# Arm Supercomputer Captures The Energy Efficiency Crown

Arm Supercomputer Captures The Energy Efficiency Crown

The Next Platform
Arm Supercomputer Captures The Energy Efficiency Crown
Michael Feldman Michael Feldman
2 days ago

When it comes to energy-efficient supercomputing, sometimes less is more. That was illustrated this week by Fujitsu with its A64FX prototype, which captured the top spot on the Green500 list. The machine has no accelerators, network cards, or main memory on the motherboard. Everything has been sucked onto the processor package.

As is evident from its name, the A64FX prototype is equipped with the Fujitsu chip of the same name, and the one that will be powering the upcoming “Fugaku” supercomputer at RIKEN lab in Japan, a fact that has earned it the nickname micro-Fugaku. The prototype is essentially a two-rack, 768-processsor version of its much larger brother.

According to the new Green500 rankings released this week at SC19, the prototype delivered just a skosh under two petaflops on the High Performance Linpack (HPL) benchmark and did so with just 118 KW of power. That translated into an energy efficiency rating of 16.9 gigaflops/watt, which was just enough to capture the number one spot on the new Green500 list.

The lack of an accelerator makes the prototype an extreme outlier. For the past several years, the upper echelons of the Green500 has been dominated by supercomputers outfitted with these PCI-Express coprocessors, mostly of the GPU persuasion. The last time a non-accelerated system made it to the number one spot was June 2012, when an IBM Blue Gene/Q supercomputer captured the title.

Even on the current Green500 list, all the systems between the top-ranked A64FX prototype and TaihuLight, at number 35, are equipped with accelerators. But TaihuLight is about one-third as efficient as Fujitsu’s machine, with a Green500 result of 6.1 gigaflops/watt. It’s powered by the 260-core ShenWei 26010 processor.

The A64FX processor is a 64-bit Arm implementation developed by Fujitsu and RIKEN that uses the Scalable Vector Extension (SVE) technology. In a sense, the A64FX’s 512-bit SVE unit acts as an on-chip accelerator, since it can deliver about 3 teraflops at double precision on its own. That puts its double precision floating point performance in the general vicinity of a GPU. The speediest Volta V100 GPUs from Nvidia delivered 7.5 teraflops when it was announced in May 2017 and has been tweaked in recent years to push that up to 7.8 teraflops. The “Vega 20” CPU used in AMD’s Radeon Instinct MI50 and MI60 accelerators run at 6.7 teraflops and 7.4 teraflops, respectively. But they all need about 300 watts to hit those peak values. A closer analogy is the now-orphaned Intel “Knights Landing” Xeon Phi processor, which was launched in June 2016, also delivers 3.46 teraflops, but draws 245 watts in its peak configuration. Clocking it down a bit and turning off some cores cuts the price by 20 percent and reduces throughput to 3 teraflops, but in a 215 watt thermal envelope. Faster is not always better.

The A64FX tops out at about 170 watts, which is a good deal more power efficient than the Xeon Phi, but not as efficient as the current crop of GPUs. Of course, GPUs need a host processor and a PCI-Express connection to the host, elements that an A64FX-based system is able to dispense with.

So what makes the A64FX machine so green?

Although some people believe the Arm architecture is inherently energy-efficient, that’s not the case. If it were, then the Astra supercomputer, which uses the Marvell ThunderX2 Arm processors, would rank a lot higher on the Green500 than number 176, where it currently sits.

According to Toshiyuki Shimizu, the Senior Director of the System Development Unit at Fujitsu, the efficiency of the prototype system is the result of both hardware and software innovations. The hardware side centers on the A64FX itself, which is made using the 7 nanometer FinFET process and 2.5D Chip-on-Wafer-on-Substrate (CoWoS) packaging technology from Taiwan Semiconductor Manufacturing Corp to integrate Fujitsu’s Tofu D interconnect and main memory.

The A64FX is one of three HPC architectures that put all of their main memory on the package, in this case, in the form of four 8 GB HBM2 modules. NEC’s Aurora vector engine uses HBM2 memory as well, and the predecessor Sparc64-XIfx processor from Fujitsu used Hybrid Memory Cube memory from Intel and Micron Technology. The Knights Landing Xeon Phi processors used a mix of MCDRAM on package from Intel, a riff on Hybrid Memory Cube, and DRAM on the system board. With the Fugaku system architecture There is no DRAM sitting on the motherboard. As a result, less power is used to drive bits to and from memory, since the four HBM2 modules are sitting right next to the processor on the package instead of at the end of a wire in the form of a DIMM. Depending on who you believe, HBM2 is between 3X and 10X more energy efficient from a bandwidth perspective than DDR4 memory.

It’s worth pointing out that 32 GB of memory is somewhat on the low side for an HPC node these days, even for a single-socket system like the A64FX machine. DRAM chews up a fair amount of power, so systems with more memory tend to be less energy efficient, all other things being equal. Most systems today are using 128 GB per node, albeit for two sockets. A system somewhat analogous to the prototype is the Oakforest-PACS system built by Fujitsu the University of Tokyo and the University of Tsukuba in Japan, which uses a single 3 petaflops Xeon Phi processor per node. But in this case, in addition to the 16 GB of on-package Xeon Phi memory, there is also 96 GB of conventional DDR memory. GPU accelerators tend to have 16 GB or 32 GB these days, and they offload to host memory when they can.

The A64FX on-chip Tofu D interface undoubtably saved a few watts, since a network adapter plugging into the single PCI-Express 4.0 port on the system would draw more power. In general, integrated interconnects are uncommon, since they add complexity and can limit choice, but the advantage of on being on-chip not only makes for better energy efficiency, but potentially better network performance as well.

