Beyond velocity and acceleration: jerk, snap and higher derivatives (2016)(iopscience.iop.org)
iopscience.iop.org
Beyond velocity and acceleration: jerk, snap and higher derivatives (2016)
https://iopscience.iop.org/article/10.1088/0143-0807/37/6/065008
153 comments
Jerk is also very important for road or rail track design. If you imagine needing to make a 90 degree bend, the "obvious" way to do it is by rounding off the corner with a circular radius.
But if you do that, it means the vehicle goes from having 0 sideways acceleration to experiencing 100% of the centripetal acceleration to move an object on a circular path (a = v^2 / r) instantaneously.
As an occupant of the car, that means you go from sitting comfortably to suddenly being thrown sideways.
It's much more comfortable if you ease into the turn, with the track design considering the rate of change of acceleration. If the designer didn't consider jerk you would definitely notice.
But if you do that, it means the vehicle goes from having 0 sideways acceleration to experiencing 100% of the centripetal acceleration to move an object on a circular path (a = v^2 / r) instantaneously.
As an occupant of the car, that means you go from sitting comfortably to suddenly being thrown sideways.
It's much more comfortable if you ease into the turn, with the track design considering the rate of change of acceleration. If the designer didn't consider jerk you would definitely notice.
The curve that is used is a Clothoid:
https://en.wikipedia.org/wiki/Euler_spiral
Usually for any curve you go straight-clothoid-arc-clothoid-straight
For trajectory AND for pitch and roll
https://en.wikipedia.org/wiki/Euler_spiral
Usually for any curve you go straight-clothoid-arc-clothoid-straight
For trajectory AND for pitch and roll
Back when I studied highway engineering they called it spiral-circle-spiral, and the vertical curves were more parabolic. The methods for laying them out were very low tech aimed at drafters and on site contractors rather than mathematicians. I can't remember the layout methods though.
Neat!
That's why loops on roller coasters aren't perfect circles as well then, I guess?
The forces you experience in a loop must be a bit more complicated because the turning forces in a car are perpendicular to gravity and in a loop are sometimes in-line, but yeah I would think that's why the entry and exit are a softer curve.
Yeah, the more circular ones are pretty intense - https://guidetosfot.com/rides/shockwave/
One thing that is strange is that we can easily imagine the first two derivatives: position we can just imagine a static point, velocity we can imagine a constant speed i.e. a straight line on a position-time graph, acceleration we just imagine a parabola, but jerk is somehow conceptually indistinguishable. The difference between a point, a line, and a parabola are stark, the third order jerk is not so easy to distinguish, instead still just looking like the parabola.
I've always wondered why this is, why curves in general are perceptually similar if scaled correctly, while a straight line is so clearly different. Perhaps it is because our perceptions developed to distinguish between inertial and non inertial reference frames?
I've always wondered why this is, why curves in general are perceptually similar if scaled correctly, while a straight line is so clearly different. Perhaps it is because our perceptions developed to distinguish between inertial and non inertial reference frames?
I like and agree with your observation. But I think you can use conceptual tricks to get just a little further: Acceleration is "due" to a force (F=ma), so you can think of jerk as a change in that force linearly increasing over time.
That doesn't help me recognize a cubic from a quadratic when looking at a small piece of it, but I can imagine an elevator ramping up it's lifting power or similar. It kind of feels like the tricks to conceptualize 4D as 3D position plus a temperature at each spot.
That doesn't help me recognize a cubic from a quadratic when looking at a small piece of it, but I can imagine an elevator ramping up it's lifting power or similar. It kind of feels like the tricks to conceptualize 4D as 3D position plus a temperature at each spot.
I agree the linearisation trick can be used and is often used in physics, but we must do that as a consequence of the thing I'm confused about the origin of, which is not why do we only greatly distinguish between the first few derivatives of position, but why do we only greatly distinguish between the first few derivatives of most functions? I.e. why do we have to do these tricks in the first place?
I don't have any answers, but I suspect it's because we're evolved from things that didn't need to know.
Related, I sometimes wonder how many derivatives you need to go down in order to find the one that is discontinuous when you decide to make a motion. For instance: pressing the first key to type this reply, my finger didn't instantly jump from zero to non-zero acceleration (or jerk/snap) I assume. How many terms in the Taylor series for moving a muscle?
Related, I sometimes wonder how many derivatives you need to go down in order to find the one that is discontinuous when you decide to make a motion. For instance: pressing the first key to type this reply, my finger didn't instantly jump from zero to non-zero acceleration (or jerk/snap) I assume. How many terms in the Taylor series for moving a muscle?
> the thing I'm confused about the origin of, which is not why do we only greatly distinguish between the first few derivatives of position, but why do we only greatly distinguish between the first few derivatives of most functions?
Because higher derivatives are insignificant. That's the entire concept of Taylor series approximation. If you change a high derivative of a function, the value of the function won't noticeably change - why would you care?
Because higher derivatives are insignificant. That's the entire concept of Taylor series approximation. If you change a high derivative of a function, the value of the function won't noticeably change - why would you care?
Tje difference is because we cannot easily tell between “curve of second order” and “curve of other order”.
You can get an idea when you try to understand why the function
y=0 for x<0 y=x^2 for x>=0
has two derivativea but not three.
But the issue is infinitesimal, so very hard to tell.
Jerk you can “linearise” if you think of a car (with no air friction) and its accelerator. Somehow…
You can get an idea when you try to understand why the function
y=0 for x<0 y=x^2 for x>=0
has two derivativea but not three.
But the issue is infinitesimal, so very hard to tell.
Jerk you can “linearise” if you think of a car (with no air friction) and its accelerator. Somehow…
> Tje difference is because we cannot easily tell between “curve of second order” and “curve of other order”.
Why not, though? Why does third order "look like" second order but second order is starkly different to first order?
Why not, though? Why does third order "look like" second order but second order is starkly different to first order?
Because a line has an infinite radius, while a curve has a finite radius. The difference between infinite and finite is stark. The difference between two finite values is not.
