Running in bare feet or in light so-called foot gloves is trendy. Its proponents claim the practice is more natural (because our prehistoric ancestors lacked shoes) and easier on a runner’s musculoskeletal system (because without a cushioning sole, a runner adopts a gentler running style).

You might think that barefoot running is also more efficient, given that runners are spared the energy penalty of lifting shoes every stride. But that turns out not to be the case. In a recent blog post, Gretchen Reynolds of the New York Times reported on research conducted by Rodger Kram’s group at the University of Colorado at Boulder.

Kram, Jason Franz, and Corbyn Wierzbinski recruited 12 men who were experienced barefoot runners. As the volunteers ran at a steady pace on motorized treadmills, the rates at which they consumed oxgen, dV_O2/dt, and produced carbon dioxide were measured. By attaching small, unobtrusive lead weights to the runners’ socks, Kram and his team could isolate the two factors most likely to affect the energy efficiency of barefoot running: weight and gait.

The volunteers ran with and without shoes. Weights were attached in both cases. As you might expect, adding weight raised the amount of oxygen the runners consumed to maintain their pace. Regardless of whether the runners were barefoot or shod, dV_O2/dt increased by 1% for every 100 g of added weight.

However, running barefoot without added weight offered no efficiency advantage over running while wearing lightweight shoes. In fact, once footwear mass was taken into account, the shod runners consumed oxygen at a rate that was 3–4% lower than the rate for barefoot runners.

When my friend Rich posted a link on Facebook to Reynold’s blog post, I speculated that barefoot runners’ gentler gait might be the cause of the disparity in power. To cushion the impact of each footfall, barefoot runners bend their knees a bit more than shod runners do. Rising from that extra dip entails doing work against gravity and could therefore be responsible for the energy penalty.

An additional 1 cm in vertical dip would cost an 80-kg runner 8 J or 0.002 nutritional calories in mgh work per stride—provided the runner were 100% efficient at converting food into mechanical work. I’m not sure how metabolically efficient runners are. Concept2, a manufacturer of sophisticated rowing machines, assumes a value of 25% for a 175-lb rower. Using the same efficiency for the 80-kg runner yields a cost per stride of 32 J or 0.0076 nutritional calories.

According to this online calculator, an 80-kg runner expends 475 nutritional calories by running for 30 minutes at a pace of 8 minutes per mile (3.35 m/s or 7.5 mph, the pace of the volunteers in Kram’s experiment). If the 80-kg runner has a cadence of 160 strides per minute, then the cost per stride is 0.1 nutritional calories.

Springs and shock absorbers

The mgh work that extra bending entails seems to be about the right size to account for the loss of efficiency when running barefoot, but that equivalence is not enough to clinch the case. For one thing, as McNeill Alexander, Robert Ker, and Michael Bennett of the University of Leeds have argued, mammalian tendons serve as springs that store and release mechanical energy. Some of the potential energy that barefoot runners give up when they make that extra dip could be recovered when they spring back up.

In their paper, Kram and his colleagues speculate that the energy penalty of barefoot running arises from the work done by runners’ muscles in absorbing the impact of their footfall. Shod runners don’t pay the full penalty because the soles of their shoes do some of the work. Indeed, according to tests done by Sadayuki Ujihashi and his colleagues from Tokyo Institute of Technology, running shoes typically absorb about 55% of impact energy.

Kram himself runs in shoes. In the video you can see him running beside the foothills of the Rocky Mountains near Boulder. I also favor running shoes—but not when I exercise on a rowing machine. Even though rowing is easier on the feet than running is, I don’t want any of my energy being wasted on compressing cushiony shoes!

Last October my friend Karl invited my wife and me to celebrate China’s mid-autumn festival with some of his Chinese friends. The venue was a Chinese restaurant in Arlington, Virginia. After we’d eaten eight delicious courses and drunk (or tentatively sampled) sorghum vodka from Taiwan, Karl challenged his Chinese friends to recite Chao Yuen Ren‘s poem “The Lion-Eating Poet in the Stone Den”:

《施氏食獅史》

石室詩士施氏，嗜獅，誓食十獅。
氏時時適市視獅。
十時，適十獅適市。
是時，適施氏適市。
氏視是十獅，恃矢勢，使是十獅逝世。
氏拾是十獅屍，適石室。
石室濕，氏使侍拭石室。
石室拭，氏始試食是十獅。
食時，始識是十獅屍，實十石獅屍。
試釋是事。

Even if you can’t read Chinese, Chao’s poem looks as though it might be straightforward for native speakers to hear and understand. But Chao, who was a linguist, wrote the poem to demonstrate the futility of transliterating classical Chinese into the Roman alphabet. Every character in the poem is transliterated as “shi.”