On the software side, Shimizu said that their long experience with the Tofu interconnect enabled them to fine-tune the communication libraries for extra efficiency. Likewise, for the math libraries, which they were able to optimize for the A64FX SVE instruction set. The Fujitsu team also did performance tuning on the HPL code using a set of analyzer and monitor tools.

As impressive as the prototype’s energy efficiency is, the technology would require nearly 60 MW to deliver an exaflop on HPL. Since the plan is to not exceed 30 to 40 MW for Fugaku, it looks like they are only going to be able to scale this system to about 400 petaflops – that according to the current performance specifications of the system from RIKEN’s website. At this point, the performance goal is to be able to run key applications one or two orders of magnitude faster than they ran on the now-decommissioned K computer, a system with a peak performance of 11.3 petaflops.

Will the A64FX create an appetite for non-accelerated HPC machines? We may soon find out. The processor will be offered in commercial products from Fujitsu in the form of their new FX1000 and FX700 systems, as well as in Cray’s CS500 line. The test case is imperfect, since the A64FX also has to fight the headwinds of Arm adoption in a market untested for this architecture. But if the chip manages to hit the right balance of performance, programmability, energy efficiency and price, chipmakers and their customers may rethink the utility of accelerators.

Categories: HPC
Tags: A64FX, Fugaku, Fujitsu, Green500, RIKEN, SC19
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# The Price of Sex

The Price of Sex

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Economics, Feminism, Sex, Top Stories
Published on November 14, 2019
The Price of Sex
written by Jerry Barnett

Working as a photographer for a charity a few years back, I was travelling through Malawi and stopped overnight in a mining town. It was a Wednesday, and I headed out to a bar. Other than a woman serving, everyone else there was male. Some were playing pool. Some were drinking, but most were doing neither. I asked the bargirl why there were no women in the place. With a look that suggested I was being dim, she explained: “The men get paid on Friday.”

On the surface, in a mining town, the gender pay gap is huge, with the vast majority of money officially going to men. And yet, by Saturday morning, much of the cash has been transferred to bar owners, prostitutes, girlfriends, and wives. A privileged observer might suggest that women in such a town ought to be liberated to earn their own money. But the point is that they already are. While most fair-minded people would no doubt agree that women should be free to take mining jobs if they choose, it’s unlikely that many women want such gruelling, dangerous, and unhealthy work when being a bar prostitute, a girlfriend, or a wife to a miner is available as an alternative.

The total value of the sex trade could be said to be the value of the net transfer of wealth from men to women. How can we begin to value an industry this big, ancient, and diverse, especially when much of it—probably most of it—is undocumented and untaxed?

During another African trip—this time to Bamako in Mali—I asked a young man whether he had a girlfriend. He explained “Non… pas moto, pas copine.” He had no moped, and so, no of course he didn’t have a girlfriend. He told me that the girls back home in his village were friendly and open, but the big-city Bamako girls had higher expectations. So, naturally, buying a moped became a priority for any aspiring young Malian. I had noticed that Bamako’s streets were filled with mopeds, mostly driven by men, but often with women riding pillion. For a man there, a moped means sex as well as transport. These anecdotes point towards the difficulty involved in calculating the extent of the sex trade. Some percentage of Bamako’s moped sales represent a hidden transfer of wealth from men to women: men buy mopeds, and women get free transport. What is this transfer of value worth?

Now consider how many similar transfers of wealth take place. The UK flower industry was worth almost £1bn last year. Of course, flowers are bought by many people for all sorts of reasons, but many are bought romantically by men for their female partners, or for courtship. What about restaurant meals, hotel rooms, concert tickets, diamonds, taxi fares, cocktails, vacations…? What proportion of money spent by men on these things is related to a promise, a hint, or a mere hope, of sex, whether fulfilled or unfulfilled? Historically, what proportion of the silk carried (invariably by men) along the Silk Road found itself worn by the wealthy wives and mistresses of Europe?

Males (in our species, and others) are, by definition, the low-value sex. The key difference between males and females in reproduction is that males are low investors and females are high investors. Female birds and reptiles lay big, nutritious eggs. Female mammals have to carry (and feed) infants for weeks or months of pregnancy, and then suckle them afterwards. Even in plants (at least those species that produce separate male and female flowers), the females are forced to invest more. It is no coincidence that marijuana farmers destroy male plants, and retain the females for their big, resin-heavy flowers. Females are more valuable, almost everywhere.

This truth about sex displays itself very differently in different species. In humans, it is expressed in a trade that is fundamental to us, and has shaped our recent evolution. In an essay entitled Why Do Men Hunt? (published in a collection entitled Why Is Sex Fun?), the science writer Jared Diamond hypothesises that hunting skills evolved in human males in order to acquire meat that could be traded for sex. Our recent evolution was heavily shaped by trade. Humans may not have the speed, strength, teeth, or claws of most predators, so our brains evolved instead. Our ancestors developed language, teamwork, advanced weapons, and the ability to strategise, because these abilities improved our chances of reproducing. A man who was a good hunter brought meat back to the clan, and a man with meat will mate more often and produce more children. The children in turn inherit the skills of their hunting fathers. The evolution of the modern human brain coincided with the extinction of the largest mammals (megafauna) on every continent, starting around 125,000 years ago. Until the rise of modern man, being big was a tried and tested survival mechanism. Humans changed that, and the largest mammals became an early casualty of the human sex trade.