Well, firstly, if you plot the first n degrees of monomials and keep the scale invariant, the visual difference between x^k and x^(k+1) literally gets smaller the higher up you go.
Secondly, presumably the distinction of "straight" vs. "curved" is quite deeply programmed into the brain's pattern recognition machinery. The degree of curvature is a quantitative parameter on top of the qualitative categorization. This may or may not have something to do with the fact that a modern human sees straight lines everywhere (something that very much was not the case in the ancestral environment).
Secondly, presumably the distinction of "straight" vs. "curved" is quite deeply programmed into the brain's pattern recognition machinery. The degree of curvature is a quantitative parameter on top of the qualitative categorization. This may or may not have something to do with the fact that a modern human sees straight lines everywhere (something that very much was not the case in the ancestral environment).
UHHHHHhhhh, it's because the last A*b is the only one that becomes a linear constant. For other polynomials, your derivative is a polynomial still, just different one.
These are mathematical derivatives, I think of them as the slope of the thing it's derived of, aka the change in the thing that it's a derivation of.
I think I don't have a sophisticated mathematical understanding, but my basic mechanic understanding makes it feel simpler than your question is acting.
These are mathematical derivatives, I think of them as the slope of the thing it's derived of, aka the change in the thing that it's a derivation of.
I think I don't have a sophisticated mathematical understanding, but my basic mechanic understanding makes it feel simpler than your question is acting.
I think it's in part because differences in gradient are quite difficult to distinguish by eye, and the difference in the higher order curves is in just that (and scaling things to be visible means the difference in curvature gets smaller as you go to higher orders). Even nearly-straight lines can be quite difficult to tell from actually-straight without a nearby reference.
It’s seems analogous to our spatial dimensions. We can all easily visualize or describe up to a 3D object, but 4D is almost impossible to fathom for most people
> American people want to have the gut feeling when riding a lift, especially an express lift in those high buildings. In difference in Asian countries the lift ride must be smooth as possible. They don't like to have the feeling of riding a lift at all. In Europe it is something in between
How representative are these stated preferences actually of the population. I'd imagine that the individual preferences vary greatly from person to person and also change with age.
How representative are these stated preferences actually of the population. I'd imagine that the individual preferences vary greatly from person to person and also change with age.
It might not be a strict "preference", more of an expectation how things should be based on previous experience. Like, if you're used to an elevator with a bit of a jerk, an elevator taking you there just as fast but smoother might feel not as fast.
Yet it is a captive market. If I am in a building, I only have access to a singular type of elevator. Why not always give the smoothest ride possible unless it is $0.12 cheaper for the installer, so everyone has to suffer forever.
An elevator that feels significantly different than the other elevators in the city probably results in more complaints to building management/maintenance about either "the elevator is too jerky!" or "the elevator is too slow!"
You could just as well ask "why not give the fastest ride possible so everyone saves time?"
I'm an American.
My thoughts are that I'd prefer to spend as little time as possible in an elevator and would rather spend that time doing other things.
If I don't feel the elevator moving, then it's moving too slowly and wasting my time.
My thoughts are that I'd prefer to spend as little time as possible in an elevator and would rather spend that time doing other things.
If I don't feel the elevator moving, then it's moving too slowly and wasting my time.
They're the preferences of the buying managers.
If I were buying, I'd ask for a sensation of horizontal force when going up/down and see what they'd come up with.
Corkscrew lift.
I imagine a spinning lift would be easier.
Finally an elevator that will force other occupants to respect my personal space.
We’re all up against the wall during this ascent!
We’re all up against the wall during this ascent!
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The terms jerk and snap while perhaps known in the rare space of elevator purchasing aren’t generally used terms in most fields. I’m surprised that’s in any way controversial ?
The terms are also understood in economics as prudence, and template. Albeit, not widely used.
Statics, dynamics, and two semesters of physics are required courses for every engineer. None of them incorporate the teaching of jerk or snap.
But all of them are based on courses that define nth derivative, and the notion of continuous vs non continuous functions. What is the value of giving them names instead of just using nth derivative?
For those interested, it's also worth taking a look at the time-integrals (or "lower derivatives") past displacement: absement, absity, abseleration, etc. https://en.wikipedia.org/wiki/Absement
This is breaking my brain a little, any eli5?
Velocity measures how fast displacement changes. In the same way, displacement measures how fast absement changes. This means if displacement is small, then absement will grow slowly; if displacement is large, then absement will grow quickly.
I think in the linked article there's a good real-world example of that with a valve:
> opening the gate of a gate valve (of rectangular cross section) by 1 mm for 10 seconds yields the same absement of 10 mm·s as opening it by 5 mm for 2 seconds. The amount of water having flowed through it is linearly proportional to the absement of the gate, so it is also the same in both cases.
I think in the linked article there's a good real-world example of that with a valve:
> opening the gate of a gate valve (of rectangular cross section) by 1 mm for 10 seconds yields the same absement of 10 mm·s as opening it by 5 mm for 2 seconds. The amount of water having flowed through it is linearly proportional to the absement of the gate, so it is also the same in both cases.
The first one comes up in control systems: you have two displacements, the target position and the real position. You subtract them to get the error, also a displacement. You can then integrate that error term to get the total error over the course of the control period. That would be “absement”, measured in m*s. You might then tune your control algorithms to optimize that value.
I’m not sure how to think about the lower orders. You might, for instance, have a learning control system you expect to come to a lower error state over time. The integral of the absement would be a decent way to capture that phenomena.
I’m not sure how to think about the lower orders. You might, for instance, have a learning control system you expect to come to a lower error state over time. The integral of the absement would be a decent way to capture that phenomena.
I did a bunch of stuff with PID back in the day, but honestly this is the first time I'm forcing my brain to look at the word "absement" to describe the integral portion. Looking back, I must have encountered the word many times in the past, but my brain just didn't process the label. I mentally knew and fully understood the concept, and did code / systems implementation involving it, but never really knew the term.
