CURVES

HORIZONTAL CURVES AND
TURNS

A horizontal curve is a curve that does not rise or fall.
There are two type of curves, flat curves and banked curves.

**FLAT CURVES**

A flat curve gives a rider the sensation of being thrown sideways. If
the roller coaster car's velocity is fast enough and the radius small
enough, the stresses on the car's under carriage can be tremendous.
For a flat curve the inward net acceleration felt by the rider is
calculated from the equation.

Where "a" is the acceleration felt by the rider to the inside of
the circle, "v" is the velocity of the car and "R" is the radius of
the curve. This acceleration can be converted to g's by dividing it
by 9.80 ^{m}/s^{2}.

**BANKED CURVES**

A banked curve reduces the rider's sensation of being thrown
sideways by turning the car sideways. The car is tilted. The trick is
to tilt the track just the right amount.

The ideal banked curve is one where no outside forces are needed to
keep the car on the track. In other words, if the banked curve were
covered with ice -no friction- and the coaster did not have a
steering mechanism the car would stay on the track. These are the
forces acting on the car as the car travels around horizontal banked
curves.

therefore

This is for the *ideal* banked curve where no friction is
required to keep the car from sliding to the outside or inside of the
curve. On a given curve if the velocity is greater or less than the
design velocity then the cars may need a little frictional help to
keep them on the track.

If your not comfortable with trigonometry functions, the equations
can be rewritten and used as shown below.

Calculating g's Felt on a Banked
Curve

Recall that the g's felt is equal to the normal force divided by mass
and then divided by g to convert to from ^{m}/s^{2} to g's.

If you use or find this page useful or have any
comments, please contact the author so maybe he'll do more.
Author: Tony Wayne

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