DETERMINISTIC CHAOS.

Could a Tilt-a-Whirl provide insights into the behavior of galaxies spinning around a black hole?

The Tilt-A-Whirl, for example, spins its passengers in one direction, then another, sometimes hesitating between forays and sometimes swinging abruptly from one motion to another. A rider never knows exactly what to expect next.

Yet these complicated, surprising movements arise from a remarkably simple geometry. A passenger rides in one of seven cars, each mounted near the edge of its own circular platform but free to pivot about the center. The platforms, in turn, move at a constant speed along an undulating circular track that consists of three identical hills separated by valleys, which tilt the platforms.  The platform movements are perfectly regular, but the cars whirl around independently in an irregular manner. Moreover, there is essentially just one adjustable parameter–the rate at which the platforms move around the track.

When the platforms travel at very low speeds, the cars complete one backward revolution as their platforms go over each hill. In contrast, at high speeds a car gets slammed to its platform’s outer edge and stays locked in that position. In both cases, the motion is predictable.

What happens at intermediate speeds?

To model dynamical systems like the Tilt-A-Whirl, mathematicians, scientists, and engineers use equations that describe how the positions and velocities of a system and its components change over time in response to certain forces.

It’s convenient to characterize a system’s dynamics by plotting how its position and velocity evolve over time. Each plotted point represents the system’s state of motion at a particular instant, and successive points generate a winding line through an imaginary mathematical space (known as phase space) representing all possible motions. Different starting points generally initiate different curves.

A simple, repeating motion, like the to-and-fro oscillations of a swinging pendulum, appears as a circle or some other closed curve. Such a plot shows that the system cycles through precisely the same state of motion again and again at regular intervals.

More complicated sequences of movements produce tangled paths that wander through phase space, sometimes never forming a closed loop.

That's without the clutch operator selectively reducing or increasing the speed of rotation the better to get a car into an extreme spin cycle.  You get sufficient deterministic chaos without the clutch operator.

To describe the Tilt-A-Whirl’s dynamics, physicists Bret M. Huggard of Northern Arizona University and Richard L. Kautz of the National Institute of Standards and Technology found a mathematical equation that approximates the motion of an idealized Tilt-A-Whirl. In essence, the movements of an individual car resemble those of a friction-impaired pendulum hanging from a support that is both rotating and being rocked back and forth while the pendulum swings. Solving the equation determines how a Tilt-A-Whirl car would behave under various conditions.

That's right, there was a publishable article on the physics of the Tilt-a-Whirl.

The resulting jumbled mixture of car rotations never repeats itself exactly, which gives the Tilt-A-Whirl its lively and unpredictable character. Indeed, no two trips are ever likely to produce exactly the same thrills and chills.

At the same time, the mathematical model used by Kautz and Huggard predicts that chaotic motion would occur at a speed close to the 6.5 revolutions per minute at which the ride is normally operated.

Interestingly, Tilt-A-Whirl fanatics know by experience that they can actually take advantage of this sensitivity. They can affect the motion of a car by throwing their weight from side to side at crucial moments, turning cycles with little or no action into thrilling whirls.

"Thus, it would seem that aficionados of the Tilt-A-Whirl have known for some time that chaotic systems can be controlled using small perturbations," Huggard and Kautz observed.

It turns out that Tilt-A-Whirl operators can also take advantage of this sensitivity. Software engineer Dave Boll described his experience one summer running a Tilt-A-Whirl, "which is easily the most entertaining carnival ride to operate."

Why? The operator can actually orchestrate the movement of individual cars. A single lever controls the ride's speed, so an operator can slightly retard or accelerate the ring of platforms at any moment. By applying just the right amount of velocity change at exactly the right time, it's possible to spin a particular car. For example, if a car is currently not spinning, is about to go uphill, and is positioned toward the inside, accelerating the platform will send the car into a very fast spin.

That orchestration might shake some change loose from a rider's pockets, or it might require that spinning car to be hosed out afterwards.  But I digress.

The scholarly article is "Chaos at the amusement park: Dynamics of the Tilt‐A‐Whirl" in American Journal of Physics, and the Computer Science club of the University of Waterloo have archived the reprint.  The laws of physics imply that at low rotational speeds of the platform, a car completes one backward circle from bottom to next bottom, while at high rotational speeds, centrifugal force wins and the car remains at the outer edge of its track.  What happens at intermediate speeds requires 39 equations to characterize.