If Diamond has answered the question Why Do Men Hunt?, the answer to the corollary question Why Don’t Women Hunt? ought to be obvious. Women didn’t hunt (in the traditional sense at least) because they didn’t have to. Hunting was dangerous and required a large investment of valuable calories. Why hunt when men will bring you meat? This does not mean, of course, that women were freed from intra-sexual competition. While men competed with each other in terms of hunting abilities such as strength, agility, and technical innovation, women competed to win the best meat (and sperm) from successful hunters. While female competition was less physical than the male variety, it was no less intense, and was focused on presenting attractiveness and youth (which are proxies for fertility and genetic health). Women therefore took a lot of interest in their own, and their rivals’ appearances, in order to copy techniques that other women employed to maximise their attractiveness, and to socially shun and stigmatise younger and better-looking rivals.

And so, a primitive economy emerged. The sex trade launched technological and economic growth, and the sex roles continued broadly as they had begun. Men relied on innovation, risk-taking, and social status to attract mates, and women became skilled in the arts of attracting (and preferably keeping) a mate. As the male-led industries evolved and diversified from their origins in hunting and fishing, thousands of new industries, roles and professions were spawned.

The original female industry—the sex trade—was undoubtedly far bigger than any of the other (male-created) industries, because its role was to collect a dividend on all male-led activity. The greater the innovation and diversification of male-run industries, the larger the sex trade became.

As civilisation evolved, so did the sex trade. It began with “primitive prostitution”—straightforward trades of meat (and other rare gifts such as honey or decorative items) for sex, but with technological advances such as private property, money, and contracts (verbal or written), it became increasingly sophisticated. Private property allowed a man’s social status to be evaluated by his wealth (which, of course, he took care to display). Publicly acknowledged contracts allowed the development of marriage, in which women could offer exclusive access to their fertility in exchange for a male promise to provide for them (and their children). Sexual exclusivity was valuable to men, because it provided certainty over paternity. In exchange for this guarantee, men paid far more for sex with wives than they would for casual sex.

The price of (female) sex is driven by men’s ability to pay, and by availability. Unlike virtually any other commodity, the supply is fairly inelastic, since biology mandates (approximately) a 50-50 population balance between men and women. This means that, as the male-led industries have grown exponentially, the price of sex has kept track. While the average price of sex is very hard to estimate accurately, the price of prostitution is a good proxy and it is easy to measure. Cultural, economic, and demographic changes have all had the effect of increasing or reducing the price of sex. Wars and famines that reduce the male population more than the female population will naturally affect the ratio of supply to demand and lower the cost of sex. The sex-selective abortion of girls in countries like China and India, on the other hand, will increase it. Similarly, mass migration will tend to raise or lower the price, depending on the culture and gender balance of the migrants. When Polish people won free movement across the EU in 2004, I heard complaints from both low-skilled male friends in the building industry, and from sex workers that rates were being undercut by the new arrivals. The Economist suggested in 2014 that German sex workers had felt a similar effect. But (the same article reports), the price of sex has declined globally in recent decades, reflecting other trends, including online advertising for sex workers, hook-up culture driven by dating apps, and reduced social stigma for sex workers and women engaging in casual sex.

Unsurprisingly, sex workers are better aware than most of the value of sex, and less ashamed to discuss it without euphemism. I’ve seen social media posts from sex workers asking for free services, from photoshoots and car repairs, to video editing and rodent removal.

How does one value all this free stuff, given willingly by men in exchange for sex, or in the hope of sex, or merely to impress an attractive woman? This question is probably unanswerable to any degree of certainty. One thing is sure though: for men, sexual and romantic relationships can be expensive. In 2017, the Institute for Fiscal Studies found that men from poor backgrounds in their forties were twice as likely to be single as men from wealthy backgrounds. Another British study revealed that men spend about £1,300 a year more than women on dating. Dating is not just a way to discover a person’s personality, but a way to assess a man’s wealth and generosity. Women are advised by friends to “value themselves” and not sleep with men on a first date. The latest generation of dating apps produce data that reveals the extent of difference between male and female courtship behaviours. A study on Tinder, for example, found that men have to swipe right about 15 times more than women to get a similar level of response. These are not marginal differences, and they shine a light on an old reality: that female sex is vastly more valuable than male.

We may not be able to calculate the extent of the wealth transfer from men to women, but we can gauge the scale of the trade by examining male and female relative outcomes. The gender pay gap has become well known, and is widely (and falsely) presented as evidence of female disadvantage. The gap is typically calculated at between ten and 20 percent. Not only do women earn less than men on average, but they work fewer years of their lives than men. On this basis women must—surely—be poorer than men? If they are, this will be easy to demonstrate via various metrics. A naive researcher might expect the outcomes for gender to be similar to the racial disparities in the United States, where African Americans are paid less (on average) than Whites or Asians. Predictably, this racial pay gap is represented in other metrics: African Americans are more likely to be jailed, to be shot by police, and (most important) to die younger than other groups. Life expectancy is an excellent proxy measure of general wellbeing.

And yet, when the same measures are applied to gender, the outcomes are the reverse of what might be expected. American men are more than ten times more likely to be imprisoned than women and around 20 times more likely to be shot dead by police. Similarly, women outlive men significantly. How is it that women should be nominally poorer than men (based on pay differences, at least), yet by all metrics of wellbeing appear to be better off? This difference in lifespan tends to be blithely dismissed as “biology,” but this alone is no explanation. Yes, biology is the underlying reason men have worse outcomes than women. Not because men are inherently prone to die younger, but because the sex trade requires men to take the greatest risks and the toughest jobs.