Granted, Mandarin uses four tones that help distinguish otherwise identical-sounding words: high level, rising, falling and then rising, and high falling. But adding the corresponding diacritical marks does little to ensure comprehensibility.

As we discovered around the dining table, the poem is also incomprehensible—hilariously so—when recited in modern Mandarin. Of course, most sentences uttered by Mandarin speakers do not consist of the same syllable, but they do feature different tones. Listening to the recitals made me wonder: How important are tones to the comprehensibility of Mandarin, Cantonese, and other Chinese dialects?

Formants and fundamentals

Five months later, I came across an answer to my question in a paper in JASA Express Letters by Yin Shan-Kai of the Institute of Otolaryngology at Shanghai Jiao Tong University and his colleagues.

The starting point for Yin’s work is the idea, originated by Gunnar Fant in 1960, that speech can be passably reproduced by modulating the amplitudes of a small number of sine waves of certain fixed frequencies. Those frequencies do not include the overall pitch of a person’s voice, what you might call its fundamental frequency F₀. Rather, the frequencies correspond to the strongest peaks that are present in the frequency spectrum when a person utters a given vowel or consonant.

Fant called those characteristic frequencies formants. Only two formants, f₁ and f₂, are needed to reproduce vowels. For example, the “oo” in “boot” can be represented with one sine wave with a frequency f₁ of 320 Hz and a second, weaker sine wave with a frequency f₂ of 800 Hz.

Mandarin’s four tones are conveyed by modulating vocal pitch, F₀. Because sine-wave speech dispenses with F₀, Yin and his colleagues hypothesized that Mandarin speakers would have a tough time understanding sine-wave Mandarin.

To test the hypothesis, Yin and his colleagues asked 41 native speakers of Mandarin to listen to two sets of sine-wave speech. The first set consisted of 10 unconnected monosyllables pronounced with each of the four tones. The second set consisted of 20 short sentences.

Listeners to the unconnected monosyllables could not reliably identify the correct tone. On average, they got the tone right only 33% of the time, which is little better than the 25% they’d score if they just guessed. Listeners did much better with the short sentences. Some listeners understood all the sentences completely. The worse comprehension rate was 78%; the mean was 92%.

Yin speculates that the Mandarin speakers in his study, being familiar with the syntax and semantics of their native language, exploited contextual clues in the sentences to compensate for the lack of tonal information. That speculation is consistent with the result of a linguistic experiment that I’ve conducted: Native speakers of English can converse with each other even when they replace every vowel with “uh.” The conversation may sound odd, but it’s comprehensible. Try it yourself!

For some people learning Chinese, tones constitute an awkward, additional complication. At first glance, Yin and his colleagues’ work might therefore bring some relief. Tones, it seems, aren’t essential to comprehension, at least for sine-wave Mandarin. But the relief is illusory. Reaching the point where you can dispense with tones doubtless requires mastering the whole language, tones and all.

In April this year my wife and I were involved in a four-car pileup. Neither of us was hurt, but our car, a 1993 Honda Civic hatchback, was written off as a total loss by our insurance company. We had to get a new car.

Because we live in an inner city neighborhood and park on the street, we wanted a small car. We also wanted an economical car, one that would cost little to own and run over a lifetime at least as long as our old Civic’s 18 years.

The cost of 18 years’ of gasoline is significant. For some cars, it’s comparable to the initial cost of buying the car. Would getting a hybrid car end up saving money?

Consumer Reports provides estimates for the overall mileage of cars derived from a representative mix of highway and city driving. For the Honda Fit (the car at the top of our shopping list), CR‘s overall mileage is 33 mpg. For the Toyota Prius (the world’s most popular hybrid), it’s 44 mpg.