According to Trentonian contributor Jeff Edelstein, the Tilt-a-Whirl is life.  "Dizzying. Chaotic. Uncertain. Filled with laughter and fear and a one-time ticket to ride."

The astronomy or cosmology?  I'll leave that to others.

A CENTENNIAL.

Somewhere on the midway there ought to be a Tilt-a-Whirl.

The first of these operated at the 1926 Minnesota State Fair.

With screams and giggles, whipping ponytails and white-knuckle grips, Minnesota fairgoers are taking delight in the magic of the Tilt-A-Whirl ride as it turns 100 years old.

The iconic ride and its brightly colored cars debuted at the Minnesota State Fair in 1926, and it has been a mainstay at fairs across the country ever since.

The inventor originally hoped to create a watergoing carroussel that would offer less predictable motion than the up-and-down of a horse on a sliding pole.

Herbert Sellner “created a water merry-go-round and, basically, one boat was driving, and all the other boats were tied together,” [Rice county historian Jenna] Nelson said. “It got destroyed by a storm in 1925.” Herbert’s brother, Martin, suggested adapting it for land.

In January 1926, Sellner started sketching drawings for this new ride, calling it the Tilt-ulator. On April 24, he filed a patent in Minneapolis, and a month later, according to Sellner’s notes, he had made a significant change: The new ride — with nine cars, as one advertisement put it, “tilting, sweeping, spinning, swooping, swaying, speeding, sliding, skidding, rounding, rotating, rising, revolving, hesitating, flying, falling, curving and circling” — would be called the Tilt-A-Whirl.

The concept is elegant.  Motors power a segmented undulating turntable on which nine (now seven) cars freewheel around a center pivot on each segment.  Sometimes a car simply rocks back and forth.  Other times, it gets into a positive feedback loop and pivots ever faster, which might be what the hardcore riders are hoping for.

The ride is powered by seven individual motors around a circle — and gravity makes the car spin around its dips. Weight from the riders shifts the cars’ positions as they lean, sending the cars off balance, said ride operator Thomas Lauthier, who brings his Tilt-A-Whirl to fairs around the country.

Lauthier has been operating the Tilt-A-Whirl at the Minnesota State Fair for the last 12 years. He said Midwesterners have a particular affinity for the ride.

The Sellners were skilled in the woodworking and mechanical arts.

Herbert Sellner was born in Faribault in 1887. His father was a skilled cabinetmaker, and Herbert inherited his father’s creativity and talents. In 1912, at the age of 25, he established the Sellner Woodcraft Company in Faribault to manufacture mission furniture, lamps, and other wood articles. Sellner also created the Ideal Lamp Company. A 1917 catalog listed magazine racks, smoking and telephone stands, folding dining tables, and lamps with leaded stained glass shades. When World War I affected supply availability, Sellner began manufacturing wood toys for children.

By 1923, Sellner’s creativity evolved, and he invented both a water toboggan slide and a water wheel that became popular items at bathing beaches. The slide was thirty feet high, featured a 100-foot-long track, and occupied a space of 18 by 100 feet. With 12 toboggans priced at 50 cents a ride, the owner could earn $6.00 every hour.

During the War, the Tilt-a-Whirl factory retooled to produce bomb carts.  Larson International in Texas subsequently purchased the Sellner firm and they continue to produce Tilt-a-Whirls.

A century ago, Minnesota creativity gave us Burma-Shave and its roadside signs, and a midway classic, as long as your stomach is up to it.

WE EMBRACE OUR AUGUST MILLION.

Sometime between morning coffee and midafternoon pop break (with much of the back yard mowed) Google's visit counter ticked over fifteen million.  The view count for individual posts suggests some interest in our observations on energy movements.

Whatever your motivation for looking in, and whether you are carbon-based or silicon-based, thank you for your continued interest.

The back yard is mowed.  I'm beginning the fall shortening-up program a week or two early.

TRUST, ONCE LOST, IS HARD TO REGAIN.