The reality of these outcome gaps that black people represent a disproportionate proportion of America’s least successful 20 percent, and so do men. America’s prisons are full of poor people (disproportionately black and disproportionately male) who broke the law, in many cases, because they could find no other way to survive. Middle-class women with little understanding of how poor communities function, may instead be predisposed to find “toxic masculinity” a satisfactory explanations for male criminality. But working-class women tend to see things more clearly. When I interviewed Lady Andromeda, a black, south London sex worker, she explained simply: in poor communities, women can sell sex and do relatively well. In fact, working-class women in London who sell sex can easily earn more than most middle-class men. But what options do men have in the poorest communities? “They steal cars, or sell drugs,” she said. It is not, of course, that women cannot do these things. But they have a safer, better-paying, and (in London, at least) legal alternative. This is why poor men are far more likely to end up in prison, or murdered than either poor women or wealthier men.

So, women, thanks to the sex trade, have better outcomes than men. This still leaves the chicken-and-egg question: does the sex trade exist because women choose it, or because (as feminist theorists may claim) it is forced upon them by systemic misogyny and glass ceilings? Clearly, women do much better than men in poor communities and mining towns, but what about at the high end of society? We are often told that the gender disparity in corporate board positions is proof of a male-rigged system. Wouldn’t women become CEOs too, given the opportunity? It appears not. The book Superfreakonomics outlines a study of male and female MBA graduates. While women earned similarly to men early in their careers, the wage gap rapidly increased. It was found that women “…who leave the workforce are disproportionately those with very high-earning husbands.” It appeared that female MBA graduates often used their MBA to marry high-earning men rather than pursue long-term business careers. On paper, their earnings fell behind men, but in practice, their lifestyles were upheld by switching some of their corporate earnings for sex trade earnings. After all, being a senior manager of a large corporation is punishing, involving long hours, endless travel, and missing out on social and family time. Is it better to be a CEO or a CEO’s wife? Each occupation shares the same wealth, home, vacations, but the CEO’s wife arguably has a better lifestyle than her husband.

From Jared Diamond’s question Why Do Men Hunt? to the modern versions: Why Do Men Mine?, Why Do Men Sell Drugs? or Why Do Men CEO? the answers are similar. But the direction of travel looks positive for equality. The social trends of recent decades—for women to join the once-male economy, for increased sexual freedom, and for the price of sex to fall—point towards a narrowing of the gap in outcomes between men and women. Economic innovations such as Universal Basic Income may help narrow the gap further. Conversely, the current trends towards conservatism and nationalism may halt and reverse the liberal revolutions of the twentieth century, with potentially unhappy consequences for men and women.

Jerry Barnett is a technologist, author, and campaigner. His book Porn Panic! documents recent moral panics against free expression that have arisen on the identitarian Left. He runs the Sex and Censorship page on Facebook and you can follow him on Twitter @PornPanic

Featured Image: The Salon in the Rue des Moulins by Henri de Toulouse-Lautrec (wikicommons)

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Filed under: Economics, Feminism, Sex, Top Stories

jdfree49

Let’s get the obligatory over with: http://www.denisdutton.com/baumeister.htm

Now, let’s all think about how absurd ratio’s of men’s to women’s “income” are in a world where much of men’s earnings are still being consumed by the women who share their beds.
PeterfromOZ

Am I alone in finding all this cod evolutionary psychology about the roles of men and women a load of bollocks?
So women only trade sex and that sex has an economic value? One wonders how people come up with such asinine ideas. How do the proponents of this ridiculous cant factor in the fact that a substantial number of women will priortise physical attraction over any other attribute of a man.
Farris

“Why hunt when men will bring you meat?”

Yet among a pride of lions, the females do the bulk of the hunting in addition to bearing and rearing young. I guess the lionesses didn’t get the memo.
gagamba

That’s because the lionesses aren’t planting the rice and the washing the clothes.

In a pride there is one adult male, several juvenile males who are ejected at age two or so, and many lionesses with their cubs. What happens to these sole males without a pride? They learn to hunt independently (using what skills they learnt in the pride), sometimes in a coalition with a brother who left with him, they scavenge, or they die – only one in eight survive to adulthood. Only physically strong and intelligent males survive to become adults in charge of a pride. Because of their larger size and darker manes that betray camouflage, males tend to be ambush hunters in the dense, thick brush, which is more difficult to film and study – and present on TV. They also hunt more often at night. In the open savannah they are more easily seen than the females, who use stalking techniques, though this conspicuousness can be used to flush their prey toward females. Further, the type of prey hunted plays a role. Wildebeests and antelope are very different from Cape buffalo and the attack strategies differ. Lionesses are about 30% faster than lions, so their speed is more advantageous when hunting light, fast prey. When hunting slower, larger animals, there are repeated charges and counter charges from both parties until the targeted buffalo is separated from the herd, with the male then sent in to pull down the prey. For prides that hunt elephants, the male is also quite involved.

“ Female lions do all of the hunting”

False. Both male and female lions hunt. The reason females hunt more frequently, is because the male must spend more time defending his territory. Another reason is that males are more conspicuous in the bush with their dark coloured manes, while females are more camouflaged and therefore less likely to be detected. When hunting together, females often chase down and catch the prey while the male uses his superior strength to give the fatal blow, particularly for large prey species such as Cape buffalo and giraffe. Additionally, males who live in coalitions without females or a pride will hunt for themselves when they aren’t successful in scavenging meals from weaker predators.

“Male lions are lazy”

False. Male lions have a reputation for being lazy, but that is far from the truth. A male’s job is critical to the protection of his pride. Male lions patrol the territory where the pride lives, and will fight to protect it. They travel vast distances to patrol their territory, by scent marking and vocalizing, to ensure other lions who may be a threat, stay away. It is critical for male lions to keep out other males, because if another male or coalition comes to dominate, they will kill all the cubs to keep from expending energy on raising cubs that are not their own offspring.

