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I can't pin down which part that I hate most, the "stylish" presentation with random SFX and virtual pen circling around, or the fact they always insert some super low quality video conference footage instead of just letting the narrator paraphrasing (I get it they're the domain experts, but still..).
Earlier quoted context omitted.
Jounce, crackle and pop for the 4th, 5th and sixth derivatives
It feels wrong to me that pop comes after crackle. Crackle seems like the ultimate high-frequency effect. In fact, "pop" seems like it should come before "snap". But I guess it is somewhat arbitrary.
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…
It's not strictly a matter of threshold -- people might tolerate a higher jerk if it's for a much shorter duration, for example. In practice it doesn't much matter which metric you minimize; you'll end up with similar results. The simplest option is to minimize the mean absolute jerk, which has the side benefit of utterly confusing any non-physics-literate people listening in. (You want to do what to whom?)
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
Thus is similar to corners in roads not working well when they're circular arcs. Going from straight to circular arc means your steering wheel needs to jump instantly from one fixed position to another. Using something like a linear change in curvature (i.e. a clothoid curve) is much smoother. This kind of thinking applies to other areas too: https://en.wikipedia.org/wiki/Euler_spiral
Curiously Dubins paths do have instantaneous steering changes. https://en.wikipedia.org/wiki/Dubins_path
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…
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.
Earlier quoted context omitted.
I have a t-shirt which has "don't be a" and the equation for the third derivative
Better than my schwarzchild radius nerd shirt!
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.
Also by the time you get to the apex it’s going slower than when it entered the loop.