My 10-mile commute breaks down into 4 miles of city driving and 6 miles of highway. My wife gets to work on the Washington, DC, Metro. In a typical year, we drive about 6250 miles. Maintaining that rate over 18 years yields a lifetime total of 112 500 miles. Driving that distance with CR‘s overall mileage rates, a Fit would consume 3409 gallons; a Prius, 2557 gallons.

The Prius is considerably more expensive than the Fit. CR gives the range of their MRSP as $23 520 – $39 525 for the Prius and $15 175 – $19 540 for the Fit. Given our driving habits, would a Prius prove cheaper than a Fit in the long, 18-year run?

Not knowing the future price of gasoline, I framed the question as follows: At what gasoline price, averaged over 18 years, would the Prius become cheaper? The answer is $9.79. We bought the Fit shown here.

Going electric

Why not get an electric car? The Nissan Leaf is a four-door hatchback like the Prius and the Fit. At $35 200 – $37 250, its MSRP is as high as that of a fully tricked-out Prius. Even with its high fuel economy (CR gives the Leaf’s overall “gas” mileage as 106 mpg), the Fit would still prove cheaper to run. What’s more, the Leaf’s modest 100-mile range is too short for comfort.

At last week’s Industrial Physics Forum in Nashville, Tennessee, I learned that the limit on an electric car’s range is due not so much to the capacity of lithium-ion batteries but to their density. You can’t arbitrarily increase an electric car’s range by adding more batteries without weighing it down.

Even if the ranges of electric cars did match those of gasoline-power cars, electric cars are more expensive. What’s more, given that 70% of the electricity in the US is generated by burning fossil fuels, electric cars aren’t necessarily greener than gasoline-powered cars. The greenness argument appears valid, but it misses a key point: efficiency.

In the case of electric and gasoline-powered cars, the sequence of energy-conversion steps starts with a fossil fuel and ends in a moving vehicle. Both cases entail burning a fossil fuel to drive a mechanical device, either a power station’s turbine or a car’s internal combustion engine. The additional steps are different for the two types of car.

For an electric car, you need to convert kinetic energy into electricity, transmit the electricity to an outlet, charge the battery, and power the engine. For a gas-powered car, you need to refine the crude oil and transport the gasoline to a gas station.

I haven’t been able to find figures about the efficiencies of all those steps, but everything I’ve read about oil refining says it consumes a lot of energy. Indeed, according to a 2004 study by the California Energy Commission, oil refineries are the biggest consumers of energy in California.

So my hunch is that even if you live in a state, such as Kentucky, that gets most of its electric power from coal-fired stations, running an electric car is still likely to be the greener option. And if scientists and engineers succeed in building a better battery, I expect my next car will be electric.

Charles Day

The 13th James Bond movie, Octopussy, came out in 1983, two years before West Germany’s first-generation cellular phone system, C-Netz, was launched. In the movie, Bond learns of a plot to explode a nuclear warhead at a US Air Force base in Germany. Lacking a mobile communications device, he has to deliver the news in person. In fact, he has to defuse the bomb in person.

By the time the 18th Bond movie, Tomorrow Never Dies, arrived at cinemas in 1997, the number of cell phone subscribers in rich countries had reached 18 per 100 inhabitants—too many, I presume, for the movie’s screenwriter, Bruce Feirstein, to have Bond use an ordinary cell phone. Indeed, Bond’s Ericsson phone came equipped with a stun gun, fingerprint reader, and remote control for his armored, weapons-laden BMW 750i.

Tomorrow Never Dies is the most telecommunications-intense movie in the Bond series. The villain, Elliot Carver, is a media magnate who seeks to provoke a war between Britain and China. Besides a ratings boost, the payoff for Carver is exclusive media rights in China for 100 years.

Carver and his henchmen set their plot in motion by tampering with the GPS signal received by HMS Devonshire, a Royal Navy frigate cruising in the South China Sea. Fooled into believing that his ship is far outside Chinese territorial waters, the captain is surprised when two MiGs from the People’s Liberation Army Air Force warn him off. Carver’s stealth ship sinks the Devonshire and shoots down one of the MiGs to create what looks like an act of mutual aggression. Thanks to Bond and Chinese agent Wai Lin, shown above, war is averted.