“Male lions eat first”

False. Male lions do not always eat first. If they are on a large carcass with plenty of food, they will share with both females, younger males and cubs at the same time. It is usually only when there is limited food, that the male will fight and chase off the others so that he gets enough to eat.
Madikwe Safari Lodge – 8 Sep 17

Myths About Lion Behaviour | Madikwe Safari Lodge. There is a number of misconceptions about lion hunting and feeding behaviour…

Of course the lives of lions and humans – even primitive, stone-age ones – vary greatly, so perhaps not the best like-for-like comparison.
Stephanie

I think it is necessary to consider the voluntary wealth transfer from men to women when considering “male privilege,” the gender wage gap, and the resulting demands for greater involuntary wealth transfers through redistribution. However, characterising this dynamic as “sex trade” seems grossly reductionist and dismissive of the husband-wife partnership that is the building block of civilization. Unsurprising then that someone who adopts such a cynical premise ends with:

Conversely, the current trends towards conservatism and nationalism may halt and reverse the liberal revolutions of the twentieth century, with potentially unhappy consequences for men and women.

The author assumes that diminishing the wealth transfer from men to women is a good thing, and that the resurgence of conservative values will render men and women less happy. This is contradicted by women today being less happy than in previous generations. Most women want to raise a family. Feminist ideology pushing them to waste prime reproductive years on casual sex, removing the obligation on men to care for them, and adding the expectation of a solid career contradicts biological programming and has resulted in a measurable increase in stress and decrease in happiness.

I don’t know how the author ends up tripping up at the end when everything that came before spoke to the privileged place women are born into, but it was an unfortunate way to end an otherwise interesting article.
LonelyProfessor

This is yet another article and series of posts aimed at convincing the reader that:

The well-being of men is much less important than the well-being of women: it not only is that way, but should be that way; and

Wealth redistribution is bad, bad, bad… that is, unless it is redistribution from men to women, in which case conservatives have nary a peep to say about it.
dirk

Another, very important something to know where sex roles in Africa and elsewhere are considered: In the West (but also in the Middle East and India if I,m not wrong), the family of the bride pays the young bridegroom the wedding and a sum for taking over the responsibility for their daughter and future offspring. In Africa, the poor youngster has to PAY FOR his bride (generally his parents do, he still has not much money, or cattle, in which units most bride prices are paid, even now). The sex involved is a minor detail I guess, it is the responsibilities, housing, local permissions, education of kids, etc etc, that counts. The wife ( in the villages at least) also works the field, plantain-banana tree corner, feeds the ducks and chicken, harvests the cassava, brings in the water from the well (all on her own, maybe helped by daughters or other women), cuts the firewood, cooks the food and even makes the beer for the men (from millet or banana), until, of course, Western social habits, urbanisation, wages in the mines, and commercial beer takes over (the Dutch Heineken nowadays makes most of their profits in the new African nations, thanks to beer-girls promotion, and seductive TV ads). Where the hell is all this going to end??
lonaleemanning

What an interesting article. I don’t think this article is intended to be prescriptive. It’s observational, a way of looking the world. Look at the energy (in terms of growing antlers and feathers) that males put into courtship displays. And of course there would be caveats and exceptions. For example, instead of being purchased (wife) or rented (sex worker), sometimes, and more often in the past, women were stolen in skirmishes, like the Sabine women.
I haven’t watched the Handmaid’s Tale or read the book, but I was just thinking that the premise didn’t make sense to me. If fertile women were at a high premium, this ought to increase their value in the market. In such a society I’d expect to see fertile women doing extremely well for themselves, living in penthouses and so on,not being house slaves.
MorganFoster

This still leaves the chicken-and-egg question: does the sex trade exist because women choose it, or because (as feminist theorists may claim) it is forced upon them by systemic misogyny and glass ceilings?

No woman ever quit her job to enter the sex trade because her business career was stalled at “Vice-President in charge of Regional Sales”.
GeorgeQTyrebyter

Women do not hunt in most societies. Women do not engage in war in most societies. It’s not difficult to understand why.

Babies. If you have a baby to care for, you cannot either hunt or play war games, which require you to travel long distances, and to be silent for extended periods. Babies cannot be made to be silent. Plus they are awkward to carry, require frequent feeding, and take up the use of one arm, sometimes 2.

You can be a gatherer. If you gather roots or crops, the baby can be put in a carrier at the edge of the field, and you can hear the baby when needed.

This is why I have such contempt for the librul dummy idea that women can be warriors. There have been women warriors, but they are, in human history, probably 1:10000. Prior to contraception availability, women over the age of 25 were pregnant or caring for a baby probably 50% of the time. You cannot be a warrior or hunter under those circumstances. The exceptions are the rich women. But if you are rich enough to have a child-care person, you are also rich enough to hire a hunter/bodyguard/warrior.
DOK

Pretty young women on the arms of old rich guys suggests many find wealth and power attractive.
dirk

@George: something I overheard in my neighbourhood some time ago.
I would have said, – no sweetie, that’s something for the rough boys, not for you-.
In the meantime, I note ads for movies and series in which fierce women warriors are fighting, in tight jeans around their nice bums, (and win all the time from men and other girls), use crossbows and other dangerous weapons and look fiercely around, as if they can devour whatever comes nearby. Just only have a look at the heroines in The Black Panthers. I really wonder whether all this is doing much good for the psyche of the upgrowing small girls nowadays. Please, I would say, stop this nonsense
Dcl

What a strange article. It makes some very interesting points – namely, the invisibility of the cost of sex for men in particular, and how that drives the economy; many points well observed – but then also frequently lurches into utterly unfounded assertions as fact, with zero data. This is definitely not the first time I’ve read such an article and I’m beginning to wonder about Quillette’s standards. Does it really want simply a series of assertions based on anecdote? I mean, anyone can say anything with this method. A personal essay is one thing; so is an opinion piece. But an essay with a controversial or debatable thesis needs supporting facts, else it’s just bloviating. To my mind.

