E6
Science
KLMNO
TUESDAY, AUGUST 24, 2010
Will efficiency study make a big splash in rowing circles? rowing continued from E1
to fascinate Barrow, who is better known for his work on cosmology and popularizing science than his prowess on the water. “I’ve never rowed competitively, but I’m fas- cinated by the links between mathematics and sport,” he says. Barrow began by modeling the problem using an idealized crew. His rowers are identical automa- tons that are equally spaced and that move in perfect unison, un- troubled by the vagaries of bi- omechanics or oar design. The forces generated as they pull through perfect symmetrical arcs are identical, varying in time in exactly the same way. This varia- tion, or force-curve, is important. That’s because the sideways com- ponent of the force changes direc- tion halfway through each stroke: During the first half, it is directed toward the boat, while in the sec- ond half, it is directed away. (See diagram.) It is easy to imagine that a sym-
metrical arrangement of such idealized rowers would cancel the sideways force at every point dur- ing their stroke. Yet Barrow’s
Wiggle-free rowing
Every time a rower puts an oar in the water, the stroke not only pushes his boat forward, but it also creates a sideways force. During the fi rst half of the stroke, that force moves toward the boat; during the second half, the force moves away.
JOHN BARROW’S ALTERNATIVE RIGS STROKE 2 1
analysis shows that a convention- ally rigged boat should constantly wiggle from side to side as it moves through the water. “This takes extra energy from the row- ers and slows the forward prog- ress of the boat,” he says.
The right moment To understand why, Barrow
looked at one measure of the ef- fect of the sideways force — its “moment.” This is its tendency to rotate an object around some point; the combined rotational ef- fect of all the forces on an object is the sum of all their moments around a point. Barrow chose to take moments around the stern of a conventionally rigged racing four. If the rowers sit 1 meter apart facing the stern and the dis- tance from the stern to the first rower is 1 meter, then that rower creates a moment about the stern of 1F, the second rower contrib- utes -2F (because he is 2 meters from the stern and is pulling on the opposite side to the first row- er), the third rower 3F and the fourth -4F. The total moment about the stern during the first half of a stroke is (1-2+3-4)F, or
BOAT
With a conventional arrangement of rowers, the combined sideways forces swing from one side to the other at the midpoint of the rowers’ strokes, causing the boat to wiggle and lose effi ciency.
CONVENTIONAL RIG
-2F. For convenience we can sim- ply set F equal to 1, making the moment about the stern -2. Dur- ing the second half of the stroke, the sideways forces are reversed, so the moment about the stern becomes +2. This is why boats us- ing the conventional rig should wiggle as they move: They con- stantly experience a twisting in- fluence that changes direction at the midpoint of the rowers’ stroke. Then Barrow asked the obvious question: Are there configura- tions of rowers for which the side- ways forces, the “moments,” can- cel? For a crew of four, the number of possible configurations is pleasingly small. There is the con- ventional rig — which we can rep- resent as LRLR — which produc- es a moment about the stern of ±2. There are also two others: LLRR and LRRL (and their mir- ror images, of course). For the LLRR rig, the moment about the stern is ±4, clearly a disaster. But for the LRRL rig, the moment of forces is 0, exactly what Barrow was looking for. This rig has actu- ally appeared in competition. Now known as the Italian rig, it
was first used in 1956 by a rowing team from the Moto Guzzi motor- cycle manufacturer, based on the shores of Lake Como in Italy. The team went on to win gold for Italy in the men’s coxed fours at the Olympic games in Melbourne, Australia, that year. What of the eights? Barrow showed that there are four ar- rangements where the moments exactly cancel. (See diagram.) One of these is LRRLLRRL, in which the Italian rig is simply re- peated. Indeed, this rig was used by Italian teams in the 1950s and ’60s.
Such innovation wasn’t lost on Karl Adam, one of the rowing world’s most famous coaches, who worked at a rowing club in Ratzeburg, Germany. Adam and his crews began to experiment with another arrangement, LRLRRLRL, with much success in the ’50s and ’60s. Now known as the German rig, this also turns out to have zero moment and it was used by the Canadian team that won gold at the 2008 Beijing Olympics.
Barrow has also found two oth- er rigs with zero moments and which, as far as he knows, haven’t
appeared in competition. One of these is LRRLRLLR, which is the Italian rig followed by its mirror image. The second is more exotic: the LLRRRRLL rig, which was put through its paces by the Im- perial College crew. So why have these arrange- ments never been adopted in a race?
One clue comes from our test on the Thames. The Imperial Col- lege crew noticed that the LLRRRRLL rig is affected by an unexpected ergonomic issue. In their usual rig, the rowers use the person two in front of them to synchronize their movements. However, you can’t do that with the LLRRRRLL rig.