When I first saw the movie, I wondered about the feasibility of tampering with GPS signals in a way that secretly alters position information. In their 2006 book The Science of James Bond (Wiley), Lois Gresh and Robert Weinberg don’t discuss that element of Tomorrow Never Dies‘s plot, but they do devote three paragraphs to a similar plot element in Dr No, the first Bond movie. Using radio waves to throw a rocket’s gyroscopic controls off balance—called toppling in Dr No—is, they conclude, “a bit of a stretch.”

Still, it’s perfectly feasible to jam GPS signals, or any other radio signals if you know the frequency—which brings me, at last, to my news. Last week I received a press release from QinetiQ, a defense manufacturer based in Britain. In partnership with the Canadian company NovAtel, QinetiQ has developed what purports to be the first-ever single-enclosure GPS antijam antenna for military land vehicles. According to NovAtel’s press release, the antenna, which is called GAJT and pronounced “gadget,” is a

commercial off-the-shelf (COTS) product, providing short order lead times and enabling quick deployment to the field. Manufactured in Canada, and incorporating Canadian and UK technology, GAJT only requires Canadian and UK export approval, which means exporting to authorized customers in foreign countries is greatly simplified.

I’m not sure whether the scientists, engineers, and marketers at QinetiQ and NovAtel were inspired by James Bond. But it does strike me as plausible that QinetiQ’s odd spelling is derived from Bond’s gadget supplier, Q.

Charles Day

When I go to my gym, I sometimes see people lifting weights in physically inappropriate ways. By “physically inappropriate” I don’t mean that they exhibit poor, injury-inducing form or that they use weights that are dangerously heavy or ineffectually light. I mean that they don’t, to use the language of physics, do much work.

First defined in the 1830s by Gaspard-Gustave Coriolis, work entails moving a force’s point of application. If you’re handling a barbell, dumbbells, or other free weights, doing work means raising the weight’s center of mass against the pull of Earth’s gravitational field.

But if you don’t raise the weight, if you move it about in a horizontal plane, your workout will be workless and quite possibly worthless. One near-workless routine I’ve witnessed involves hoisting a weight above your head while simultaneously bending at the knees, thereby ensuring that weight remains at the same height.

There’s no doubt that the woman in this video is doing work as she raises her own center of mass and those of two 45-pound plates and a 45-pound bar.

Although knowing the concept of work is helpful in the gym, calculating how much work you do when you lift weights can be disheartening. The work required to lift 135 pounds five times through a distance of 1 meter is 3 kJ or just 0.7 nutritional calories.

Charles Day

Sixty-four years ago George Orwell, the author of Homage to Catalonia, Animal Farm, and Nineteen Eighty-Four, wrote an instructional essay for London’s Evening Standard entitled “A Nice Cup of Tea.”

To justify why anyone, let alone a famous writer, should bother to prescribe how to make tea, Orwell began by pointing out that

If you look up ‘tea’ in the first cookery book that comes to hand you will probably find that it is unmentioned; or at most you will find a few lines of sketchy instructions which give no ruling on several of the most important points.

This is curious, not only because tea is one of the main stays of civilization in this country, as well as in Eire, Australia and New Zealand, but because the best manner of making it is the subject of violent disputes.

Then, in dogmatic tones almost free of irony or humor, Orwell enumerated the 11 rules for good tea making, “every one of which I regard as golden.”

Some of those rules are a matter of personal taste. Unlike Orwell, I don’t disdain tea from China. Having lived in Japan and visited China, I enjoy those countries’ red, white, green, and black teas. I do, however, agree with him that tea made with cream, rather than milk, tastes sickly.

But other rules are a matter of physics and chemistry. The black Indian and Sri Lankan teas that Orwell favored are best brewed in water that’s just below the boiling point. The goal, as the Wikipedia entry on tea puts it, is “to extract the large, complex, flavorful phenolic molecules found in fermented tea.”

Orwell rightly advocates promptly using just-boiled water poured into a pre-warmed pot. But I don’t see why the teapot is best warmed on the stove, rather than with boiling water. Heat is heat. While it’s true that briefly swilling out a teapot with hot water won’t transfer much heat, filling the pot with hot water and letting it sit for a minute will.