I also distinctly remember being about to go into an exam in undergrad EE, and having a decades-older MechE ask if I knew about "jerk". I had a temporary panic because I didn't know the term - but then when they started explaining it, I already knew it all, I just had never been exposed to the term "jerk" as the word to use for it.
So maybe it's just a terminology thing? I've been in situations where I definitely knew the concept thoroughly, both absement and jerk, but didn't know those labels.
I also distinctly remember being about to go into an exam in undergrad EE, and having a decades-older MechE ask if I knew about "jerk". I had a temporary panic because I didn't know the term - but then when they started explaining it, I already knew it all, I just had never been exposed to the term "jerk" as the word to use for it.
So maybe it's just a terminology thing? I've been in situations where I definitely knew the concept thoroughly, both absement and jerk, but didn't know those labels.
The funny thing is I’m almost certain everyone here has been exposed to the term “jerk”, in the exact technical meaning, but didn’t make the relation that the colloquial meaning and the technical meaning are the same.
Acceleration feels like a constant force (because… it is). When that force changes, you feel “jerked”.
Acceleration feels like a constant force (because… it is). When that force changes, you feel “jerked”.
There's some good examples in the wiki link, I liked: "A vehicle's distance travelled results from its throttle's absement. The further the throttle has been opened, and the longer it's been open, the more the vehicle's travelled." Plus the fact that the units are m*s instead of m/s.
Reaching your hand into an oven (for some reason), you not only care about how far it is into the over, its position, you also care about how long it's been at its current position.
Why bother with giving words for something which is longer than their mathemathical definition? The word can be unknown, but if the function is unknown the word is useless?
A long time ago I wrote an engine for a newspaper that was helping journalists discover what was happening on social media. I was counting the number of times an URL was posted on Twitter and Facebook. I started with velocity and acceleration, but after I while I discovered that I could go one level higher and use jerk to understand when an URL was shared by an influencer.
I have a hard time imagining another level above that.
I have a hard time imagining another level above that.
When it comes to a measured time-series, the function is always discrete and arbitrary; there is no 'curve' like that generated by a function well-defined on the reals, and so there is no real closed-form derivative. In this context derivatives are not equations so much as derived data, reducing two points to one. And this process is recursive, such that you can take 4 points, reduce the two adjacent ones to 1 point, and then reduce those two into 1 point. In fact for 2^n points you can get the nth derivative in this way. The utility of this data is highly questionable in almost every context, but its available for every time-series. (One application that comes to mind is a kind of checksum, where you recursively derive a time series and stop when local neighbors go to 0, and you're left with a sparse list of high-order numbers that in some sense characterize the series.)
Snap could be the acceleration of "influencers" sharing an article? Basically, how fast it spreads from one to many
That might be more exponential than polynomial.
DDoS attacks, high inflection from a lot of disparate sources.
Favorite economics quote:
"In the fall of 1972, President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case fore reelection. - by Hugo Rossi"
"In the fall of 1972, President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case fore reelection. - by Hugo Rossi"
Another similar "hidden but intuitive" property is higher order geometric curvature continuity. For example squircles/superellipses have more smoothly changing curve than naive rounded rectangle, or industrial design using Gn continuity/class A surfaces:
https://en.wikipedia.org/wiki/Class_A_surface
https://www.johndcook.com/blog/2018/02/13/squircle-curvature...
I do see quite clear parallels between higher order time derivates and these higher order curvature measures, although I don't know if there is any formal relation here
https://en.wikipedia.org/wiki/Class_A_surface
https://www.johndcook.com/blog/2018/02/13/squircle-curvature...
I do see quite clear parallels between higher order time derivates and these higher order curvature measures, although I don't know if there is any formal relation here
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.
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.
>I wish designers of vehicles - particularly cars, trains and busses, would work to minimize jerk, snap and crackle.
They do.
>Turns out if you minimize those, you get a far more comfortable ride. It matters far more than acceleration.
They know that this is the case. And put a lot of effort into making sure your car has the desired feel.
Besides your comfort these considerations are extremely important for the durability analysis for the vehicle.
>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.
Finite element simulations are undesirable, they are extremely calculation expensive for those kind of large models and somewhat unsuitable. They are used in crash tests.
For the application you described multi body systems are used, where the car is decomposed into its functional components, which can be modeled either as stiff or flexible. With that you have a reasonably accurate model of a car which you can use to test on a virtual test track.
Basically every competent car manufacturer is doing this.
They do.
>Turns out if you minimize those, you get a far more comfortable ride. It matters far more than acceleration.
They know that this is the case. And put a lot of effort into making sure your car has the desired feel.
Besides your comfort these considerations are extremely important for the durability analysis for the vehicle.
>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.
Finite element simulations are undesirable, they are extremely calculation expensive for those kind of large models and somewhat unsuitable. They are used in crash tests.
For the application you described multi body systems are used, where the car is decomposed into its functional components, which can be modeled either as stiff or flexible. With that you have a reasonably accurate model of a car which you can use to test on a virtual test track.
Basically every competent car manufacturer is doing this.
I recently rode the Blue Line in Chicago, and found the jumps in acceleration to be quite jarring. Some of that is due to the track, but it felt like the majority could be fixed using a modern motor controller and a bit of math.
I have two questions:
1) does this hold for all 3 of jerk, snap and crackle, like OP suggested?
2) In applications where no humans are involved (robot actuators etc.), would it make sense to minimize jerk, snap and crackle too?
1) does this hold for all 3 of jerk, snap and crackle, like OP suggested?
2) In applications where no humans are involved (robot actuators etc.), would it make sense to minimize jerk, snap and crackle too?
>1) does this hold for all 3 of jerk, snap and crackle, like OP suggested?
They aren't the fundamental quantities you would look at, typically the output of a multi body system are displacement/velocity/acceleration, but of course if you look at a plot of acceleration you can just see these quantities (at least the first and second derivative are quite easy to see) or calculate them. And of course the ride comfort is related to the smoothness of the forces you experience, which is the same as wanting to minimize the derivatives of force. But I would suggest that these quantities are quite hard to analyze quantitatively as they are, naturally, subject to far more noise.