That recovery is particularly difficult when it is people entrusted with making decisions on the basis of their wisdom or their probity betray it in an egregious way.  In The (Not Detroit) Free Press, Erick Erickson notes, "The same government that used pandemic powers to shutter churches and businesses now wants surveillance cameras on street corners and data centers in backyards. You can’t blame people for saying no."

It's not that the warning signs haven't been with us for some time.  Cold Spring Shops posts have used variations on "governance by wise experts" since the fall of 2009, generally in a skeptical way.

That People in Authority dismissed the observations of — wait for it — medical doctors noticing masked people's glasses fogging up in grocery stories and suggesting the mask mandates and six foot circles and the rest were theater, not policy, probably resurrected the notion of a credibility gap.  Yes, dear reader, my life from adolescence onward has been structured by credibility gaps: thus another one emerging during the Jarrett regency's corona tyranny didn't come as a shock.

THANKS YET ANOTHER MILLION.

Two weeks ago the Google counter ticked past thirteen million, and overnight came the fourteenth million page view, with close onto a quarter of a million today.

I hope the data centers are mining nuggets, and that the live readers among that number are finding content that is informative or provocative or fun.

MISSED OPPORTUNITIES.

One of the challenges of playing games with algorithms is accurately communicating your capabilities.  A frequent complaint in my irregular Saturday bridge column is the algorithm getting high on its own supply, which can put somebody in an untenable position.

Then there's this position from a few months ago.

I've learned to take the hints the algorithm offers for bid choices seriously, and Two No Trump described more accurately my holdings than Three Diamonds, as did Three No Trump rather than venturing Four Hearts.  Garbage in could lead to garbage out ...

West led the ♠ Five.  No time to get cute here, the defenders cannot get an opportunity to lead Clubs or Spades: Six, Ten, Jack.  Cash the ♦ Ace, then the ♠ Ace.  Now there's a way to run 'em all, which is why human players making bidding plans with partners matters.  Three more Diamond honors clear the defenders of those cards, and a few little Clubs come off the board.

THANKS YET ANOTHER MILLION.

Cold Spring Shops opened early in September of 2002.

I'm not sure when Google started counting page views, their counter rolled to a million in April 2016.

Four years later, the second million was recorded in August of 2020.

A third million arrived in the middle of April, 2024.

That tally doubled early in July, 2025.

We recorded the next doubling in July, 2026.

Overnight, another million came in, running the counter past thirteen million.

I continue to have plenty of material to carry on about, or for algorithms to peruse.

To those live readers who are looking in, thank you for your interest.

RAILROADS, CONNECTING PEOPLE.

Union Pacific's Semiquincentennial Steam Tour cheered up Northeasterners.  Trains posted a photo gallery, complete with a photograph that longtime editor David P. Morgan would surely have hailed, showing the articulation principle at work, with the lead engine helping Big Boy bend the corner around.

Steve Smedley photograph retrieved from Trains Magazine.

Big Boy and Reading and Northern T-1 Northern 2102, a different sort of War Baby, ran a side by side excursion in advance of Big Boy's visit to Steamtown and an Independence Day event in Philadelphia.  The excursion also acknowledges the 1976 American Freedom Train, as sister engine 2101 was on the head pin east of Chicago.

 JOIN

OUR HAPPY

INFORMED THRONG

TWELVE MILLION READERS

CAN'T BE WRONG!

ACROSS THE CONTINENT AND TO THE MOON.

Less than a century after American Independence, a by-then continental country survived a second British invasion that involved a sack of its capital, followed a great civil war that tested whether such a country could long endure, and spiked down a railroad from Council Bluffs to Sacramento.

Within a century, men from Planet Earth first set foot on the Moon.

This year, the semiquincentennial of American Independence, another crew of astronauts launched from that nation again circled the Moon, and Union Pacific's Big Boy has gone east to participate in the Independence festivities.