He’s right, too, to promote the release of flavor from the tea by stirring the pot. Diffusion is a slow process. Stirring a hot liquid, or what a physicist might call convective advection, speeds things up considerably.

Dwelling too much on the science of tea detracts from enjoying it and recognizing its universal, eternal charms. Forty years before Orwell’s essay appeared, Okakura Kakuzo wrote in The Book of Tea,

The world is groping in the shadow of egotism and vulgarity. Knowledge is bought through a bad conscience, benevolence practiced for the sake of utility. The East and the West, like two dragons tossed in a sea of ferment, in vain strive to regain the jewel of life. . . . Meanwhile, let us have a sip of tea. The afternoon glow is brightening the bamboos, the fountains are bubbling with delight, the soughing of the pines is heard in our kettle. Let us dream of evanescence, and linger in the beautiful foolishness of things.

Charles Day

Thanks to tea drinkers Paul Guinnessy and Jenny Stout for drawing my attention to Orwell’s essay.

Two weeks ago I received a free book through the mail. Written by Mark Frary and published by Rodale Books, the book bore the promising title Better Living Through Science: The Basic Scientific Principles You Need To Solve Every Household Conundrum. I’d forgotten about the book until yesterday when Kate, a communications assistant at Rodale, sent me an e-mail saying she’d love to talk to me about my plans to cover it.

Physics Today doesn’t routinely review books like Frary’s. The magazine’s books editor prefers to devote his limited pages to titles aimed at the physics community—with good reason. For some of those books, Physics Today is the only publication that provides a review.

But my hunch is that you, the readers of my blog, might want to know more about a book that purports to help you in your everyday lives.

The 142-page book contains an introduction, plus 34 illustrated chapters with titles like How to combat garlic breath, How to win at pool, and How to sail a yacht. Each chapter succinctly describes the science behind the problem and the solution. “This book,” writes the author in the introduction, “explains things in an easy-to-understand manner that can be enjoyed by anyone, no matter what grades you got back in high school.”

If you’re a scientist like me, you’ll probably find the book offers a mix of things you already know or could easily deduce and things you don’t know. The chapters on throwing balls, stopping cars, and other applications of Newtonian mechanics didn’t teach me anything new, but I did learn how to remove a red wine stain from clothing (apply a mixture of liquid soap and hydrogen peroxide).

My biggest beef with the book is that it doesn’t live up to its subtitle. I didn’t expect such a short book to discuss “every household conundrum.” But, having outlined 34 quotidian problems, the author could have gone on to explain how to approach solving all the others.

According to a much-quoted Australian aboriginal proverb, “The more you know, the less you need.” Frary’s solutions, most of which don’t require special tools, exemplify that piece of folk wisdom. But his omission of a general discussion of the scientific method brings to mind an addendum to the proverb: “The more you understand, the less you need to know.”

Charles Day

As you might expect, the Wall Street Journal has a small sports department. But despite its modest size, the department is often more interesting than those of the other newspapers I subscribe to, the Redskins-obsessed Washington Post and the Yankees-obsessed New York Times.

For example, in today’s WSJ, David Biderman reasoned that

because college athletes occasionally do things other than play football, practice football, watch football and play football video games, we decided to go through the media guides of every major-college football team to see what these guys study.

Biderman and his team found 1104 student footballers whose majors were disclosed. The four most popular majors were business (155 students), sociology (134), communications (108), and liberal arts (103). The least popular, with one student apiece, were Spanish and philosophy. Physics scored zero.

Having seen thousands of physicists thronging at meetings of the American Physical Society, I can confidently generalize that most of us don’t look like football players. Still, achievement in athletics and physics are not mutually exclusive.

When he was an undergraduate at Peterhouse, the oldest and smallest of Cambridge University’s constituent colleges, William Thomson won the university’s single sculling championship.

Thomson became a great physicist. He is better known as Lord Kelvin, the title bestowed on him by Queen Victoria. I couldn’t find a picture of Thomson in a single scull. But to give you an idea of what he might have looked like in his rowing prime, here’s the reigning Olympic single sculls champion, Olaf Tufte of Norway.

Charles Day