Where these quantities definitely are considered is when you look at vibrations.
>2) In applications where no humans are involved (robot actuators etc.), would it make sense to minimize jerk, snap and crackle too?
Yes, if you care about durability. Parts can break for different reasons, intuitively you easily understand that exceeding certain loads breaks them. Another, far more insidious, failure case is a cyclic load, which never exceeds a particular threshold. Again, vibrations play an important role there.
They aren't the fundamental quantities you would look at, typically the output of a multi body system are displacement/velocity/acceleration, but of course if you look at a plot of acceleration you can just see these quantities (at least the first and second derivative are quite easy to see) or calculate them. And of course the ride comfort is related to the smoothness of the forces you experience, which is the same as wanting to minimize the derivatives of force. But I would suggest that these quantities are quite hard to analyze quantitatively as they are, naturally, subject to far more noise.
Where these quantities definitely are considered is when you look at vibrations.
>2) In applications where no humans are involved (robot actuators etc.), would it make sense to minimize jerk, snap and crackle too?
Yes, if you care about durability. Parts can break for different reasons, intuitively you easily understand that exceeding certain loads breaks them. Another, far more insidious, failure case is a cyclic load, which never exceeds a particular threshold. Again, vibrations play an important role there.
In response to #2, consider that every material is fundamentally "springy"[1], and many engineering materials deflect a human-noticable amount when enough force to move them is applied. Thus, you can model every connection between an actuator and an object as a spring. When the actuator starts accelerating, it applies a force through that spring, which causes the spring to extend, and the force actually applied to the object is provided only by the extension of the spring. It's only once the spring is applying the same force as the actuator is that the two objects are moving at the same speed. However, at that point, the actuator and object are moving at different speeds, so the spring is still extending. As a result, you end up with an oscillation in the velocity of the object, which is almost never desirable. For a start, if one of the parts is metal, this causes fatigue, which will cause the part to fail much sooner. Secondly, you generally want the object being moved to follow a precise path, and that oscillation will show up as ringing[2]
[1] Yes, this is a vast oversimplification, but the model I'll build using it is reasonably accurate.
[2] Most 3d printing enthusiasts are familiar with this issue; e.g. https://www.simplify3d.com/resources/print-quality-troublesh... . However, most of the advice you see amounts to "make everything stiffer", which helps, but the real solution is to be less jerky.
[1] Yes, this is a vast oversimplification, but the model I'll build using it is reasonably accurate.
[2] Most 3d printing enthusiasts are familiar with this issue; e.g. https://www.simplify3d.com/resources/print-quality-troublesh... . However, most of the advice you see amounts to "make everything stiffer", which helps, but the real solution is to be less jerky.
Modern cars are designed on GUI simulation software like MATLAB, they model head accelerations few inches ahead of the most important headrest and run optimizer on variables. If it can be made into equations, they can cancel it.
btw, minimizing higher orders of derivatives improve passenger comfort only so much if the driver isn't so good at look-ahead path planning, you can't make coffee cup rides not sickening by software.
btw, minimizing higher orders of derivatives improve passenger comfort only so much if the driver isn't so good at look-ahead path planning, you can't make coffee cup rides not sickening by software.
>Modern cars are designed on GUI simulation software like MATLAB
MATLAB is the programming language. You are talking about Simulink. But there are also dedicated software packages for car multi body dynamics.
>you can't make coffee cup rides not sickening by software.
Plainly false.
MATLAB is the programming language. You are talking about Simulink. But there are also dedicated software packages for car multi body dynamics.
>you can't make coffee cup rides not sickening by software.
Plainly false.
> >you can't make coffee cup rides not sickening by software.
> Plainly false.
I'm not sure how this is false, but I'm also not sure what the person you're replying to is getting at. coffee cup rides have no driver and therefore no look ahead path planning at all.
The entire appeal of these rides is that they exaggerate perception of third and higher derivatives by deliberately creating a chaotic field of view for their occupants, combined with constantly changing both the rate and direction of the acceleration of their squishy bodies in the rigid capsules to which they are loosely secured.
Smoothing this out with software would be possible, sure, but then the result would no longer be a coffee cup ride. I feel like this is a poorly formed example.
> Plainly false.
I'm not sure how this is false, but I'm also not sure what the person you're replying to is getting at. coffee cup rides have no driver and therefore no look ahead path planning at all.
The entire appeal of these rides is that they exaggerate perception of third and higher derivatives by deliberately creating a chaotic field of view for their occupants, combined with constantly changing both the rate and direction of the acceleration of their squishy bodies in the rigid capsules to which they are loosely secured.
Smoothing this out with software would be possible, sure, but then the result would no longer be a coffee cup ride. I feel like this is a poorly formed example.
I was thinking what would be the most steady and disorienting activity with higher integrals of lateral accelerations, and couldn't come up with a better example than a cup ride. I admit it wasn't a good one.
It's designed for in the road/track, not the vehicle. For train tracks in the UK the recommended max jerk is 0.35 mm/s/s/s. The jerk is limited by using 'Euler spiral' sections to join up the straights and the curves. Travelling along an Euler spiral at constant speed means you feel constant jerk laterally, so can be scaled to keep the jerk below any arbitrary value.
Do you have proof for that, or is this like audiophiles asking for gold connectors because "they make the sound better"?
Not proof, but jerk is a factor when bringing a car to a smooth stop. You have to learn how to brake smoothly in order to avoid the "drivers ed stop" where the car and its passengers lurch forward and then bounce back. But the controls for automated vehicles like airport trams have to be designed to avoid this. The underlying reason is that some components such as the tires and suspension are elastic.
This is in fact an issue for the designers of controls for mechanical systems. I learned about it in Process Control class, albeit 40 years ago.
This is in fact an issue for the designers of controls for mechanical systems. I learned about it in Process Control class, albeit 40 years ago.
Cars 20+ years ago vs more recent cars - I've definitely noticed them auto-doing what I was taught to do with older cars: ease off the brakes right at the end.
