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Getting sloshed: it's the way you walk
Mackenzie was horrified. As an engineer, he understood that scaling up from 20 metres to 600 would bring immense complications. For a start, the model had only involved plain ice. “It was just to see if a refrigeration unit could sustain the ice structure,” says Langley. The full-size carrier would need a hull of much stronger stuff.
Splash and burn
Pleasingly mad As it turned out, even pykrete would have been inadequate. At temperatures above -15 °C, pykrete slowly deforms. Even with enough refrigeration plants to keep it cold, it still wouldn’t have been able to support a 600-metre ship. Steel reinforcement would be needed too. Probably a lot of it. And, of course, a vast quantity of wood pulp would be needed, the equivalent of a small forest for each carrier. Perutz later said he had come to realise that the construction and navigation of a bergship might prove “as difficult as a voyage to the moon”. In any case, this pleasingly mad idea was soon made redundant by somewhat more mundane developments, including longer-range bombers and new airbases in Iceland. In December 1943, project Habbakuk was dropped. Since the war, a few engineers have toyed with the idea of using pykrete for other purposes – such as protecting Arctic oil rigs from stormy seas, or making a quay in Oslo harbour. Although nothing has come of it so far, Langley is hopeful that pykrete will one day make more than an icy bath toy. “It still has amazing possibilities, but it has not found its niche yet,” she says. “We just have to get the right people interested.” In the spirit of Pyke’s original plan, perhaps some aspiring seasteaders will see the material’s potential, and build themselves a floating city of ice. n Stephen Battersby is a writer based in London
spl
Match this image to one on the grid on page 77, where you will find details of the competition
K
It can be painful and messy if your cup runneth over. How do you avoid a scalding, asks Bob Holmes
N
O ONE can accuse H. Norman Abramson of sitting in an ivory tower. “It is common everyday knowledge to each of us that any small container filled with liquid must be moved or carried very carefully to avoid spills,” the US engineer and fluid dynamicist wrote almost half a century ago. “Experience has taught us that the unrestrained free surface of the liquid has an alarming propensity to undergo rather large excursions, for even very small motions of the container.” Hardly rocket science, you might think. The irony is, it was. Abramson’s words come from the introduction to a 464-page report he wrote for NASA in 1966. At the time, the US space agency was aiming to catapult astronauts to the moon atop rockets filled with liquid propellants. Abramson’s magnum opus, entitled The Dynamic Behavior of Liquids in Moving Containers with Applications to Space Vehicle Technology, presented the sum of human knowledge on a phenomenon of life-or-death importance to the space race: sloshing. It is a problem even now. Fuel sloshing has probably caused the failure of several rocket launches, and in 1998 a sloshinduced tumble cut short a course adjustment and set back by a year the Near Earth Asteroid Rendezvous (NEAR) mission to the asteroid 433 Eros. In 2005, the European Space Agency launched an entire mission, dubbed Sloshsat, to study
fluid dynamics in microgravity. NASA’s own investigations continue. Back on Earth, we are still baffled by the burning question Abramson touched on. Why does hot coffee leap from its cup so readily, and can we do anything about it? From space fuel to coffee, this much we know: sloshing results largely from the interplay of two things. One is a liquid’s inertia, which stops it following when its container changes speed suddenly. This causes waves. The other is resonance, in which these waves get bigger as a result of some external pulse, or forcing frequency, that roughly matches the liquid’s natural oscillation frequency. The same effect makes an unplucked guitar string vibrate if a sound with its natural pitch is played through a nearby speaker. The carried coffee problem is a tougher bean to grind, because the forcing comes not from a single frequency but from a complex biomechanical process with a simple name: walking. “It makes the story more interesting, but characterising the problem more difficult,” says Rouslan Krechetnikov of the University of California, Santa Barbara. Walking’s intricate rhythms, with accelerations in all three dimensions, mean sloshing is better understood when it happens in a spacecraft than in a common cup of coffee. It was the sight of mathematicians struggling with their mid-morning coffees at a conference in 2011 that convinced Krechetnikov and his > 22/29 December 2012 | NewScientist | 65
