Are there other endeavors where snap, crackle and pop are used? At what point does one decide that you’ve gone deep enough into derivatives?
I would imagine that gun recoil and crash safety would involve some of the finer derivatives.
Are there other endeavors where snap, crackle and pop are used? At what point does one decide that you’ve gone deep enough into derivatives?
I would imagine that gun recoil and crash safety would involve some of the finer derivatives.
Not that I knew before you ask, but automating movement between two set points seems to provide many opportunities to use high order derivatives.
" The immediate onset of acceleration has a large jerk that can be detrimental to equipment, can result in loud bangs, and can be uncomfortable for riders in transportation systems. A better strategy is to ramp up the acceleration by placing a limit on jerk. A potentially even better strategy is to ramp up the jerk by
limiting the next higher derivative, and so on. A solution is presented for a minimum time move between stationary positions with limits on any number of derivatives.
There are no standard names for derivatives higher than third. Snap, crackle, and pop are not official but have been used respectively for the fourth, fifth, and sixth derivatives. An internet search has found references to these derivative names which then qualify their use by respectively calling them “facetious” and “not serious,” as though engineers are not entitled to an easily remembered mnemonic. Most people know Snap, Crackle, and Pop as the three elves on Kellogg’s Rice Krispies cereal boxes, introduced in the early 1930s.
Algorithms are presented and then compared for two strategies: 1) a many-derivative-limited trajectory between stationary points, and 2) a two-derivative-limited trajectory followed by a linear filter. The so-called “linear jerk filter” reduces not just the jerk but all of the higher derivatives. A minimum time move with limits on velocity and acceleration is a classic result of optimal control, which has the very nice feature that it can be implemented starting from any point in the error and velocity phase space, in other words, a change can be made in the target before coming to a stop. The same is theoretically true for the first strategy, but the implementation starting from any point in the multi-dimensional phase space is very complicated. The second approach has the not insignificant advantage of being much simpler and hence more robust. But which strategy to use depends on the application. The first approach is good for numerically controlled moves for tools, printers, amusement park rides, and the like. The second strategy is better for command following applications as varied as aircraft autopilots and telescope mount control."
Given that “barn” was adopted as a name for nuclear cross section, then snap/crackle/pop for acceleration derivatives seem perfectly reasonable to me.
This discussion of the jerk parameter makes me think of orbital launch vehicles. Some of them use liquid-fueled engines that slowly ramp up to full thrust, but some employ solid rocket boosters that appear to go from zero thrust to full thrust in a tiny fraction of a second. ISTM that structures as large and delicately built as those probably have a meaningful degree of elasticity that must affect how quickly solid-fuel motors are designed to develop full thrust (i.e. how large the jerk is allowed to be).
Thinking on it a bit further, even liquid-fueled engines don’t save a launch vehicle from jerk: they develop full thrust before the hold-down bolts are severed, so it seems like no matter what the propulsion system is, the launch vehicle is pretty much guaranteed to experience a very high jerk value at the moment of release.
The Saturn 5 used a fabulous mechanism to control the first 6 inches of flight. After the hold down arms released, the vehicle was still held down to the pad by 12 tapered pins. These pins were in turn restrained inside dies. The force of the launching rocket extruded the pins through the dies gently releasing the rocket.
There were no explosive bolts, the booster was always going to win.
When the value or approximation for it is infinity high infinitesimally thin spikes ?? then the next one and all subsequent ones are spikes too.
Say acceleration is 0 until it is 5 ms^-2 from t=10… well the jerk then is a spike at t=10 … it wont help our models accuracy by trying to include it in our model. but it did exist, it caused the jump at t=10 … After that the snap,crackle,pop,etc are a spike at t=10… existing in theory , in practice they are of finite width, but since they weren’t measured with any time span, we can’t include them
The spikes do not lead to greater accuracy of the model, so there’s no reason to make use of them.
If the pulse was wide enough that you couldnt treat it as a spike, you would use it in your model.
I found a paper on devices to measure snap and crackle. No pop.
Thanks, this jarred my memory; it’s something my dad told me about many years ago.
It looks like the space shuttle might not have used a system like that. NASA used to have the "Space Shuttle News Reference Manual, but I can’t find it on NASA’s website anymore. Instead, there’s this copy hosted elsewhere. The Launch and Flight Operations section has a detailed list of events occurring during pre-launch countdown, and it includes the following:
At T minus zero, the holddown explosive bolts and the T-O umbilical explosive bolts are blown by command from the on-board computers and the SRBs ignite.
So maybe the shuttle stack isn’t quite as fragile as the Saturn V was.
I tried googling “space shuttle launch jerk” (without the quotes), and interestingly, Jeff Bezos was among the images in the results. I did however find this stack exchange discussion, which led me to this NASA PDF, “ISS Crew Transportation and
Services Requirements Document”, which says the following:
4.3.10.2.5 Acceleration Rate of Change
The crew exposure to jerk during sustained events shall be verified by analysis. The analysis shall use a validated simulation to identify and assess bounding acceleration cases including GN&C, vehicle, and environmental dispersions. The verification shall be considered successful when the analysis indicates that the simulated jerk is no greater than 500 g/s during any nonimpact phase of flight. [V.CTS.220]
However, this appears to be about limitations for the safety of the crew and not necessarily the integrity of whatever launch vehicle they’re strapped to.
The Space Launch System is so new there doesn’t seem to be as much detailed information publicly available yet. The most I’ve been able to find about it is this:
Unlike the space shuttle, there are no hold-down bolts connecting the solid rocket boosters to the mobile launch platform, which was designed specifically for the Space Launch System.
Four support posts, fitted with strain gauges to measure loads during stacking, rollout, and launch, serve as structural mounting points for each booster on the deck of the mobile platform.
I guess it’s not as tippy as the space shuttle was, with its off-center engine ignition sequence and the resulting “twang” event. Still weird to think of it just resting on its own weight until launch.
That’s the kind of really cool creative mechanical engineering that sometimes seems missing in our digital “it could all be controlled by a computer” age. Thanks for that story.
I like the “non-impact” qualifier in there. How … thorough … of them. And which exactly are the planned impact phases of flight? Well?
Engineers have a different, and drier, sense of gallows humor than do crewmembers. But it’s still the same impulse. As long as said impulse is less than 500g/s we’re good.