I wonder if this is a change in braking material, specifically a reduction in difference between dynamic coefficient of friction and static coefficient of friction between the pad and rotor (or equivalently, the shoe and drum).
If older cars had a higher differential, you’d need to let up more as the brake finally locks up.
If older cars had a higher differential, you’d need to let up more as the brake finally locks up.
Don't forget vehicles got heavier, rims got bigger/rubber has thinner sides, suspensions geometry evolved and got stiffer (and possibly non-linear, at least on the high end) and so on and so forth, reducing the amount of elastic energy.
There's mechanical braking assistance (not just ABS) which means pressing the same pedal distance may produce different breaking strength depending on the speed at which the pedal is pressed; e.g pressing hard triggers force assistance from, say, a vacuum reservoir that reuses engine pump loss, which means conversely pressing lightly for a normal stop does not need to exert as much pressure, hence an eased in stop.
Also with more stable vehicles with better chassis, suspension, and overall balance, I feel like rear braking has been tuned upwards over time, making for a more stable stop: notice how lightly pulling the handbrake has a straight-rolling car "sitting" instead of "diving". More consistent use of disc brakes instead of drums on the rear end certainly helps, as well as the ability for the vehicle to remain stable even when braking while in a turn.
Regarding brake friction itself, I can think of at least one major change: the ban of materials such as copper or asbestos in brake pads.
There's mechanical braking assistance (not just ABS) which means pressing the same pedal distance may produce different breaking strength depending on the speed at which the pedal is pressed; e.g pressing hard triggers force assistance from, say, a vacuum reservoir that reuses engine pump loss, which means conversely pressing lightly for a normal stop does not need to exert as much pressure, hence an eased in stop.
Also with more stable vehicles with better chassis, suspension, and overall balance, I feel like rear braking has been tuned upwards over time, making for a more stable stop: notice how lightly pulling the handbrake has a straight-rolling car "sitting" instead of "diving". More consistent use of disc brakes instead of drums on the rear end certainly helps, as well as the ability for the vehicle to remain stable even when braking while in a turn.
Regarding brake friction itself, I can think of at least one major change: the ban of materials such as copper or asbestos in brake pads.
I was thinking of both the changing of material composition of existing organic or semi-metallic pads, but also the general drift towards ceramic pads for low-dust.
Some of the German marque factory pads have exceptional initial bite, coupled with exceptional high levels of dust.
Some of the German marque factory pads have exceptional initial bite, coupled with exceptional high levels of dust.
I used to work at a self-driving car company, and all the vehicle's motion was planned around how much jerk to apply.
Your muscles are pretty good at applying a constant force (or responding to a constant acceleration). Hold your arm out straight: it's no effort to keep your arm still and counteract the force of gravity. Now imagine gravity varies quickly and randomly between 0.5g and 2g. I guarantee your arm won't stay still.
The same prinicple applies on a bus or in a car, except this time the forces are smaller, and it's your neck keeping your head still!
Your muscles are pretty good at applying a constant force (or responding to a constant acceleration). Hold your arm out straight: it's no effort to keep your arm still and counteract the force of gravity. Now imagine gravity varies quickly and randomly between 0.5g and 2g. I guarantee your arm won't stay still.
The same prinicple applies on a bus or in a car, except this time the forces are smaller, and it's your neck keeping your head still!
Ok, minimizing jerk makes sense, but how about snap and crackle? Because GP said:
> (...) jerk, snap and crackle. Turns out if you minimize those, you get a far more comfortable ride.
> (...) jerk, snap and crackle. Turns out if you minimize those, you get a far more comfortable ride.
Snap and crackle I couldn't tell you about. But jerk is definitely important.
It's broadly recognized that minimizing jerk and snap is important to comfort in roller-coasters, so there is evidence for that proposition:
e.g. https://iopscience.iop.org/article/10.1088/1361-6552/aba732
e.g. https://iopscience.iop.org/article/10.1088/1361-6552/aba732
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.
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.
I think bus is braking with a constant breaking force.
But, the bus has a non-constant kinetic energy (going up with the velocity*velocity, down as velocity goes down.)
So, you're actually producing a non-linear acceleration. This is jerk, but you can also think of it as just a non-linear acceleration and people are reacting to the fact it's not at all near constant deacceleration, and this is most noticable as velocity hits zero.
So, yes, it's jerk, but no, I think it can be intuitively better understood with pure acceleration terms and no jerk needed
But, the bus has a non-constant kinetic energy (going up with the velocity*velocity, down as velocity goes down.)
So, you're actually producing a non-linear acceleration. This is jerk, but you can also think of it as just a non-linear acceleration and people are reacting to the fact it's not at all near constant deacceleration, and this is most noticable as velocity hits zero.
So, yes, it's jerk, but no, I think it can be intuitively better understood with pure acceleration terms and no jerk needed
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?
If we zoom in on a single electron absorbing the momentum of a single photon, it will accelerate “instantly”. The same goes for e.g. an unstable atomic nucleus that ”splits”.
At macroscopic scales, I’m not aware of exactly instantaneous acceleration, since you would need some time to “sync” the movement of each atom in the object. But some processes will of course look instantaneous at any given time scale.
At macroscopic scales, I’m not aware of exactly instantaneous acceleration, since you would need some time to “sync” the movement of each atom in the object. But some processes will of course look instantaneous at any given time scale.
Aren’t you describing infinite acceleration, or discontinuous velocity?
Voltages can change abruptly. Therefore, forces can change abruptly, and hence acceleration as well.
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.
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.
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.
That’s the essence of a legitimate question: over small enough time periods (as the bolts explode over a non-zero period of time), is it continuous or discontinuous?
Over a macro scale, it’s discontinuous, of course.
Over a macro scale, it’s discontinuous, of course.
It's nature, it's continuous at small enough scales.