Arterra Picture Library / Alamy
Beer is bad news for the slosh-prone
Baffled and stymied
student Hans Mayer that the problem merited more systematic study. Back in their lab, the pair rigged an electronic spill sensor to a standard, cylindrical mug filled with coffee, and filmed themselves as they carried it down the uncarpeted hallway outside Krechetnikov’s office. “I don’t have any special training to carry coffee, so I considered myself a good subject,” says Krechetnikov. A frame-by-frame analysis of the films revealed two things. First, a high initial acceleration – starting out too quickly – can lead to instant spillage as the inertial waves send the coffee over the mug’s lip. No surprise there. If you’re less of a jackrabbit, the coffee’s surface merely wiggles at first. As you walk, however, the rhythm of your gait sets up a resonance in the liquid that amplifies those initial wiggles into ever-larger waves. And herein lies the problem. Unlike a guitar string, liquid in a container has what physicists call a wide resonance well: even a rough match between the natural and forcing frequencies can cause
Match this image to one on the grid on page 77, where you will find details of the competition getty
further away from the danger zone. The same is true for a mug that narrows a little from base to lip. A wider cup is more spill-prone for a second reason, says Andrzej Herczynski, a physicist at Boston College, Massachusetts. Whenever an initial acceleration or resonance causes the surface of the liquid to deflect from horizontal, the larger radius means that a wave of a given slope has become big enough by the time it reaches the edge of the cup to go overboard. That also explains why it is so hard to carry a bowl of soup without slopping it.
H 66 | NewScientist | 22/29 December 2012
”All things being equal, eggnog should be a safer drink to walk with”
resonance. Krechetnikov and Mayer found the natural oscillation frequency of coffee in standard-sized mugs to be between 2.6 and 4.3 hertz, depending on the mug’s height and diameter. The forward-backward component in most people’s gaits, meanwhile, supplies a forcing frequency between 1 and 2.5 hertz – a close enough match for resonance to cause slopping within seven to 10 steps. Random variation in real walking rhythms introduces higherfrequency noise that also contributes to resonance forcing. The best antidote seems to be simple concentration: on average, when cup-carriers focused on not spilling, they made it further slopfree (Physical Review E, vol 85, p 046117). These findings were enough to earn Krechetnikov and Mayer this year’s Ig Nobel Prize in Fluid Dynamics. But what practical lessons can we draw to minimise spillages – preferably without the social dampener of obsessing about our drink? The first is that a taller, narrower mug has a higher resonant frequency, taking it
Some relief might also be achieved by using a more flexible cup, which can absorb more of the energy of sloshing than a rigid mug. For those in search of a more engineered solution, Krechetnikov recommends a series of baffles or ridges around the inside of the container. These cause vortices in the liquid and break up any resonant tendencies. Alcoholic drinks produce their own challenges to the slosh-prone. Beer is probably a bad choice. A standard UK pint glass is about 14.5 centimetres high and 9 centimetres in diameter at the lip, and should resonate at about 3.2 Hz by Krechetnikov’s reckoning, well within the danger zone. Some beer glasses, such as the “nonic” glass familiar to British pubgoers, have a bulge near the top that may act like a baffle and stymie resonance, but Krechetnikov is reluctant to say without more research. Meanwhile, Herczynski recommends swapping to a thicker tipple such as eggnog. “The energy that’s supplied to the sloshing eggnog from your walking is dissipated through friction,” he says. “All things being equal, it should be safer to walk with.” The most elegant of all solutions to spilled drinks, though, says Krechetnikov, might be to carry your drink on a tray suspended from a carrier ring, as servers often do in the Middle East. The set-up acts as a pendulum with its own, far slower frequency, which buffers the liquid from the rhythm of your walk. As far as solutions to Abramson’s problem go, you might call rock-it science. n Bob Holmes is a consultant for New Scientist based in Edmonton, Canada
