Why roller coaster loops aren’t circular anymore
vox.com
vox.com
The first derivative of postion (with respect to time) is velocity. The second derivative is acceleration (ie rate of change of velocity). And the third derivative is jerk (rate of change of acceleration).
And 'jerk' has to be kept below a certain threshold for humans to find movement comfortable.
13² − 10² = 69
And this is also why the passengers jerk of a vehicle jerk backwards after it comes to a complete stop. Their muscles statically counter the relative forwards acceleration of their torsos during braking and require time to react to the acceleration suddenly going away. This effect can be prevented by gradually letting off the brake before reapplying it fully upon stopping, but few drivers and rapid transit systems seem to be aware.
I find that amazing. What the heck are drivers ed instructors doing? It's not just hard on the passengers, it's hard on the machinery.
It's the same with the clutch. I've driven with enough people who fancy themselves as great shifters, but they jerk the hell out of the clutch every time, never attempting to match the shaft speed with the engine speed. If I comment on it, they always deny doing that :-/
If I'm on my game, I can shift smoother than an automatic. The bonus is the clutch will last a very long time.
And you can tell how somebody treats their car by examining how long the clutch lasts, if they drive a manual.
I mean to be completely fair - this is not their job. Driving instructors are there to keep everyone on the road safe - first.
Dinging me over their interpretations of ambiguous driving laws, if my experience is any indication.
Not a double clutch one, e.g. DSG
1) lots of comments are attributing the jerk felt by occupants to the vehicle suspension. But that isn't the case! The occupants visibly move backwards relative to the car body, but the backwards motion of the car itself should rather have the opposite effect.
2) a commenter contradicts what several commenters here have noticed:
> I wager this has to do with the driver; most drivers I've noticed don't ease up off the breaks when slowing down, and so the 'slowing force' feels like it ramps up along the deceleration profile, up until the point when the car comes to a complete start and there's a 'jerk'.
[1] https://www.reddit.com/r/askscience/comments/20mljk/what_cau...
The only video linked to in that thread has been removed so I wasn't able to see this, but I will point out that the timing is critical to interpreting this observation. During deceleration, the occupants will move forward relative to the car body so that the car can apply a decelerating force to their bodies (via seat belts or friction against the seats and floor of the car). At some point after the car has stopped, they will necessarily move back to their neutral position. This will have nothing to do with the transient motion of the car when acceleration drops to zero.
I will also note that it is not that difficult to come to a complete stop with no perceivable transient if you ease off the brakes as the car comes to a halt. It's actually a useful skill to cultivate IMHO.
This is surprising to read. Everyone whose car I've ridden in knows to do that, and it's only in extremely urgent and unexpected stops where it's neglected. Also, when fully stopped, only minimal pressure should be necessary to keep the car still.
Why? To keep the brake fluid lines from bursting or something?
I also do that, and don't know anyone who doesn't. I vaguely remember that I learned it in driving school, most likely because my driving instructor didn't want to be jerked around on the passenger seat for an hour every week.
Train/tram drivers here also usually do that in stations, except when they try to make up for delays, or when they have wrongly estimated the breaking distance.
For one instance multiple units (especially electrically powered ones) commonly have computerised braking controls, often transition from dynamic to friction braking shortly before coming to a standstill, and might possibly have some sort of automatically applied parking brake.
If the manufacturer didn't properly adjust this whole system, the friction brake as it takes over for the last few kph might be applied with too much of a "bite" and therefore cause a jerky stop which even a skilled driver might not be able to fully prevent.
In some cars there's hysteresis in the brake pedal (perhaps caused by the booster or self-energizing system) that makes it hard to smoothly release the brake even when the driver tries to. But metros seem to increase their braking force—visible in standing passengers leaning progressively more—as speed decreases. Is there some physical cause to that?
> only minimal pressure should be necessary
I gathered that it was best practice to fully brake when stopped in case someone hits you, especially at a light where you might be rear-ended and roll into the intersection.
Is this why it seems to be mostly Americans that are into the idea of self-driving cars, because the standard of driving is so low?
Just for the record, the transition curve is usually (not always but very often ) a clothoid (or Euler's spiral or Cornu spiral)
On the surface (or when the computer control system was borked) the starts and stops were a lot less pleasant.
If you have a ball sitting on the floor in the aisle of a stationary bus and the bus starts accelerating forward the ball rolls toward the back of the bus. If you have a bus moving at a constant velocity and it start decelerating the ball rolls toward the front of the bus.
Suppose you also have a helium balloon floating in the bus. Does it also move toward the back of the bus when the bus accelerates and toward the front when the bus decelerates? Or does it stay where it is? Or does it move toward the front when the bus accelerates and toward the back when the bus decelerates?
It helps (me) to imagine an air bubble in a sealed, nearly-full fish tank on that same accelerating bus. The heavier water gets "flung" harder away from the direction of acceleration, and the bubble gets pushed out of the way in the opposite direction. Same principle.