But, checkout Zeno's paradox for more on your philosophical questions
But, checkout Zeno's paradox for more on your philosophical questions
In railroad design it is important for the track to not be a curved segment of a circle (starting from a straight line), as the acceleration forces start suddenly (aka a high jerk). So this concept exists and is well known in some circles (heh).
>Do you have proof for that, or is this like audiophiles asking for gold connectors because "they make the sound better"?
The proof is that roughly 100% of cars have components designed to limit this.
The proof is that roughly 100% of cars have components designed to limit this.
It is an active research topic in train engineering.
Lore has it that Snap, Crackle, and Pop are named after the three elves on Kellogg’s Rice Krispies cereal boxes.
I use them in the context of N-Body Simulations. Curious to learn about other contexts for their use - anyone?
https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_deriv...
I use them in the context of N-Body Simulations. Curious to learn about other contexts for their use - anyone?
https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_deriv...
The color printing industry has Snap, Gracol and Swop. Yes, the Gracol logo is a blackbird perched on CMYK dots.
https://duckduckgo.com/?q=snap+gracol+swop
https://duckduckgo.com/?q=snap+gracol+swop
Like grackle I presume.
> Lore has it that Snap, Crackle, and Pop are named after the three elves on Kellogg’s Rice Krispies cereal boxes.
Surely this is true. Is there any likely alternative explanation?
Surely this is true. Is there any likely alternative explanation?
Do these higher order derivatives say anything meaningful?
I always got the sense from physics that outside of purely mathematical constructions such as Taylor series, higher order time derivatives aren't providing much interesting information. Though I'm not sure whether this is the inherent laziness of physicist math[1] or a property of the forces in nature.
[1] since e^x = 1 + x is generally true, why'd you even need a second order derivative
I always got the sense from physics that outside of purely mathematical constructions such as Taylor series, higher order time derivatives aren't providing much interesting information. Though I'm not sure whether this is the inherent laziness of physicist math[1] or a property of the forces in nature.
[1] since e^x = 1 + x is generally true, why'd you even need a second order derivative
Yes. That is the point of the article.
> Jerk and snap can be observed in various areas of physics and engineering. In physics and engineering jerk and snap should always be considered when vibration occurs and particularly when this excitation induces multi-resonant modes of vibration. They should also be considered at all times when a transition occurs such as: start up and shutdown; take-off and landing; and accelerating and decelerating.
> Acceleration without jerk is just a static load, and therefore constant acceleration alone could never cause vibration. In a machine shop, a toolmaker can damage the mill or the job if the setup starts vibrating. This vibration happens because of jerk and snap.
> In mechanical engineering it is important in automotive design to ensure that the cam-follower does not jump off the camshaft. It is also important in manufacturing processes as rapid changes in acceleration of a cutting tool can lead to premature tool wear and result in an uneven and rough surface finish.
> In civil engineering railway train tracks and roads should be designed for a smooth exit from a straight section into a curve, and it is common to use a transition called a clothoid, which is part of a Cornu spiral (also referred to as an Euler spiral). When a clothoid is implemented the change in acceleration is not abrupt and the levels of jerk and possibly snap are significantly reduced. If the transition between different radii of curvature is sudden, the transition is uncomfortable for passengers and potentially dangerous as it could cause the car or train to be thrown off the road or track. With good physics design engineers are attempting to produce a gradual jerk and constant snap, which gives a smooth increase in radial acceleration, or preferably a zero snap, constant jerk, and linear increase in radial acceleration. Just as road and railway engineers design out jerk and snap using the clothoid transition so, too, do roller coaster designers when they design loops and helices for the roller coasters [11, 12].
> Jerk and snap can be observed in various areas of physics and engineering. In physics and engineering jerk and snap should always be considered when vibration occurs and particularly when this excitation induces multi-resonant modes of vibration. They should also be considered at all times when a transition occurs such as: start up and shutdown; take-off and landing; and accelerating and decelerating.
> Acceleration without jerk is just a static load, and therefore constant acceleration alone could never cause vibration. In a machine shop, a toolmaker can damage the mill or the job if the setup starts vibrating. This vibration happens because of jerk and snap.
> In mechanical engineering it is important in automotive design to ensure that the cam-follower does not jump off the camshaft. It is also important in manufacturing processes as rapid changes in acceleration of a cutting tool can lead to premature tool wear and result in an uneven and rough surface finish.
> In civil engineering railway train tracks and roads should be designed for a smooth exit from a straight section into a curve, and it is common to use a transition called a clothoid, which is part of a Cornu spiral (also referred to as an Euler spiral). When a clothoid is implemented the change in acceleration is not abrupt and the levels of jerk and possibly snap are significantly reduced. If the transition between different radii of curvature is sudden, the transition is uncomfortable for passengers and potentially dangerous as it could cause the car or train to be thrown off the road or track. With good physics design engineers are attempting to produce a gradual jerk and constant snap, which gives a smooth increase in radial acceleration, or preferably a zero snap, constant jerk, and linear increase in radial acceleration. Just as road and railway engineers design out jerk and snap using the clothoid transition so, too, do roller coaster designers when they design loops and helices for the roller coasters [11, 12].
I think up to jerk is intuitive, even if the term isn't well-known. Most people have no problem figuring out how to ease-up on brakes in a car, and a hobbyist can usually figure out how to make things smoother when ramping up or down a motor.
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.
> 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).
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).
How do you know this is not second derivative (acceleration), but the third or higher?
Genuinely curious.
Genuinely curious.
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).
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).
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).
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).
>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).
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).
> 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.
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.
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.
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.
Here is a video of a guy that tried to automate a grinding machine by installing an electric motor. Initially the movement was very unsatisfactory, it was not smooth, or very jerky. He then received an upgraded motor that included a “jerk control” feature and the movement of his machine became smooth.
It came as a surprise to me but it seems like jerk is something that can be felt in real life.
https://youtu.be/FPhNc6GwX1o?si=8cf7wU14puB8lsaa
It came as a surprise to me but it seems like jerk is something that can be felt in real life.
https://youtu.be/FPhNc6GwX1o?si=8cf7wU14puB8lsaa
If you're driving along and want to stop for the traffic lights, you start decelerating. The car in front of you slams the brakes and leaves less space then you anticipated. You now need to decelerate faster. That's negative jerk. If you apply the change in deceleration instantaneously, you will also experience jerkiness in your braking (= way to remember what this derivative is called).
