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Am I high or is the picture of the flip flap railroad loop decidedly not circular?
You’re high. But also the photo was taken at an angle to the track, so it’s not gonna trace out a circle on your screen.
A true circular loop the entrance and exit would be directly side by side.
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…
And this is also why the passengers jerk of a vehicle jerk backwards after it comes to a complete stop. Their muscles statically counter the relative forwards acceleration of their torsos during braking and require time to react to the acceleration suddenly going away. This effect can be prevented by gradually letting off the brake before reapplying it fully upon stopping, but few drivers and rapid transit systems seem to be aware.
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…
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…
Also seen in the planning of curves in roads (where jerk corresponds to the rate at which a steering wheel must be turned) and railways. And this is also why the passengers jerk of a vehicle jerk backwards after it comes to a complete stop. Their muscles statically counter the relative forwards acceleration of their torsos during braking and require time to react to the acceleration suddenly going away. This effect c…
I find that amazing. What the heck are drivers ed instructors doing? It's not just hard on the passengers, it's hard on the machinery.
It's the same with the clutch. I've driven with enough people who fancy themselves as great shifters, but they jerk the hell out of the clutch every time, never attempting to match the shaft speed with the engine speed. If I comment on it, they always deny doing that :-/
If I'm on my game, I can shift smoother than an automatic. The bonus is the clutch will last a very long time.
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…
I have a t-shirt which has "don't be a" and the equation for the third derivative
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…
Also seen in the planning of curves in roads (where jerk corresponds to the rate at which a steering wheel must be turned) and railways. And this is also why the passengers jerk of a vehicle jerk backwards after it comes to a complete stop. Their muscles statically counter the relative forwards acceleration of their torsos during braking and require time to react to the acceleration suddenly going away. This effect c…
https://www.datagenetics.com/blog/march42014/index.html
Vox re-heating a gizmodo article[0] which re-publishes (with permission) the one above.
[0]: https://gizmodo.com/why-roller-coaster-loops-are-never-circu...
Note that the narrow-loop shape in modern roller-coasters means that the tightest curve is at the top, where the G-forces are partially countered by gravity. That's an 1-G that they can subtract, and it means the radius can be significantly larger on entry to the loop, resulting in smaller G-forces.
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…
Jounce, crackle and pop for the 4th, 5th and sixth derivatives
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…
Jounce, crackle and pop for the 4th, 5th and sixth derivatives