There were several red flags for me:
“While most fair-minded people would no doubt agree that women should be free to take mining jobs if they choose, it’s unlikely that many women want such gruelling, dangerous, and unhealthy work when being a bar prostitute…is available as an alternative.”

Really? Based on what study? Personally, I’d prefer to be anything else, including a homeless bum covered in urine. Maybe a miner is the worst job ever – it may well be – but to assert that being a bar prostitute is without explanation the obvious choice over a miner, is just silly. Yes, there are some women – especially those who have been sexually abused and/or who have severely limited economic choices – who turn to it matter of factly, but no. The high risk of injury, disease, abuse, and plain old servitude (you have to do what your customer wants you to do no matter how degrading and no matter how you’re feeling), is just repulsive to me and many women. I’m not saying the author is necessarily wrong, but he needs data to back up a questionable claim.
“The total value of the sex trade could be said to be the value of the net transfer of wealth from men to women.”
Interesting point, but the author ignores all other sex exchanges, including child trafficking and non-hetero sex exchanges. In some sense he does this because it’s not his point (he is focusing on men having to pay a lot for sex, basically), but it also undercuts his narrative. To take gay sex, you have a male and a male. So how does that fit in with his thesis? In that case, men are offering up their bodies for sex and men are paying. And to take child sex trafficking, this is a booming business, but again, how does that fit in with his thesis, for children are not choosing to do this and the monies go to many other hands, not children.

Indeed, he also ignores the wider economic equation of the men who ultimately get the money, the pimps, any male-run businesses, and so on.

What I’m trying to say is that this issue is a whole lot more interconnected and complex than a simple exchange of monies from men to women.
“A man who was a good hunter brought meat back to the clan, and a man with meat will mate more often and produce more children. The children in turn inherit the skills of their hunting fathers…The largest mammals became an early casualty of the human sex trade… The answer to the corollary question Why Don’t Women Hunt? ought to be obvious. Women didn’t hunt (in the traditional sense at least) because they didn’t have to. Why hunt when men will bring you meat? ” Indeed.

So it’s so obvious that he doesn’t’ need anything but an assertion to talk about it? I disagree. There are many factors at play here. First, perhaps women didn’t hunt because they were busy dying in childbirth, bearing and raising children, breastfeeding, all of which were extremely risky to their health, especially giving birth (on top of doing other essential economic activities such as agriculture and making clothes and preparing food).

Men hunted not simply to bring home meat for their women so they could have sex. Talk about a hammer in search of a nail. They also gained social status amongst men, and power and money; if you control the source of sustenance, you are powerful.

Why hunt when your man will hunt for you?–Because the risk of the chase can be thrilling? Because you take power into your hands? Because your tribe needs more food? Because you or your babies need more food? There are other motivators besides sex. Throughout, the author acts as though women simply lie back and let men do all the dangerous stuff because they get sex and sperm. The thing is, yes, in part – in our reptilian brains – this is partly true, though I’d frame it differently. But on a deeper level, it’s far more complex and interconnected that he asserts.
“While men competed with each other in terms of hunting abilities such as strength, agility, and technical innovation, women competed to win the best meat (and sperm) from successful hunters.”

So women did nothing else but dress up for men? They didn’t bear and raise kids, weave, tell stories, sing, pray, bury, care for the elderly and infirm, plant crops, prepare food, and so on? This didn’t involve strength, agility, and innovation? Or does the author simply ignore any action of a woman that doesn’t directly lead to sex?

I mean yes, it’s interesting to look at it this way, and again, there’s truth to the idea that women can afford to be far more choosy than men, and that a great deal of evolution is spurred by women’s choices of who to have sex with, as opposed to men’s. But the article tips into speculation and a strange view of women.
“Men relied on innovation, risk-taking, and social status to attract mates, and women became skilled in the arts of attracting (and preferably keeping) a mate.”

This is just silly. Women did a whole lot more than simply attracting and keeping a Man with their Arts. I refuse to believe the author is unaware of the innovations and risks women took (eg childbirth, which is extremely risky; and many innovations within their own purview). So therefore, he is just going on with his own thesis regardless of facts that contradict it or muddle it,
“Is it better to be a CEO or a CEO’s wife? Each occupation shares the same wealth, home, vacations, but the CEO’s wife arguably has a better lifestyle than her husband.”

Ok so argue it. But no. He just asserts it. Guess what–A nonworking wife is dependent on her husband’s salary. Whether that’s a good or bad lifestyle depends on the woman. You will certainly find women who are willing to give up their autonomy in exchange for this social status and power and economic comfort that stems from her husband. But that doesn’t mean her lifestyle is ‘better’ than the husband’s. In some ways, yes, in some ways no. And her lifestyle is utterly dependent on him, so she is far more trapped than women with other arrangements. To my mind it’s worse, but that’s my own opinion. How do most women feel? Who knows. The author doesn’t bother to ask.
“Conversely, the current trends towards conservatism and nationalism may halt and reverse the liberal revolutions of the twentieth century, with potentially unhappy consequences for men and women.”