It's not strictly a matter of threshold -- people might tolerate a higher jerk if it's for a much shorter duration, for example. In practice it doesn't much matter which metric you minimize; you'll end up with similar results. The simplest option is to minimize the mean absolute jerk, which has the side benefit of utterly confusing any non-physics-literate people listening in. (You want to do what to whom?)
They call these constraints by G and a number.
G1 would be a positional constraint: the two surfaces meet each other at the same point
G2 tangential: same as G1, but the surfaces are tangential
G3: same as G2, but the curvature (radius^-1) of the surfaces is the same at the point where the two meet. This essentially means the curvature combs of the surfaces shall meet at the same position (G1)
G4: same as G3, only now the meeting curvature combs have to be tangential as well
G5: same as G4, only now the curvature combs of the curvature combs have to meet at the same position
This makes me think "tangential to what?".
Do you mean that, along the seam between G1 and G2, the tangent plane to G1 at a given point is equal to the tangent plane to G2 at the same point?
Here is how it is defined in terms of basis vectors. https://people.eecs.berkeley.edu/~jfc/cs184f98/lec19/lec19.h...
https://99percentinvisible.org/article/circling-square-desig...
https://www.datagenetics.com/blog/march42014/index.html
Vox re-heating a gizmodo article[0] which re-publishes (with permission) the one above.
[0]: https://gizmodo.com/why-roller-coaster-loops-are-never-circu...
One that I've used as inspiration for a programming class I was teaching is his analysis of Snakes and Ladders: https://datagenetics.com/blog/november12011/index.html
An inverted loop, where the loop is lower than the track, and with a very long train, where the center of mass continues to decrease in height due to the part of the train not presently looping.
Also maybe of interest is Blue Flash [3], a backyard roller coaster that has a loop that reminds me of old school circular loops.
[2] https://en.wikipedia.org/wiki/Tsunami_(roller_coaster)
[3] https://www.atlasobscura.com/places/blue-flash-backyard-roll...
I had no idea roller coasters have been around this long. The photos are laugh-out-loud terrifying. I was shocked that anyone would pay to ride them until I read the quote above. Now it makes sense. I’d pay to watch that too!
We used to have a much different view on systematic rare danger.
When I was a kid, we used to rid maybe 6 kids in the back of a pickup truck flat bed.
That was normal. It would not only be illegal today, but probably considered very immoral.
Hockey players didn't even wear helmets, not even the goalies (!).
Nobody wore helmets when I grew up skiing, now almost everyone does.
We are considerably safer about everything today.
Likewise, I've never once worn a seatbelt in an NYC taxi.
We have more science, more education. 10% of kids under age 1 would die at the turn of the century (1900), which means, everyone knew a family with a child that had died, and that's traumatic.
Our views of safety and risk have evolved.
My grandfather, he worked in a lumber camp, the stories ... my god.
We also react to it differently now. Even in our language i.e. 'I feel unsafe' or people talk about 'harm' or 'violence' with just language.
where i live, because of paucity of transportation means, it is not uncommon to have the back door of a car straight open and 3 kids sit there, dangling their feet. that is considered very normal in these parts of the world.
A video of the coaster in the photo exists (the playback framerate seems somewhat too fast): https://commons.wikimedia.org/wiki/File:Flip_Flap_Railway_ea...
Modern tubular steel rails also allow for rickety-looking yet safe single-car coasters: https://commons.wikimedia.org/wiki/File:Rat%C3%B3n_Vacil%C3%...
https://upload.wikimedia.org/wikipedia/commons/6/68/Chicago-...
Note how large the cars relative to the tiny people standing in them. This thing was unimaginably massive. It's easy to think of 1893 as being before the modern technological era, but we were more modern than most people like to think.
Curiously Dubins paths do have instantaneous steering changes. https://en.wikipedia.org/wiki/Dubins_path
Once you see this, you begin to notice it everywhere, just like with kerning. Apple used both ways on iPhones for rounding the phone's corners, iirc. Also I've been told that the principle applies to road turns: you don't want people to have to suddenly turn into the curve. (In related news, I wish a month of bad hiccups on Herman Tilke.)
https://99percentinvisible.org/article/circling-square-desig...
[1] https://en.wikipedia.org/wiki/Norm_(mathematics)#p-norm
[2] https://en.wikipedia.org/wiki/Lp_space#/media/File:Vector-p-...
I can't pin down which part that I hate most, the "stylish" presentation with random SFX and virtual pen circling around, or the fact they always insert some super low quality video conference footage instead of just letting the narrator paraphrasing (I get it they're the domain experts, but still..).
A true circular loop the entrance and exit would be directly side by side.
"You can check-out any time you like But you can never leave!"
>New York City's Coney Island, home to several amusement parks, followed with its own looping coaster in 1901. Using an ellipse rather than a circle for the loop,
I looked up this term to be sure and I'm convinced it's as meaningless as I thought it was and is a strange way of saying “force” or in this case a centrifugal force.