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

Jerk (how fast acceleration changes) is useful. I've found being a passenger in newer electric buses to pose more challenges than ICE buses because EVs can change their acceleration so rapidly. While their maximum acceleration isn't very high, they can go from standstill to accelerating in a split second, toppling anyone standing unless they hold on to something. ICEs need more time to reach maximum acceleration. In other words, EVs jerk more.

How do you know this is not second derivative (acceleration), but the third or higher?

Genuinely curious.

> EVs jerk more. Giggity

More seriously though, I think this might be about driver training and maybe calibrating the foot pedal. It's great that EVs have a much better torque curve, but it means the old muscle memory of opening the throttle wide at low RPMs and letting the clutch slip is simply not the way to do it (nvm that there's no clutch to operate in an EV).

>they can go from standstill to accelerating in a split second

Every car can go from a standstill to accelerating in a split second.

>their maximum acceleration isn't very high

What is the maximum acceleration of an EV? Do you have some numbers?

>ICEs need more time to reach maximum acceleration

I don't think what you're describing is jerk, it's acceleration (and velocity).

ICEs don't develop same torque at every rpm, it takes a while to get to maximum. It's noticeable in how a car speeds up.

Jerk is by definition how fast the acceleration changes. And it's true that there is more delay in ICE engines before you get full power and thus the acceleration changes more slowly.

I know it is the third derivative specifically because a rapid _change_ in acceleration easily puts you off-balance. A change in acceleration effects a change in the forces acting on you (F=ma). When those changes happen slowly, it's easy to adapt and change your stance to neutralize those forces, thus preventing your body from accelerating relative to your frame of reference (the bus).

> Every car can go from a standstill to accelerating in a split second

Going from a standstill to accelerating at say 3 m/s² is very different in a normal ICE car vs. an EV. It's anecdotal, but you must have noticed this if you've driven an EV before.

> What is the maximum acceleration of an EV?

I was talking specifically about the electric buses in my city. They don't have massive acceleration compared to, say, a Tesla.

> I don't think what you're describing is jerk

I am talking about how rapidly electric buses change acceleration. That's the definition of jerk.

Constant acceleration as bus passenger can be fully compensated by just leaning at an angle. This is not unpleasant.

But if the jerk (or higher derivatives) are non-zero, you have to change your "lean angle" quickly to avoid getting jerked around (which is obviously much more disruptive).

You can work it out from the principles of the engines (electric motor can produce their maximum torque at zero speed, combustion engines generally produce very little torque at zero speed, especially when modulated through a clutch or torque converter which you need in practice. And that's before looking at turbo-lag), but it's also something you can feel fairly viscerally: jerk is how quickly the feeling of acceleration changes. In a fast accelerating ICE car you might find yourself sinking more into the back of the seat as the car picks up speed. In an EV you basically just go from still to pressed all the way back, and then you start to pick up speed (and in fact the feeling of acceleration slackens off as the EV reaches a certain speed, though this will also happen with an ICE once they reach their peak acceleration point).