What in the actual? How on earth does he conclude this based on everything that went before? What on earth is he saying? Nationalism may prevent cheap powerless illegal immigrant women from flooding the market for easy sex and prostitution, so nationalism is bad? The “liberal revolutions” –does he mean women sleeping around more and having sex be cheaper? That is increasingly showing to be quite bad for women. Not everything is about sex. Plus, for women, it’s also about babies, not merely getting pregnant. Sleeping around a lot is not good for women in general, ignoring our biological clocks is also bad for women. Women now are unhappier rather than happier in this glorious new ‘lifestyle.’ How does this fit in with his conclusion?

This seemed a mess to me, filled with some rather interesting points and then some very sloppy thinking, and overall a lack of data to back up any point. I don’t mind reading a viewpoint I partly agree with and partly disagree with, but I would prefer more articles that are not strings of assertions and anecdotes.
pkriens

Excuse me? I work in software and my experience is that many women are swept into history. Not because they did anything impressive but solely they lacked those dangly bits. Nobody would know the name of Ada Lovelace if it was not for the fact that she was a woman. For every Bletchley girl there were hundreds of men on the same or higher level that nobody ever heard of.
pkriens

Agree, that was the most bizarre story of all … a computer was at the time a person doing repetitive computations. Same thing for the women of the ENIAC where these women are now heralded as if they had been inventing the first computer while they only wired the computer according to instructions of men that had designed the software and the hardware. Don’t get me wrong, these women were often very clever, well educated, and very important for the projects. However, there were thousands of men on the same level or higher that were never recognized. And none of these women was a Newton, Babbage, Turing, Neumann, Mauchly, Eckert, Knuth, Minsky, Zuse, Kay, Ingalls, Wirth, Jobs, Gates, Bezo, Musk, etc. Sadly, our youth is convinced that the discrepancy is only because women were held back forcefully in the past.

Sadly, all those recent movies have convinced our youth that this is only because women had no opportunities, ignoring the obvious fact that feminists, unearthing all those women in history, show there were actually many women involved They used to invisible because very few did rise to the level of the geniuses in my field. In the past 50 years, when women have become legally 100% equal to men. Key developer websites like Github and Stackoverflow are 100% free and anonymous if wanted but its users are still way more than 90% male but this does not seem to give them the idea that the discrepancy might have other causes that oppression.

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# Thorstein Veblen’s Theory of the Leisure Class—A Status Update

Thorstein Veblen’s Theory of the Leisure Class—A Status Update

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Published on November 16, 2019
Thorstein Veblen’s Theory of the Leisure Class—A Status Update
written by Rob Henderson

I was bewildered when I encountered a new social class at Yale four years ago: the luxury belief class. My confusion wasn’t surprising given my unusual background. When I was two years old, my mother was addicted to drugs and my father abandoned us. I grew up in multiple foster homes, was then adopted into a series of broken homes, and then experienced a series of family tragedies. Later, after a few years in the military, I went to Yale on the GI Bill. On campus, I realized that luxury beliefs have become fashionable status symbols. Luxury beliefs are ideas and opinions that confer status on the rich at very little cost, while taking a toll on the lower class.

In the past, people displayed their membership of the upper class with their material accoutrements. But today, luxury goods are more affordable than before. And people are less likely to receive validation for the material items they display. This is a problem for the affluent, who still want to broadcast their high social position. But they have come up with a clever solution. The affluent have decoupled social status from goods, and re-attached it to beliefs.

Human beings become more preoccupied with social status once our physical needs are met. In fact, research reveals that sociometric status (respect and admiration from peers) is more important for well-being than socioeconomic status. Furthermore, studies have shown that negative social judgment is associated with a spike in cortisol (hormone linked to stress) that is three times higher than non-social stressful situations. We feel pressure to build and maintain social status, and fear losing it.

It seems reasonable to think that the downtrodden might be most interested in obtaining status and money. But this is not the case. Inhabitants of prestigious institutions are even more interested than others in prestige and wealth. For many of them, that drive is how they reached their lofty positions in the first place. Fueling this interest, they’re surrounded by people just like them—their peers and competitors are also intelligent status-seekers. They persistently look for new ways to move upward and avoid moving downward. The French sociologist Émile Durkheim understood this when he wrote, “The more one has, the more one wants, since satisfactions received only stimulate instead of filling needs.” And indeed, a recent piece of research supports this: it is the upper class who are the most preoccupied with gaining wealth and status. In their paper, the researchers conclude, “relative to lower-class individuals, upper-class individuals have a greater desire for wealth and status…it is those who have more to start with (i.e., upper-class individuals) who also strive to acquire more wealth and status.” Plainly, high-status people desire status more than anyone else.

Furthermore, other research has found that absolute income does not have much effect on general life satisfaction. An increase in relative income, on the other hand, has a positive effect. Put differently, making more money isn’t important. What’s important is making more than others. As the researchers put it:

Increasing an individual’s income will increase his or her utility only if ranked position also increases and will necessarily reduce the utility of others who will lose rank…[which] may explain why increasing the incomes of all may not raise the happiness of all, even though wealth and happiness are correlated within a society at a given point in time.

Baby Millionaires

You might think that, for example, rich kids at elite universities would be happy because their parents are in the top one per cent of income earners. And they will soon join their parents in this elite guild. But remember, they’re surrounded by other members of the one per cent. Their social circle, their Dunbar number, consists of 150 baby millionaires. Jordan Peterson has discussed this phenomenon. Citing figures from his experience teaching at Harvard in the 1990s, Peterson noted that a substantial proportion of Ivy League graduates go on to obtain a net worth of a million dollars or more by age 40. And yet, he observes, this isn’t enough for them. Not only do top university graduates want to be millionaires-in-the-making; they also want the image of moral righteousness. Peterson underlines that elite graduates desire high status not only financially, but morally as well. For these affluent social strivers, luxury beliefs offer them a new way to gain status.