Mind the puddles There is a more serious prob-
lem, says Volker Nolte, professor of biomechanics at the University of Western Ontario and former coach of the Canadian national rowing team. When a rower fin- ishes a stroke and lifts the oar blade out of the water, it leaves behind a vortex, known in rowing as a puddle, that creates a swell, raising the surface of the water by several centimeters. In a conventional rig, when rowers on the same side are two apart, there is enough time for the swell to die down before the next oar passes over it. But when the rowers on the same side are directly behind each other, the swell from the oar in front re- mains high enough to catch the one behind. With four rowers be-
hind one another in Barrow’s rig, this is a problem that crews can do without and may help to ex- plain why the conventional rig has prevailed. In fact, says Nolte, Adam tried all these rigs in the 1960s. His problem was that boats of the time were relatively slow, so even with a conventional rig, rowers toward the stern of the boat end- ed up putting their oars into the turbulent water left by rowers at the bow. This turbulence reduced the thrust generated. Adam found that both the Ger- man and LLRRRRLL rigs mini- mized this problem. But when he discovered the limitations of the latter, he settled on the German rig. Today’s boats go fast enough to outpace their own turbulence so this is no longer a consider- ation, says Nolte. So why did the Canadian row- ers use the German rig in Beijing? It turns out this had little to do with turbulence or Barrow’s mo- ment analysis. According to Nolte, the Canadians chose this rig because, when everything else had been taken into account, it al- lowed the team’s lighter rowers to sit nearer the bow. This made the bow lift out of the water, causing the boat to “surf” along when traveling at speed, thus reducing friction with the water. So much for moments of force.
health-science@washpost.com
Mullins is a consultant editor at New Scientist, from which this article was adapted.
www.newscientist.com.
NEW SCIENTIST Mathematical physicist Barrow’s calculations show that if the rowers were rearranged in any of several alternative rigs, the sideways motions would cancel each other out, resulting in no wiggle and no loss of effi ciency. T eoretically, anyway.
Cosmologist’s view of black holes puts a new spin on the universe
by Anil Ananthaswamy ALAMY
We could be living inside a black hole. This head-spinning idea is one cosmologist’s conclu- sion based on a modification of Einstein’s equations of general relativity that changes our pic- ture of what happens at the core of a black hole. In an analysis in Physics Let- ters B of the motion of particles entering a black hole, published in March, Nikodem Poplawski of Indiana University in Blooming- ton showed that inside each black hole there could exist another universe. “Maybe the huge black holes at the center of the Milky
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Way and other galaxies are bridges to different universes,” Poplawski says. If that is correct — and it’s a big “if” — there is nothing to rule out our universe itself being inside a black hole. In Einstein’s general relativity (GR), the insides of black holes are “singularities,” regions where the density of matter reaches in- finity. Whether the singularity is an actual point of infinite density or just a mathematical inadequa- cy of GR is unclear, as the equa- tions of GR break down inside black holes. Either way, the modi- fied version of Einstein’s equa- tions used by Poplawski does away with the singularity alto- gether. For his analysis, Poplawski turned to a variant of GR called the Einstein-Cartan-Kibble-Scia- ma (ECKS) theory of gravity. Un- like Einstein’s equations, ECKS gravity takes account of the spin or angular momentum of elemen- tary particles. Including the spin of matter makes it possible to cal- culate a property of the geometry of space-time called torsion. When the density of matter reaches gargantuan proportions (more than about 1,050 kilo- grams per cubic meter) inside a black hole, torsion manifests it- self as a force that counters grav- ity. This prevents matter from compressing indefinitely to reach infinite density, so there is no sin- gularity. Instead, says Poplawski, matter rebounds and starts ex- panding again. Now, in what is sure to be a controversial study, Poplawski has applied these ideas to model the behavior of space-time inside a black hole the instant it starts
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rebounding. The scenario resem- bles what happens when you compress a spring: Poplawski has calculated that gravity initially overcomes torsion’s repulsive force and keeps compressing matter, but eventually the repul- sive force gets so strong that the matter stops collapsing and re- bounds. Poplawski’s calculations show that space-time inside the black hole expands to about 1.4 times its smallest size in as little as 10-46
seconds.
“Maybe the huge black holes at the center of the Milky Way and other galaxies are bridges to different universes.”
— Nikodem Poplawski, who has a novel theory about the expanding universe we observe today
This staggeringly fast bounce- back, says Poplawski, could have been what led to the expanding universe we observe today. How would we know if we are living inside a black hole? Well, a spinning black hole would have imparted some spin to the space- time inside it, and this should show up as a “preferred direc- tion” in our universe, says Po- plawski. Such a preferred direc- tion would result in the violation of a property of space-time called Lorentz symmetry, which links space and time. It has been sug- gested that such a violation could be responsible for the observed oscillations of neutrinos from one type to another. Sadly, there is no point in our looking for other universes inside black holes. As you approach a black hole, the increasing gravita- tional field makes time tick more and more slowly. So, for an ex- ternal observer, any universe in- side would form only after an in- finite amount of time had elapsed.
health-science@washpost.com
Ananthaswamy is a London-based science writer. This article is reprinted from New Scientist magazine (
www.newscientist.com).
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