Splash and burn
Pleasingly mad As it turned out, even pykrete would have been inadequate. At temperatures above -15 °C, pykrete slowly deforms. Even with enough refrigeration plants to keep it cold, it still wouldn’t have been able to support a 600-metre ship. Steel reinforcement would be needed too. Probably a lot of it. And, of course, a vast quantity of wood pulp would be needed, the equivalent of a small forest for each carrier. Perutz later said he had come to realise that the construction and navigation of a bergship might prove “as difficult as a voyage to the moon”. In any case, this pleasingly mad idea was soon made redundant by somewhat more mundane developments, including longer-range bombers and new airbases in Iceland. In December 1943, project Habbakuk was dropped. Since the war, a few engineers have toyed with the idea of using pykrete for other purposes – such as protecting Arctic oil rigs from stormy seas, or making a quay in Oslo harbour. Although nothing has come of it so far, Langley is hopeful that pykrete will one day make more than an icy bath toy. “It still has amazing possibilities, but it has not found its niche yet,” she says. “We just have to get the right people interested.” In the spirit of Pyke’s original plan, perhaps some aspiring seasteaders will see the material’s potential, and build themselves a floating city of ice. n Stephen Battersby is a writer based in London
spl
Match this image to one on the grid on page 77, where you will find details of the competition
K
It can be painful and messy if your cup runneth over. How do you avoid a scalding, asks Bob Holmes
N
O ONE can accuse H. Norman Abramson of sitting in an ivory tower. “It is common everyday knowledge to each of us that any small container filled with liquid must be moved or carried very carefully to avoid spills,” the US engineer and fluid dynamicist wrote almost half a century ago. “Experience has taught us that the unrestrained free surface of the liquid has an alarming propensity to undergo rather large excursions, for even very small motions of the container.” Hardly rocket science, you might think. The irony is, it was. Abramson’s words come from the introduction to a 464-page report he wrote for NASA in 1966. At the time, the US space agency was aiming to catapult astronauts to the moon atop rockets filled with liquid propellants. Abramson’s magnum opus, entitled The Dynamic Behavior of Liquids in Moving Containers with Applications to Space Vehicle Technology, presented the sum of human knowledge on a phenomenon of life-or-death importance to the space race: sloshing. It is a problem even now. Fuel sloshing has probably caused the failure of several rocket launches, and in 1998 a sloshinduced tumble cut short a course adjustment and set back by a year the Near Earth Asteroid Rendezvous (NEAR) mission to the asteroid 433 Eros. In 2005, the European Space Agency launched an entire mission, dubbed Sloshsat, to study
fluid dynamics in microgravity. NASA’s own investigations continue. Back on Earth, we are still baffled by the burning question Abramson touched on. Why does hot coffee leap from its cup so readily, and can we do anything about it? From space fuel to coffee, this much we know: sloshing results largely from the interplay of two things. One is a liquid’s inertia, which stops it following when its container changes speed suddenly. This causes waves. The other is resonance, in which these waves get bigger as a result of some external pulse, or forcing frequency, that roughly matches the liquid’s natural oscillation frequency. The same effect makes an unplucked guitar string vibrate if a sound with its natural pitch is played through a nearby speaker. The carried coffee problem is a tougher bean to grind, because the forcing comes not from a single frequency but from a complex biomechanical process with a simple name: walking. “It makes the story more interesting, but characterising the problem more difficult,” says Rouslan Krechetnikov of the University of California, Santa Barbara. Walking’s intricate rhythms, with accelerations in all three dimensions, mean sloshing is better understood when it happens in a spacecraft than in a common cup of coffee. It was the sight of mathematicians struggling with their mid-morning coffees at a conference in 2011 that convinced Krechetnikov and his > 22/29 December 2012 | NewScientist | 65
