Roller Coaster
G-Forces
A GIF Animation
Roller coaster rides are notorious for creating accelerations and
g-forces which are capable of transforming stomach contents
into airborne projectiles. As a rider starts the descent down the
first drop, she begins a one-minute adventure filled with various
sensations of weightlessness, heaviness, and jerkiness. The
part of the rides which are most responsible for these sensations of
weightlessness and heaviness are the clothoid loops. The
explanation for the various sensations experienced on a roller
coaster loop are associated with Newton's laws of motion and the
physics of circular motion.
A clothoid loop is approximately the shape of a circle (in
actuality, it is considered to be a section of a cornu spiral
having a constantly changing radius). A coaster rider is continuously
altering her direction of motion while moving through the loop; at
all times, the direction of motion could be described as being
tangent to the loop. This change in direction is caused by the
presence of unbalanced forces and results in an acceleration. Not
only is there an acceleration, the magnitude and direction of the
acceleration is continuously changing. Within a one second time
frame, the riders may experience accelerations of 20 m/s/s downwards
to 20 m/s/s upwards; such drastic changes in acceleration normally
occur as the rider moves from the top of the loop to the bottom of
the loop. These drastic changes in accelerations are the cause of
much of the thrill (and the occasionally dizziness) experienced by
coaster riders.
To understand the feelings of weightlessness and heaviness
experienced while riding through a loop, it is important to think
about the forces acting upon the riders. To simplify the discussion,
we will assume that there are negligible amounts of air resistance
acting upon the riders. Thus, the only forces exerted upon the riders
are the force of gravity and the normal force (the force of the seat
pushing up on the rider). The force of gravity is at all times
directed downwards and the normal force is at all times directed
perpendicular to the seat of the car. Since the orientation of the
car on the track is continuously changing, the normal force is
continously changing its direction. The magnitude and direction of
these two forces during the motion through the loop are depicted in
the animation below.
In order for an object to move through a circle, it is necessary
that there be a net inward force acting upon the rider. This
is commonly referred to as the centripetal force requirement. Thus,
the net force acting upon the rider is always directed inwards
(towards the center of the circle). Since the net force is the vector
sum of all the forces, the head-to-tail addition of the normal force
and the gravity force should sum to a resultant force which is
directed inward. The diagram below depicts the free-body diagrams for
a rider at four locations along the loop. The diagram also shows that
the vector sum of the two forces (i.e., the net force) points towards
the center of the loop for each of the locations.
Feelings of weightlessness and heaviness are associated with the
normal force; they have little to do with the force of gravity. A
person who feels weightless has not lost weight; the force of gravity
acting upon the person is the same magnitude as it always is. Witness
in the animation above that the force of gravity is everywhere the
same. The normal force however has a small magnitude at the top of
the loop (where the rider often feels weightless) and a large
magnitude at the bottom of the loop (where the rider often feels
heavy). The normal force is large at the bottom of the loop because
in order for the net force to be directed inward, the normal force
must be greater than the outward gravity force. At the top of
the loop, the gravity force is directed inward and thus, there is no
need for a large normal force in order to sustain the circular
motion. The fact that a rider experiences a large force exerted by
the seat upon her body when at the bottom of the loop is the
explanation of why she feels heavy. In actuality, she is
not heavier; she is only experiencing the large magnitude of
force which is normally exerted by seats upon heavy people while at
rest.
For more information on physical descriptions of motion,
visit
The
Physics Classroom. Specific information on circular motion will
be available soon at The Physics Classroom. Currently, specific
information is available about the following topics:
This page was created by
Tom
Henderson of
Glenbrook South
High School.
Comments and suggestions can be sent by e-mail to
Tom
Henderson.
This page last updated on 6/5/97.