27,000 lbs.
g = 32.17 ft/s^{2}
u is
dependent on the weather conditions, humidity, etc.
For example,
assuming the train is traveling at 7 mph as it rounds the top of the
first hill (reasonable) and that it does not lose any energy through
friction on the first drop (unreasonable, but simple), the
theoretical speed can be found at the bottom of the first hill.
E_{TO}_{P}
= E_{KINETIC}
+ E_{POTENTIAL}
E_{BOTTOM}
= E_{KINETIC}
+ E_{POTENTIAL}
+ E_{FRICTION}
Because the energy
has to remain constant, setting these equal, we get
E_{KINETICTop}
+ E_{POTENTIAL}_{Top} =_{ }E_{KINETICB}_{ottom}
+ E_{POTENTIALBottom}
+ E_{FRICTION}
^{1}/_{2}mv^{2
}+
mgh
= ^{1}/_{2}mv^{2 }+
mgh
+ 0
First, we must
convert the 7.00 mph to ft/s so that all units are consistent (the
height is in feet and the acceleration of gravity  32.17  is in feet/second^{2}).
(7.00 mi/hr) x
(5,280 ft/mi) x (1 hr/3600 s) = 10.267 ft/s
Now, we can plug
the given values into the above equation to find v.
(^{1}/_{2})(27,000)(10.267)^{2}
+ (27,000)(32.17)(221) = (^{1}/_{2})(27,000)v^{2}
+ (27,000)(32.17)(0)
Factoring out the
27,000 lbs from each term and solving, we get:
52.702 + 7,109.57
= ^{1}/_{2}v^{2}
7,162.272 = ^{1}/_{2}v^{2}
v^{2}
= 14,324.54
v = 119.69 ft/s
(119.69 ft/s) x (1
mi/5280 ft) x (3600 s/hr) = 81.6 mph
81.6 mph is
clearly not an unreasonable answer, as this is assuming an empty
train (27,000 lbs.) with no friction. The actual speed of an empty
train hovers around 77mph (friction accounts for the difference), but
the train can achieve this higher speed with people in it (making the
actual weight as high as 34,000 pounds).











The Forces on Riders
There are three
main types of forces felt by riders while on Superman. They are
vertical G's, lateral G's, and longitudinal G's. As described on the Forces
page, vertical G's are what cause riders to feel as if they are
coming out of their seats (or, just the opposite  being pushed in),
lateral G's cause riders to move side to side, and longitudinal G's
cause riders to move forward or back in their seats.
The root of these
forces is the basic concept of intertia. As stated, an object in
motion tends to continue in a straightline path unless an outside
force is applied. In addition to this helping the train to move along
the track, it also affects the riders in the train.
As for the
vertical G's, these are most noticeable at the tops and bottoms of
inline hills (when the other two types of forces are minimal). As
the train rounds the top of the second hill, for example, the train
is being pulled over the top by the track, however, the riders'
bodies want to continue upward (or at least in a parabolic projectile
motion path). This is the cause of the outofseat, airtime feeling.
The opposite effect is at the bottom of a hill when the train begins
moving upward and the riders' bodies want to continue downward or
straight ahead. The force of the train pushing up on the body is what
makes riders feel heavier.
The same goes for
the other two forces: Lateral and longitudinal. In the case of the
former, the forces are felt as the train moves to the left or right
and the body wants to continue straight ahead. And in the case of
longitudinal forces, any change in speed will cause the body to move
forward or backward. 







