Jerk is also very important for road or rail track design. If you imagine needing to make a 90 degree bend, the "obvious" way to do it is by rounding off the corner with a circular radius.
But if you do that, it means the vehicle goes from having 0 sideways acceleration to experiencing 100% of the centripetal acceleration to move an object on a circular path (a = v^2 / r) instantaneously.
As an occupant of the car, that means you go from sitting comfortably to suddenly being thrown sideways.
It's much more comfortable if you ease into the turn, with the track design considering the rate of change of acceleration. If the designer didn't consider jerk you would definitely notice.
Back when I studied highway engineering they called it spiral-circle-spiral, and the vertical curves were more parabolic. The methods for laying them out were very low tech aimed at drafters and on site contractors rather than mathematicians. I can't remember the layout methods though.
The forces you experience in a loop must be a bit more complicated because the turning forces in a car are perpendicular to gravity and in a loop are sometimes in-line, but yeah I would think that's why the entry and exit are a softer curve.
In part, maybe. The bigger reason is the roller coaster slows down near the top of the loop, so even for an constant vertical acceleration you need a non-circular shape.
But if you do that, it means the vehicle goes from having 0 sideways acceleration to experiencing 100% of the centripetal acceleration to move an object on a circular path (a = v^2 / r) instantaneously.
As an occupant of the car, that means you go from sitting comfortably to suddenly being thrown sideways.
It's much more comfortable if you ease into the turn, with the track design considering the rate of change of acceleration. If the designer didn't consider jerk you would definitely notice.