It is only fitting and proper that the railroads participate.  The last surviving signer of the Declaration of Independence, Charles Carroll of Carrollton, laid the first stone of the Baltimore and Ohio on Independence Day, 1827 supposedly remarking that so doing was at least as significant, if not moreso, than signing the Declaration.  Railroad lawyer Abraham Lincoln authorized construction of the Pacific Railroad, while the country was engaged in a great civil war.  He chose a central route in consideration of the military exigencies of the times.  That chalking on 4014's smokebox door, "Big Boy" above a V-for-Victory, predates United States participation in the War, and yet, without the big steamers, moving men and material to ports on two coasts would not be as easy.  Legend has it that a German war prisoner, late in the War and being transported to the forests of the Pacific Northwest, it being the practice to offer prisoners an opportunity to earn money by assisting at civilian work, noticed a Big Boy on a nearby track, counted the wheels, and lamented that it would not be possible to defeat a nation that had locomotives such as those.  Not even, to crack wise for a moment, with rocket scientists that did the engineering for the Moon missions of the late 1960s. 

BOTTOM STORY OF THE DAY.

Literally.  Here we were, thirteen years ago.

The Sports Illustrated swimsuit issue is a glossy provocation to the Perpetually Aggrieved.

What's the over-under that at least one participant in the semiotics workshop wishes she could be a swimsuit model?

In recent years, it might have gotten easier for semioticians to make the cut.

Not too long ago, Sports Illustrated decided that putting Rubens models on the cover of the swimsuit edition was a good idea.  (It wasn't.)

Now comes a new pharmacopeia, and (looking past all manner of potentially nasty side effects, there's nothing that kills the appetite quite like a drug ad coming on during snack time) some might take the pounds off effortlessly, compared with diet, exercise and resting.  That might reduce the value of Rubens models.  "As a plus-size swimsuit model, I'm not worried about GLP-1 drugs. I'm uneasy about what we celebrate when women get smaller."

ANOTHER WEEK, ANOTHER MILLION PAGE VIEWS.

Sometime during Fathers Day weekend our page view counter rolled through eleven million, a week since it rolled through ten million, a month since it rolled past nine million, and two months since it hit eight million.  Two million plus views counted in June alone.  I hope the algorithms are scraping nuggets of wisdom.  Individual posts still generally register forty to sixty views, and I trust live readers are making good use of them.  Thanks to viewers, human and algorithmic, for your continued interest.

THE BOTS HAVE BEEN EVEN BUSIER.

I hope they are learning something.  Sometime during the Flag Day weekend our page view counter rolled through ten million, about three weeks since the counter rolled past nine million and about two months since the counter took a weekend stroll through eight million.  It's half past June and the page counter is nearly at a million for the month.

It's been the same pattern, episodes of activity in the tens of thousands of page views, interspersed by days with our more common experience of two hundred to two thousand page views in a day, and views of specific posts in the thirty to sixty range.

I extend my thanks, once again, to the two hundred to two thousand real readers who look in each day, and I surely don't lack for things to carry on about.  It's still likely that I'm going to carry on about how expensive ignorance is, based on the ongoing public conversations about data center construction.  Not today.

WHERE ARE YOU HEADED, BIG BOY?

Last week Tuesday offered fine weather for setting a lawn chair under a tree and watching trains.  Big Boy was expected out of Rochelle around 3.15.  The vagaries of railroading.  Union Pacific dispatchers threaded the special through freight traffic in both directions, including a Bird, loaded and empty hoppers, and Dead Freight.

Over the weekend, Union Pacific allowed Norfolk Southern pilots into the cab, and an expanded train with Norfolk Southern's America 250 diesel and several additional office cars set off for Philadelphia.

PROGRESS OF A CENTURY.

North America's first stretch of electrified high speed railroad opened in June of 1926.  In the winter of 1960, rail enthusiasts were gathering for final rides.

Unattributed photograph, probably a Kodachrome, retrieved from The Trolley Dodger.

The North Shore Line built this section of railroad in order to offer service between Milwaukee and Chicago that wasn't jousting with automobiles on street trackage and subject to franchise restrictions requiring limited trains to stop on the streets of Wilmette.

THEY DON'T BUY CARS.

Years ago, one of the senior executives at a Detroit car company was showing off some new machine tools to a representative of the United Auto Workers.  They never show up hung over, or malinger, or go on strike, he crowed.  The union representative thought he got off a good riposte with the line that introduces this post.

GOOD.

"Six Flags bans influencer from all parks 'for life' after his shocking video violating safety rules."