Yes. The higher derivates are useful in many cases, both as sought properties and observations. The invariances implied by relativity,(the trivial notion that the universe behaves the same regardless of where you select the center), mean that most laws are defined on the second derivative. Taylor approximations are useful to approximate something locally, but properties of the system over wider regions generally need to account for the higher derivatives. You can see this in e.g. simulating a system over time requires that the derivatives at the borders of the valid taylor approximation region to be included as diracs.
Or in other words, you can approximate exp(x) as a set of first order taylor approximations that each covers a small window to arbitrary precision, but the combination of them is still has well defined higher derivatives that are not 0.
Or in other words, you can approximate exp(x) as a set of first order taylor approximations that each covers a small window to arbitrary precision, but the combination of them is still has well defined higher derivatives that are not 0.
I believe they have applications in missle guidance systems.
I cannot remember what it's called but essentially given a target position in space the missle uses parametric data about its current position/orientation/speed and their higher derivatives to dead reckon about where it is in regards to the target.
Anyone remember what that's called? I went on a rabbit hole with it a few years ago, it's really interesting math and programming. Everything works basically stateless except for current instrument data, last position and target position from what I remember.
I cannot remember what it's called but essentially given a target position in space the missle uses parametric data about its current position/orientation/speed and their higher derivatives to dead reckon about where it is in regards to the target.
Anyone remember what that's called? I went on a rabbit hole with it a few years ago, it's really interesting math and programming. Everything works basically stateless except for current instrument data, last position and target position from what I remember.
Accelerometers and gyros are used and integrated to get their higher order information. However the trick is neither sensor type is perfect so you fuse as much data as needed to get close to good and correct for drifts
Kalman filters come up a lot, maybe relevant to the terms you're looking for
Kalman filters come up a lot, maybe relevant to the terms you're looking for
> Do these higher order derivatives say anything meaningful?
I'm becoming seasick due to a jerkiness of a car. Not due to a speed or a acceleration, but it is jerk that does it for me. I watched it from my childhood, I hated trolleybuses for that: they are electric and they tend to change acceleration instantly. But I didn't understood how it works until much later.
I'm becoming seasick due to a jerkiness of a car. Not due to a speed or a acceleration, but it is jerk that does it for me. I watched it from my childhood, I hated trolleybuses for that: they are electric and they tend to change acceleration instantly. But I didn't understood how it works until much later.
> [1] since e^x = 1 + x is generally true, why'd you even need a second order derivative
Only true for small x (less than 1).
Only true for small x (less than 1).
The joke is that physicists aren't always rigorous enough to add that caveat.
Bob Pease brought this into the discussion space over 30 years ago: https://www.electronicdesign.com/technologies/embedded/digit...
Jerk, Snap, Crackle, and Pop are the only ones I thought had agreed upon names. But my understanding is probably 20 years out of date at this point.
However, the paper says they’re not commonly taught, but jerk is taught in many high school (AP) Physics classes — we have to keep our balance by noticing the change in acceleration.
However, the paper says they’re not commonly taught, but jerk is taught in many high school (AP) Physics classes — we have to keep our balance by noticing the change in acceleration.
Here in Victoria (Australia), we commonly see road signs stating that "speed kills" whereas the reality is that it is the jerk that kills.
No, it's the acceleration. That's what produces the forces. But there is usually a correlation between jerk and acceleration in a collision, given a certain amount of energy (speed^2)
I didn't think my play on words would cause such controversy about acceleration and jerk. Mayhaps I should not be making "Dad jokes" here.
WBRTC in India used to have noticeboards and buses painted with “Safe Drive Save Life” and “Save Drive Safe Life”
I’m not sure anyone noticed the difference between the two
I’m not sure anyone noticed the difference between the two
Here are my interpretations:
* If you drive safely, then you can save someone's life by avoiding a crash.
* If you save a driving trip (and instead walk/bike/transit/stay-home), you will have a life of safety.
* If you drive safely, then you can save someone's life by avoiding a crash.
* If you save a driving trip (and instead walk/bike/transit/stay-home), you will have a life of safety.
As Jeremy Clarkson put it "Speed never killed anybody. Suddenly becoming stationary? That's what gets you."
I have a pair of matching Nike socks, where one of them said that, and the other one replies “fast is faster”
If you want to be pedantic, you could argue that it is the collision that kills.
It isn't, though. It's the jerk.
The difference between falling from a height and landing on a trampoline, and landing on concrete from the same height, is that the trampoline smoothly accelerates you to a halt once you collide with it. The concrete does so much more rapidly: that's jerk. Both of these are collisions with the same amount of force behind them.
The difference between falling from a height and landing on a trampoline, and landing on concrete from the same height, is that the trampoline smoothly accelerates you to a halt once you collide with it. The concrete does so much more rapidly: that's jerk. Both of these are collisions with the same amount of force behind them.
No, it's the acceleration. The forces are absolutely different between your two examples. The energy is the same, but in one case the energy is dissipated over a longer time, requiring less acceleration and thus force. Jerk and acceleration will tend to be correlated in collisions, but you can construct cases with very high jerk and low acceleration which are just fine and cases with very high acceleration and low jerk which are not at all safe, though the latter case will generally require a lot more energy (fighter jets and rockets, for example).
Airbags are the most important safety feature in cars. They don't change the rate of acceleration: the car comes to a halt at the same speed, therefore, the person inside does as well.
What they affect is jerk.
What they affect is jerk.
No, they absolutely do change the rate at which the person inside stops: most importantly they affect the amount of time it takes for their head to stop moving, by starting to decelerate it before it hits the dashboard (the seatbelts also contribute to this).
In other words they change the rate of change of the acceleration. We call that derivative jerk. Jerk is responsible for the shockwave which would otherwise rattle the brain around, it's also the chief factor in producing whiplash.
