Why roller coaster loops aren’t circular anymore • Hacker News Board

Re: Why roller coaster loops aren’t circular anymore

#91

Post by treis » Sat, Jul 09, 2022, 1:47 PM UTC

function_seven wrote: post #12

treis wrote: post #6

Am I high or is the picture of the flip flap railroad loop decidedly not circular?

You’re high. But also the photo was taken at an angle to the track, so it’s not gonna trace out a circle on your screen.

I'm not high now and I read the article they cited for that fact. Nowhere in the article does it say the first loops were a circle. In fact, it says the opposite:

>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,

Re: Why roller coaster loops aren’t circular anymore

#92

Post by checker » Sat, Jul 09, 2022, 1:54 PM UTC

jonsen wrote: post #67

mgdlbp wrote: post #61

Earlier quoted context omitted.

There's definitely confirmation bias causing me to not notice stops where there isn't a jerk. And perhaps by the Baader-Meinhof effect you'll begin to notice them more frequently, too. But stops without any perceptible jerk are rare enough that when they happen I get an odd feeling of floating forwards like when the train beside your own at a station departs—perhaps it's because my subconscious, still anticipating th…

If rear-ended with your brakes engaged more of the impact energy will go into crumbling your car than if it's allowed to transfer into forward speed. If you see it coming, let go of the brake, and then step on it after impact. That's the advise I got.

Strategy sounds legit but my concern would be that the (previously distracted) incoming driver attempts to dodge at the last second. Their car will hit your car with torque that could send it into oncoming traffic. But that angled impact also means less push in your car's forward direction, so maybe this concern is overblown.

Re: Why roller coaster loops aren’t circular anymore

#93

Post by jwilk » Sat, Jul 09, 2022, 2:11 PM UTC

ben_w wrote: post #34

keithnz wrote: post #20

Earlier quoted context omitted.

I have a t-shirt which has "don't be a" and the equation for the third derivative

Reminds me of someone I knew at university whose T-shirt was the definite integral from 10 to 13 of 2x dx followed by a question mark.

∫ 2x dx = x² + C

13² − 10² = 69

Re: Why roller coaster loops aren’t circular anymore

#94

Post by danachow » Sat, Jul 09, 2022, 2:16 PM UTC

atoav wrote: post #46

tobtoh wrote: post #18

If I remember my uni engineering/calculus maths class correctly, the third derivative of position is used in planning these sort of curves. 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 mov…

A very similar thing is done in the creation of reflective surfaces on car bodies (typically in CAD software). 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 ess…

Minor point (well in this case at least) but you have an off by one error. Your G1 is G0.

Here is how it is defined in terms of basis vectors. https://people.eecs.berkeley.edu/~jfc/cs184f98/lec19/lec19.h...

Re: Why roller coaster loops aren’t circular anymore

#95

Post by yojo » Sat, Jul 09, 2022, 2:27 PM UTC

mgdlbp wrote: post #22

tobtoh wrote: post #18

If I remember my uni engineering/calculus maths class correctly, the third derivative of position is used in planning these sort of curves. 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 mov…

Also seen in the planning of curves in roads (where jerk corresponds to the rate at which a steering wheel must be turned) and railways. 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 c…

This was particularly noticeable to me riding San Francisco light rail to work. When trains run underground they start and stop under computer control. Nice, smooth acceleration and deceleration.

On the surface (or when the computer control system was borked) the starts and stops were a lot less pleasant.

Re: Why roller coaster loops aren’t circular anymore

#96

Post by phkahler » Sat, Jul 09, 2022, 2:36 PM UTC

mgdlbp wrote: post #22

tobtoh wrote: post #18

If I remember my uni engineering/calculus maths class correctly, the third derivative of position is used in planning these sort of curves. 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 mov…

Also seen in the planning of curves in roads (where jerk corresponds to the rate at which a steering wheel must be turned) and railways. 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 c…

This is fun to try in cars. The drivetrain can have a bit of twist under deceleration, and you can feel it spring back after the wheels stop. For best comfort you need to gradually reduce the braking force not just for human comfort but also to relieve that twist.

Re: Why roller coaster loops aren’t circular anymore

#97

Post by suyjuris » Sat, Jul 09, 2022, 3:02 PM UTC

aasasd wrote: post #85

A similar principle works in UI design and industrial design. Rounded rectangles often just slap circle arcs on the corners—but that looks unnatural because you don't get such a shape if you bend a straight rod. In this approach the turning radius changes from infinity to a constant at one point, but the proper way is to change it gradually. Bezier curves accomplish that, I think. Once you see this, you begin to noti…

I once implemented rounded rectangles by drawing circles with regards to arbitrary p-norms [1,2] – I did not think about it at the time, but the derivatives are probably quite nice. (It did have the advantage of using the same code for rounded rectangles and for circles.)

[1] https://en.wikipedia.org/wiki/Norm_(mathematics)#p-norm

[2] https://en.wikipedia.org/wiki/Lp_space#/media/File:Vector-p-...

Re: Why roller coaster loops aren’t circular anymore

#98

Post by tzs » Sat, Jul 09, 2022, 3:02 PM UTC

mgdlbp wrote: post #22

tobtoh wrote: post #18

If I remember my uni engineering/calculus maths class correctly, the third derivative of position is used in planning these sort of curves. 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 mov…

Also seen in the planning of curves in roads (where jerk corresponds to the rate at which a steering wheel must be turned) and railways. 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 c…

OT: that reminds me of an interesting physics problem.

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?

Re: Why roller coaster loops aren’t circular anymore

#99

Post by lisper » Sat, Jul 09, 2022, 3:11 PM UTC

mgdlbp wrote: post #64

lisper wrote: post #26

Earlier quoted context omitted.

It's a little more complicated than that in a passenger car. The deceleration compresses the front springs. When the car comes to a stop, the springs decompress and the front of the car pops up and the body of the car moves slightly backwards even though the wheels are now stationary.

Interestingly, in this /r/askscience thread:[1] 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;…

> The occupants visibly move backwards relative to the car body

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.

Re: Why roller coaster loops aren’t circular anymore

#100

Post by aasasd » Sat, Jul 09, 2022, 3:21 PM UTC

suyjuris wrote: post #97

aasasd wrote: post #85

A similar principle works in UI design and industrial design. Rounded rectangles often just slap circle arcs on the corners—but that looks unnatural because you don't get such a shape if you bend a straight rod. In this approach the turning radius changes from infinity to a constant at one point, but the proper way is to change it gradually. Bezier curves accomplish that, I think. Once you see this, you begin to noti…

I once implemented rounded rectangles by drawing circles with regards to arbitrary p-norms [1,2] – I did not think about it at the time, but the derivatives are probably quite nice. (It did have the advantage of using the same code for rounded rectangles and for circles.) [1] https://en.wikipedia.org/wiki/Norm_(mathematics)#p-norm [2] https://en.wikipedia.org/wiki/Lp_space#/media/File:Vector-p-...

Pretty sure that's how squircles are supposed to be mathematically implemented—at least in the option based on superellipses: https://en.wikipedia.org/wiki/Squircle