Beyond velocity and acceleration: jerk, snap and higher derivatives (2016)

I wish designers of vehicles - particularly cars, trains and busses, would work to minimize jerk, snap and crackle.

Turns out if you minimize those, you get a far more comfortable ride. It matters far more than acceleration.

Finite element models of the whole system (tyres and suspension components and flexing elements of the vehicle body and road/track) can quickly allow analysis of the jerk, snap and crackle, and allow tuning of damping and drive system control loops to make a far more comfortable ride.

Do you have proof for that, or is this like audiophiles asking for gold connectors because "they make the sound better"?

Anecdotal evidence:

Ever experienced that a bus is braking (near-constant deacceleration), and people seem fine; but then the bus comes to a halt and thus stops deaccelerating, and people suddenly fall on the floor?

I think at least the derivative or acceleration is important for how well people can compensate. Not sure about higher derivatives though.

Acceleration equals force, so yeah, if you abruptly change acceleration then this equals abruptly changing the force on people in the bus. Acceleration should thus be continuous (not necessarily differentiable). I don't know how you would justify constraints on higher derivatives. Perhaps they mess with our own internal control mechanism?

is it physically possible to have non-continuous acceleration?

Imagine a multistage rocket and the changes in acceleration.

Figure 4-3 in https://www.ibiblio.org/apollo/Documents/lvfea-AS506-Apollo1... shows this for Apollo 11.

I imagine if you zoom in far enough on those points you have the acceleration continuously changing as pressure slowly builds in the engines over several microseconds.

I was thinking more of the instant you shut off engines and disconnect 130,000 kg of mass of stage one.

There is an interesting Δa/Δt while fuel is consumed and mass changes.

There are discontinuities to the graph when engines are shut down and stages decoupled.