Why roller coaster loops aren’t circular anymore

Post by johnwalkr » Sat, Jul 09, 2022, 3:54 PM UTC

atoav wrote: post #46

tobtoh wrote: post #18

If I remember my uni engineering/calculus maths class correctly, the third derivative of position is used in planning these sort of curves. The first derivative of postion (with respect to time) is velocity. The second derivative is acceleration (ie rate of change of velocity). And the third derivative is jerk (rate of change of acceleration). And 'jerk' has to be kept below a certain threshold for humans to find mov…

A very similar thing is done in the creation of reflective surfaces on car bodies (typically in CAD software). They call these constraints by G and a number. G1 would be a positional constraint: the two surfaces meet each other at the same point G2 tangential: same as G1, but the surfaces are tangential G3: same as G2, but the curvature (radius^-1) of the surfaces is the same at the point where the two meet. This ess…

Post by tzs » Sat, Jul 09, 2022, 4:12 PM UTC

joexner wrote: post #102

tzs wrote: post #98

Earlier quoted context omitted.

OT: that reminds me of an interesting physics problem. If you have a ball sitting on the floor in the aisle of a stationary bus and the bus starts accelerating forward the ball rolls toward the back of the bus. If you have a bus moving at a constant velocity and it start decelerating the ball rolls toward the front of the bus. Suppose you also have a helium balloon floating in the bus. Does it also move toward the ba…

The balloon would probably move toward the front when accelerating and toward the back when the bus slows, if it moved at all. It helps (me) to imagine an air bubble in a sealed, nearly-full fish tank on that same accelerating bus. The heavier water gets "flung" harder away from the direction of acceleration, and the bubble gets pushed out of the way in the opposite direction. Same principle.

Post by iggldiggl » Sat, Jul 09, 2022, 11:50 PM UTC

lqet wrote: post #58

userbinator wrote: post #37

Earlier quoted context omitted.

This effect can be prevented by gradually letting off the brake before reapplying it fully upon stopping, but few drivers and rapid transit systems are aware. This is surprising to read. Everyone whose car I've ridden in knows to do that, and it's only in extremely urgent and unexpected stops where it's neglected. Also, when fully stopped, only minimal pressure should be necessary to keep the car still.

> Everyone whose car I've ridden in knows to do that I also do that, and don't know anyone who doesn't. I vaguely remember that I learned it in driving school, most likely because my driving instructor didn't want to be jerked around on the passenger seat for an hour every week. Train/tram drivers here also usually do that in stations, except when they try to make up for delays, or when they have wrongly estimated th…

Post by atoav » Sun, Jul 10, 2022, 9:20 AM UTC

danachow wrote: post #94

atoav wrote: post #46

Earlier quoted context omitted.

A very similar thing is done in the creation of reflective surfaces on car bodies (typically in CAD software). They call these constraints by G and a number. G1 would be a positional constraint: the two surfaces meet each other at the same point G2 tangential: same as G1, but the surfaces are tangential G3: same as G2, but the curvature (radius^-1) of the surfaces is the same at the point where the two meet. This ess…

Minor point (well in this case at least) but you have an off by one error. Your G1 is G0. Here is how it is defined in terms of basis vectors. https://people.eecs.berkeley.edu/~jfc/cs184f98/lec19/lec19.h...

Post by Doxin » Tue, Jul 12, 2022, 12:36 PM UTC

kazinator wrote: post #43

A "G force spikes" is called a "jerk" in physics; as acceleration is the rate of change of speed, jerk is the rate of change of acceleration. The jerk is huge in transitioning from a straight track to a circular one immediately, since the acceleration goes from zero to nonzero instantly.