3 ms·
Many other comments have noted "jerk", the derivative of acceleration that you can feel in a car; but here's maybe a way to make that a little more concrete. S
by an1sotropy 4y ago
Many other comments have noted "jerk", the derivative of acceleration that you can feel in a car; but here's maybe a way to make that a little more concrete.
Suppose you're driving, and you keep your speed constant (no change in the accelerator or "gas" pedal). Keeping the steering wheel at a fixed orientation then moves you uniformly along a fixed circle == constant acceleration == constant force (you feel from car) to the left or right.
But when you move the steering wheel, you're changing the circle radius, and changing acceleration, which changes the force you feel. To a first order approximation (I think), the rate of change of steering wheel position is the rate of change of acceleration, or 3rd derivative of position.
It's not a surprise that a car ride feels smoother when move the steering wheel slower, but the speed of steering wheel motion is the simplest tangible example I can think of for controlling and experiencing a third derivative.
- globular-toast 4y agoThe accelerator and brake pedals are the same. Although in many cars the maximum jerk via the accelerator seems quite limited. Jerk is also what triggers car/motion sickness. So for the comfort of your passengers, move the controls slowly. Roller coaster designers know this well and I think they even consider fourth and fifth derivatives when designing coasters.
- anonym29 4y agoSee: snap, crackle, pop https://en.m.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position https://en.m.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_der...
- hanche 4y agoI have read that for this reason, the Euler spiral (a.k.a. Cornu spiral) is commonly used in the design of modern roads. Its defining characteristic is that the curvature changes at a constant rate with respect to arc length. So a curve in the road is typically composed of three parts: First, a section of an Euler spiral starting with zero curvature, joined by a circular arc, then a new Euler spiral ending once more at zero curvature. When I first learned about this, I tried it on some recently built roads. And indeed, entering the curve I can move the steering wheel at a constant rate, hold it still through the middle of the curve, t’en move it back at a constant rate until I am once more traveling in a straight line.
- an1sotropy 4y agocool! I will try to drive safely while also pondering this the next time I'm driving.