The Physics of
Roller Coasters
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Loop Design
A Loop
Photo: Roller Coaster Loop Shapes article

loop designs
Figure 2. Different loop shapes for the condition of constant centripetal acceleration.
The first two loop shapes give a centripetal acceleration of 2g and 3g, respectively, throughout the loop, (for a particular velocity), whereas the last two loops maintain these conditions only for the bottom part of the loop, matched to a 120˚ circular arc at the top.

(Text from source explaining picture)

photo: Roller Coaster Loop Shapes article

When building a coaster, the most widely used feature is the loop. No one can forget the feeling of being upside down with a small fear of falling while going at high speeds. It is quite interesting if you stop and look at a loop. You will notice that it is not a perfect circle as you might think. The top part of the loop is semi-circular, but the bottom portion is elongated like the pictures shows, much like a teardrop. Tests show that it is better to have the coaster enter the loop at an incline then horizontally to reduce centripetal forces. As you may guess, entering a loop horizontally, then immediately going up will feel uncomfortable as you are pushed against your seat very harshly. Different angles of entry, as well as different radius's of the loop help in making the ride more enjoyable due to decreasing certain forces on you and the cart against the track.


            Also when considering loop design, you need to make sure the exit velocity is not to great of a downward force that can lead to putting the riders under great stress from the increase of g-forces. As you ride down, the carts acceleration increases due to the increase of velocity. The increase of velocity comes from the kinetic energy being transformed from the potential energy gained from going up the loop. With the increase of acceleration downward and the already present gravitational acceleration in the same direction, multiply it by your mass will give the amount of force that is acting on your body. This ends up increasing, resulting in the feeling of being very heavy. If these forces are to great, the riders can feel light headed and may pass out from the rush of the blood being forced out from the brain to the feet. Remember, every part of the body is moving freely and at the velocity of the cart. So when the cart turns, the body and blood want to continue in the original direction, leading to the blood leaving the brain as it is forced downwards.