I hope the clicks and likes were worth it.  "'Guests who violate our Code of Conduct are not welcome in our parks,' a Cedar Point rep tells EW of YouTuber Allen Ferrell, who filmed himself eating chicken nuggets on a 310-foot roller coaster."

Apparently "EW" means "Entertainment Weekly," but my reaction to what this fool did for clicks and likes was also "Ewwwww."

Ferrell, who has nearly 4 million followers on TikTok and 1.8 million subscribers on YouTube, shared a video of himself sticking a 10-piece box of chicken nuggets into his pants before boarding the Millennium Force roller coaster.

Ferrell is seen in the footage pulling the box out and eating the nuggets while the ride drops from its 310-foot height. His riding partner then extends a hand holding an open container of sauce, into which Ferrell dips his nugget before it slides off his face.

I once snagged my brother's sunglasses when the g-forces on a coaster you might have heard of did what they do.  I would not have been able to catch a stray drop of dipping sauce even with my younger self's reflexes.  This happened long ago, before people had portable 'phones to take selfies, which is another way to get yourself banned from an amusement park.  "During the ride, the phone came loose and struck another rider, which, according to local news, sent the injured person to the hospital for treatment."

The laws of physics are immutable.  Roller coasters are for riding no-handed, not for amateur photography.  And yes, I have taken point-of-view photographs on roller coasters.  With the management's permission.

THE BOTS HAVE BEEN BUSY AGAIN.

I hope they are learning something.  Sometime during the Memorial Day weekend our page view counter rolled through nine million, some five weeks since the counter took a weekend stroll through eight million.  It's been the same pattern, episodes of activity in the tens of thousands of page views, interspersed by days with our more common experience of two hundred to two thousand page views in a day, and views of specific posts in the thirty to sixty range.

I extend my thanks, once again, to the two hundred to two thousand real readers who look in each day, and I surely don't lack for things to carry on about.  It's likely that I'm going to carry on about how expensive ignorance is, based on the ongoing public conversations about data center construction.

THE BEER THAT MADE MILT FAMY WALK US.

Poor Schlitz, for the past forty years an orphan brand.

Once upon a time, Schlitz sold Old Milwaukee at a lower price than "The Beer That Made Milwaukee Furious" as a subtle form of price discrimination.  A few locals were in on the secret.

More recently, Miller Coors leased excess capacity at some of their plants to produce all of the other Great Milwaukee beers: draft-brewed Blatz, Pabst Blue Ribbon, Schlitz, and for all I know Meister Brau and Braumeister.  (Well, at least Old Milwaukee, see above, and Lone Star.)

It's now come down to Miller Makes It Wrong.  " Pabst Brewing Company and MillerCoors are going to trial, with hipster favorite Pabst contending that MillerCoors wants to put it out of business by ending a longstanding partnership through which it brews Pabst’s beers."

The dispute involves the profitability of Miller's excess capacity.

The mind boggles at a single company brewing Miller Lite (they took out a trademark on the mis-spelling) and Coors Light, which is academic at Cold Spring Shops headquarters, where Budweiser is for cooking whilst Sprecher or Spotted Cow or whoever's local Marzen is on offer is for drinking.

The mind also boggles at Pabst being located in San Antonio, which used to be where Pearl Brewery switched its works with a home-built flat car motor.  As close as Miller was to Cold Spring Shops, they never had an in-house plant railway, relying on The Milwaukee Road, as did Schlitz, which had rail-served facilities at both the Chestnut Street and the North Milwaukee end of the Beer Line.  But I digress.

PAIN FOR THE MULLAHS, NOT AT THE PUMP.

Let's set the Wayback Machine to August 2003.

The University's press liaison just rang, asked if I would speak with a reporterette about gas prices. Here's the fieldwork I did: nominal and real gasoline prices to 1997, and an inflation calculator. When you see unleaded regular at $2.73 a gallon (I'm not sure how the Energy Information Administration treats taxes) give me a holler. For an exercise, plot the size of a passenger truck against the price series you see.

In those days, Blogger did not have image embedding capabilities, which we now have.  Adjusting for inflation, when you see unleaded regular at around $6.00 a gallon, and again, my disclaimer about accounting for taxes applies, give me a holler.

That's a screen capture from an Energy Information Administration series, and the agency publish additional inflation-adjusted price series.