DataGenetics explains why roller coaster loops are not perfectly circular and are, instead, shaped like upside-down teardrops. The explanation is summed up to riders' comfort (so they don't pass out from the G-force). Even more interestingly, the mathematics are actually applied to railroad tracks and roads as well.
Many extreme roller coaster these days have vertical loops. Have you noticed that these loops are never circular? Why is this?
They all, also, seem to have the same similar inverted teardrop appearance. Why is this?
Clearly there is the same physics and mathematics involved in their designs. Lets take a look and see if we can derive a formula to describe their shape.
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