Arterra Picture Library / Alamy
Beer is bad news for the slosh-prone
Baffled and stymied
student Hans Mayer that the problem merited more systematic study. Back in their lab, the pair rigged an electronic spill sensor to a standard, cylindrical mug filled with coffee, and filmed themselves as they carried it down the uncarpeted hallway outside Krechetnikov’s office. “I don’t have any special training to carry coffee, so I considered myself a good subject,” says Krechetnikov. A frame-by-frame analysis of the films revealed two things. First, a high initial acceleration – starting out too quickly – can lead to instant spillage as the inertial waves send the coffee over the mug’s lip. No surprise there. If you’re less of a jackrabbit, the coffee’s surface merely wiggles at first. As you walk, however, the rhythm of your gait sets up a resonance in the liquid that amplifies those initial wiggles into ever-larger waves. And herein lies the problem. Unlike a guitar string, liquid in a container has what physicists call a wide resonance well: even a rough match between the natural and forcing frequencies can cause
Match this image to one on the grid on page 77, where you will find details of the competition getty
further away from the danger zone. The same is true for a mug that narrows a little from base to lip. A wider cup is more spill-prone for a second reason, says Andrzej Herczynski, a physicist at Boston College, Massachusetts. Whenever an initial acceleration or resonance causes the surface of the liquid to deflect from horizontal, the larger radius means that a wave of a given slope has become big enough by the time it reaches the edge of the cup to go overboard. That also explains why it is so hard to carry a bowl of soup without slopping it.
H 66 | NewScientist | 22/29 December 2012
”All things being equal, eggnog should be a safer drink to walk with”
resonance. Krechetnikov and Mayer found the natural oscillation frequency of coffee in standard-sized mugs to be between 2.6 and 4.3 hertz, depending on the mug’s height and diameter. The forward-backward component in most people’s gaits, meanwhile, supplies a forcing frequency between 1 and 2.5 hertz – a close enough match for resonance to cause slopping within seven to 10 steps. Random variation in real walking rhythms introduces higherfrequency noise that also contributes to resonance forcing. The best antidote seems to be simple concentration: on average, when cup-carriers focused on not spilling, they made it further slopfree (Physical Review E, vol 85, p 046117). These findings were enough to earn Krechetnikov and Mayer this year’s Ig Nobel Prize in Fluid Dynamics. But what practical lessons can we draw to minimise spillages – preferably without the social dampener of obsessing about our drink? The first is that a taller, narrower mug has a higher resonant frequency, taking it
Some relief might also be achieved by using a more flexible cup, which can absorb more of the energy of sloshing than a rigid mug. For those in search of a more engineered solution, Krechetnikov recommends a series of baffles or ridges around the inside of the container. These cause vortices in the liquid and break up any resonant tendencies. Alcoholic drinks produce their own challenges to the slosh-prone. Beer is probably a bad choice. A standard UK pint glass is about 14.5 centimetres high and 9 centimetres in diameter at the lip, and should resonate at about 3.2 Hz by Krechetnikov’s reckoning, well within the danger zone. Some beer glasses, such as the “nonic” glass familiar to British pubgoers, have a bulge near the top that may act like a baffle and stymie resonance, but Krechetnikov is reluctant to say without more research. Meanwhile, Herczynski recommends swapping to a thicker tipple such as eggnog. “The energy that’s supplied to the sloshing eggnog from your walking is dissipated through friction,” he says. “All things being equal, it should be safer to walk with.” The most elegant of all solutions to spilled drinks, though, says Krechetnikov, might be to carry your drink on a tray suspended from a carrier ring, as servers often do in the Middle East. The set-up acts as a pendulum with its own, far slower frequency, which buffers the liquid from the rhythm of your walk. As far as solutions to Abramson’s problem go, you might call rock-it science. n Bob Holmes is a consultant for New Scientist based in Edmonton, Canada