[deleted]
Matt Parker, calling himself Stand up Maths has an excellent (and mildly amusing) video about this. Spoiler, he get's a ride on a motorcycle around a race track, logs some data and tries to find the higher orders of derivatives from that data.
https://www.youtube.com/watch?v=sB2X5l5CsNs
https://www.youtube.com/watch?v=sB2X5l5CsNs
Jerk (time derivative of acceleration) had an important role in the Apollo missions. It was used to compute TGO (Time-To-Go) for the lunar module's landing program. TGO is the primary variable for the quadratic function, and it is combined with the current/desired state vectors to compute the throttle setting and thrust vector.
How about some software for jerk limited trajectory computation: https://github.com/pantor/ruckig
too bad it uses an odd cloud-based model for waypoint handling.
Anyone know of any software for jerk limited planning which allows position constraints? Whats the fastest jerk limited path from A to B the doesn't pass though the forbidden zone. The jerk limited path may deviate from a straight line. So even when the A to B line is admissible, a straightforwardly constructed jerk limited path may not be.
too bad it uses an odd cloud-based model for waypoint handling.
Anyone know of any software for jerk limited planning which allows position constraints? Whats the fastest jerk limited path from A to B the doesn't pass though the forbidden zone. The jerk limited path may deviate from a straight line. So even when the A to B line is admissible, a straightforwardly constructed jerk limited path may not be.
Someone once explained this to me in a very intuitive way. It goes like this:
You’re sitting in the driver’s seat of a car. It is standing still.
You push the gas pedal down 2 cm and hold it there. Your car begins accelerating. That’s the second derivative.
You start pressing your foot further on the gas pedal. Your foot has a velocity on the gas pedal. It is causing your car’s acceleration to grow! That’s jerk.
If you push your foot on the gas pedal faster and faster your foot accelerates on the gas pedal. That contributes to the cars snap.
You’re sitting in the driver’s seat of a car. It is standing still.
You push the gas pedal down 2 cm and hold it there. Your car begins accelerating. That’s the second derivative.
You start pressing your foot further on the gas pedal. Your foot has a velocity on the gas pedal. It is causing your car’s acceleration to grow! That’s jerk.
If you push your foot on the gas pedal faster and faster your foot accelerates on the gas pedal. That contributes to the cars snap.
For people who understand sound - how much can acceleration, jerk and snap affect the tone a piano creates?
A (mis)conception of the piano is that it is purely percussive and velocity is the only parameter you control for voicing on the piano but professionals would beg to differ...
A (mis)conception of the piano is that it is purely percussive and velocity is the only parameter you control for voicing on the piano but professionals would beg to differ...
For playing a note on a piano and doing nothing more, I'd like to suggest that the velocity of the hammer as it strikes a string is the only variable that can be adjusted by the player.
A hammer in a piano always moves on a fixed path. It always strikes the same part of the string, and it always does so in the same orientation. And after it strikes that string, it always falls away from it. That's how that part works.
Striking a percussion instrument with a stick (such as a wooden block) has more variables to toy around with than playing a note on a piano does.
But there's a lot more going on in a piano than striking strings: Strings are also muted, and the degree of muting can be manipulated. It is not binary.
And, of course, pianos are polyphonic: With ten fingers, we can strike ten different [sets of] strings at different velocities and at different times, and we can even mute them to individually-different degrees.
And then, there's also the pedals...
A hammer in a piano always moves on a fixed path. It always strikes the same part of the string, and it always does so in the same orientation. And after it strikes that string, it always falls away from it. That's how that part works.
Striking a percussion instrument with a stick (such as a wooden block) has more variables to toy around with than playing a note on a piano does.
But there's a lot more going on in a piano than striking strings: Strings are also muted, and the degree of muting can be manipulated. It is not binary.
And, of course, pianos are polyphonic: With ten fingers, we can strike ten different [sets of] strings at different velocities and at different times, and we can even mute them to individually-different degrees.
And then, there's also the pedals...
Serious, well-written, scientific information that also references children's breakfast cereal?
Moar please!
Moar please!
Is there ever a higher order derivative that is a constant in the real world? And is every real world signal continuous in every higher order derivative?
Yes, the derivatives of time are relatively constant.
Jerk is why you don't want a straight track to abruptly turn into a circular arc. Unless, perhaps, it's for a roller coaster.
i remembrer using squaed sinus acceleration curves profile for robotique at school to minimise jerk
Great find EndXA!! You melted my brain a bit.
It’s very common to say that a car has acceleration but since the introduction of powerful electric cars like Tesla, that quickness you feel is the third derivative called jerk, or the acceleration of acceleration. Jerk is a little strange to think of because it feels a lot like acceleration but for you electric car owners who know about that quick 0-60, it’s jerk which makes you gasp and smile.
Jerks on roller coasters
What value is gained from using these terms over just saying nth derivative?
> So, there must be some jerk involved.
Me every day before checking git blame.
Me every day before checking git blame.
Careful, you will give the agile people more measurements to fudge. "No no, we don't estimate jerk directly. We compute it from our acceleration."
> The terms jerk and snap mean very little to most people, including physicists and engineers.
Almost 20 years ago we defined jerk into our standards for lift applications. I know jerk is an important parameter for any modern rotating machine that includes gears.
While in lift applications it is known as the roller coaster effect, people in different parts of the world have a different taste on when they want to use a lift. I know I over simplify when I say, that American people want to have the gut feeling when riding a lift, especially an express lift in those high buildings. In difference in Asian countries the lift ride must be smooth as possible. They don't like to have the feeling of riding a lift at all. In Europe it is something in between. Lift manufacturers have to respect those (end) costumers otherwise the are not chosen.
The same in any rotating machine with some sort of gears. Because jerk and those higher orders contribute to the wear and tear of gears. As you want to have longer lasting gears many modern machine manufacturers limit those parameters to reduce wear and tear. So, with a little software change I can demand a higher price because service and maintenance can be reduced.