[HN Gopher] Beyond velocity and acceleration: jerk, snap and hig...
___________________________________________________________________
Beyond velocity and acceleration: jerk, snap and higher derivatives
(2016)
Author : EndXA
Score : 137 points
Date : 2024-06-19 10:16 UTC (12 hours ago)
(HTM) web link (iopscience.iop.org)
(TXT) w3m dump (iopscience.iop.org)
| Rygian wrote:
| The proposed hierarchy is: - position -
| velocity - acceleration - jerk - snap -
| crackle - pop - "and so on"
|
| I'm good up to jerk, but not really sure for the remaining
| higher-order concepts.
| pestatije wrote:
| this is the same as dimensions
| DrNosferatu wrote:
| 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...
| ahazred8ta wrote:
| 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
| demondemidi wrote:
| Like grackle I presume.
| n4r9 wrote:
| > 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?
| marginalia_nu wrote:
| 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
| azernik wrote:
| 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].
| johnwalkr wrote:
| 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.
| fellerts wrote:
| 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.
| playingalong wrote:
| How do you know this is not second derivative (acceleration),
| but the third or higher?
|
| Genuinely curious.
| fellerts wrote:
| 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).
| myrmidon wrote:
| 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).
| short_sells_poo wrote:
| > 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).
| itsoktocry wrote:
| > _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).
| trgn wrote:
| 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.
| readams wrote:
| 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.
| fellerts wrote:
| > 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.
| bux93 wrote:
| 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).
| hristov wrote:
| 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
| glitchc wrote:
| > [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).
| marginalia_nu wrote:
| The joke is that physicists aren't always rigorous enough to
| add that caveat.
| ImPleadThe5th wrote:
| 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.
| tomek_ycomb wrote:
| 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
| vinc wrote:
| 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.
| kevindamm wrote:
| DDoS attacks, high inflection from a lot of disparate sources.
| Akronymus wrote:
| Snap could be the acceleration of "influencers" sharing an
| article? Basically, how fast it spreads from one to many
| frenchyatwork wrote:
| That might be more exponential than polynomial.
| londons_explore wrote:
| 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.
| amelius wrote:
| Do you have proof for that, or is this like audiophiles asking
| for gold connectors because "they make the sound better"?
| analog31 wrote:
| 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.
| robertlagrant wrote:
| 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.
| sokoloff wrote:
| 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.
| lloeki wrote:
| 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.
| sokoloff wrote:
| 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.
| setopt wrote:
| 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.
| amelius wrote:
| 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?
| ccccccc1 wrote:
| is it physically possible to have non-continuous
| acceleration?
| shagie wrote:
| 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.
| zardo wrote:
| 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.
| shagie wrote:
| 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 Da/Dt while fuel is consumed and
| mass changes.
|
| There are discontinuities to the graph when engines are
| shut down and stages decoupled.
| sokoloff wrote:
| 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.
| tomek_ycomb wrote:
| It's nature, it's continuous at small enough scales.
|
| But, checkout Zeno's paradox for more on your
| philosophical questions
| setopt wrote:
| 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.
| amelius wrote:
| Voltages can change abruptly. Therefore, forces can
| change abruptly, and hence acceleration as well.
| tomek_ycomb wrote:
| 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
| NovemberWhiskey wrote:
| 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
| soVeryTired wrote:
| 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!
| amelius wrote:
| 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.
| soVeryTired wrote:
| Snap and crackle I couldn't tell you about. But jerk is
| definitely important.
| user_7832 wrote:
| 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).
| aredox wrote:
| It is an active research topic in train engineering.
| constantcrying wrote:
| >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.
| constantcrying wrote:
| >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.
| amelius wrote:
| 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?
| constantcrying wrote:
| >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.
| thequux wrote:
| 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.
| owisd wrote:
| 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.
| anymouse123456 wrote:
| Serious, well-written, scientific information that also
| references children's breakfast cereal?
|
| Moar please!
| numbol wrote:
| Here you go https://en.wikipedia.org/wiki/Cheerios_effect
| Liftyee wrote:
| 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
| VHRanger wrote:
| This is breaking my brain a little, any eli5?
| vasco wrote:
| 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.
| kruczek wrote:
| 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.
| basil-rash wrote:
| 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.
| dmoy wrote:
| 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.
| oldandtired wrote:
| Here in Victoria (Australia), we commonly see road signs stating
| that "speed kills" whereas the reality is that it is the jerk
| that kills.
| Gooblebrai wrote:
| If you want to be pedantic, you could argue that it is the
| collision that kills.
| user_7832 wrote:
| Is it not life that kills?
| account42 wrote:
| I'm pretty sure it's time.
| samatman wrote:
| 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.
| selimthegrim wrote:
| I have a pair of matching Nike socks, where one of them said
| that, and the other one replies "fast is faster"
| selimthegrim wrote:
| 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
| nayuki wrote:
| 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.
| crabmusket wrote:
| > So, there must be some jerk involved.
|
| Me every day before checking git blame.
| demondemidi wrote:
| 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?
| account42 wrote:
| Yes, the derivatives of time are relatively constant.
| mensetmanusman wrote:
| 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"
| zaps wrote:
| Jerks on roller coasters
| PinguTS wrote:
| I know, this is an old paper, but I don't follow the this
| assumption:
|
| > 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.
| account42 wrote:
| > 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.
| xxpor wrote:
| They're the preferences of the buying managers.
| amelius wrote:
| 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.
| peddling-brink wrote:
| Corkscrew lift.
| MaxBarraclough wrote:
| I imagine a spinning lift would be easier.
| function_seven wrote:
| Finally an elevator that will force other occupants to
| respect my personal space.
|
| We're all up against the wall during this ascent!
| matsemann wrote:
| 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.
| fbdab103 wrote:
| 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.
| failbuffer wrote:
| You could just as well ask "why not give the fastest ride
| possible so everyone saves time?"
| bowsamic wrote:
| 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?
| xscott wrote:
| 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.
| bowsamic wrote:
| 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?
| xscott wrote:
| 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?
| core_dumped wrote:
| 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
| pfortuny wrote:
| 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...
| bowsamic wrote:
| > 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?
| Sharlin wrote:
| 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).
| tomek_ycomb wrote:
| 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.
| meindnoch wrote:
| 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.
| wlesieutre wrote:
| 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.
| matsemann wrote:
| That's why loops on roller coasters aren't perfect circles as
| well then, I guess?
| wlesieutre wrote:
| 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.
| malfmalf wrote:
| 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
| kovezd wrote:
| The terms are also understood in economics as prudence, and
| template. Albeit, not widely used.
| fnordpiglet wrote:
| 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 ?
| godber wrote:
| Great find EndXA!! You melted my brain a bit.
| zokier wrote:
| 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
| debo_ wrote:
| 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."
| 01100011 wrote:
| Bob Pease brought this into the discussion space over 30 years
| ago:
| https://www.electronicdesign.com/technologies/embedded/digit...
| djtango wrote:
| 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...
| ssl-3 wrote:
| 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...
| sehugg wrote:
| 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.
| Zobat wrote:
| 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
| hbarka wrote:
| 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.
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