Thorstein Veblen’s famous “leisure class” has evolved into the “luxury belief class.” Veblen, an economist and sociologist, made his observations about social class in the late nineteenth century. He compiled his observations in his classic work, The Theory of the Leisure Class. A key idea is that because we can’t be certain of the financial standing of other people, a good way to size up their means is to see whether they can afford to waste money on goods and leisure. This explains why status symbols are so often difficult to obtain and costly to purchase. These include goods such as delicate and restrictive clothing like tuxedos and evening gowns, or expensive and time-consuming hobbies like golf or beagling. Such goods and leisurely activities could only be purchased or performed by those who did not live the life of a manual laborer and could spend time learning something with no practical utility. Veblen even goes so far as to say, “The chief use of servants is the evidence they afford of the master’s ability to pay.” For Veblen, Butlers are status symbols, too.

Building on these sociological observations, the biologist Amotz Zahavi proposed that animals evolve certain displays because they are so costly. The most famous example is the peacock’s tail. Only a healthy bird is capable of growing such plumage while managing to evade predators. This idea might extend to humans, too. More recently, the anthropologist and historian Jared Diamond has suggested that one reason humans engage in displays such as drinking, smoking, drug use, and other physically costly behaviors is because they serve as fitness indicators. The message is: “I’m so healthy that I can afford to poison my body and continue to function.” Get hammered while playing a round of golf with your butler, and you will be the highest status person around.

Conspicuous Convictions

Veblen proposed that the wealthy flaunt these symbols not because they are useful, but because they are so pricey or wasteful that only the wealthy can afford them, which is why they’re high-status indicators. And this still goes on. A couple of winters ago it was common to see students at Yale and Harvard wearing Canada Goose jackets. Is it necessary to spend $900 to stay warm in New England? No. But kids weren’t spending their parents’ money just for the warmth. They were spending the equivalent of the typical American’s weekly income ($865) for the logo. Likewise, are students spending $250,000 at prestigious universities for the education? Maybe. But they are also spending it for the logo. This is not to say that elite colleges don’t educate their students, or that Canada Goose jackets don’t keep their wearers warm. But top universities are also crucial for induction into the luxury belief class. Take vocabulary. Your typical middle-class American could not tell you what “heteronormative” or “cisgender” means. But if you visit Harvard, you’ll find plenty of rich 19-year-olds who will eagerly explain them to you. When someone uses the phrase “cultural appropriation,” what they are really saying is “I was educated at a top college.” Consider the Veblen quote, “Refined tastes, manners, habits of life are a useful evidence of gentility, because good breeding requires time, application and expense, and can therefore not be compassed by those whose time and energy are taken up with work.” Only the affluent can afford to learn strange vocabulary because ordinary people have real problems to worry about. The chief purpose of luxury beliefs is to indicate evidence of the believer’s social class and education. Only academics educated at elite institutions could have conjured up a coherent and reasonable-sounding argument for why parents should not be allowed to raise their kids, and should hold baby lotteries instead. When an affluent person advocates for drug legalization, or anti-vaccination policies, or open borders, or loose sexual norms, or uses the term “white privilege,” they are engaging in a status display. They are trying to tell you, “I am a member of the upper class.” Affluent people promote open borders or the decriminalization of drugs because it advances their social standing, not least because they know that the adoption of those policies will cost them less than others. The logic is akin to conspicuous consumption—if you’re a student who has a large subsidy from your parents and I do not, you can afford to waste$900 and I can’t, so wearing a Canada Goose jacket is a good way of advertising your superior wealth and status. Proposing policies that will cost you as a member of the upper class less than they would cost me serve the same function. Advocating for open borders and drug experimentation are good ways of advertising your membership of the elite because, thanks to your wealth and social connections, they will cost you less than me.

Unfortunately, the luxury beliefs of the upper class often trickle down and are adopted by people lower down the food chain, which means many of these beliefs end up causing social harm. Take polyamory. I had a revealing conversation recently with a student at an elite university. He said that when he sets his Tinder radius to five miles, about half of the women, mostly other students, said they were “polyamorous” in their bios. Then, when he extended the radius to 15 miles to include the rest of the city and its outskirts, about half of the women were single mothers. The costs created by the luxury beliefs of the former are borne by the latter. Polyamory is the latest expression of sexual freedom championed by the affluent. They are in a better position to manage the complications of novel relationship arrangements. And if these relationships don’t work out, they can recover thanks to their financial capability and social capital. The less fortunate suffer by adopting the beliefs of the upper class.

This is well-illustrated by the finding that in 1960 the percentage of American children living with both biological parents was identical for affluent and working-class families—95%. By 2005, 85% of affluent families were still intact, but for working-class families the figure had plummeted to 30%.

The Harvard political scientist Robert Putnam at a Senate hearing said, “Rich kids and poor kids now grow up in separate Americas…Growing up with two parents is now unusual in the working class, while two-parent families are normal and becoming more common among the upper middle class.” Upper-class people, particularly in the 1960s, championed sexual freedom. Loose sexual norms spread throughout the rest of society. The upper class, though, still have intact families. They experiment in college and then settle down later. The families of the lower class fell apart. Today, the affluent are among the most likely to display the luxury belief that sexual freedom is great, though they are the most likely to get married and least likely to get divorced.

The Rabble and the Rich

This aspect of luxury beliefs is worrisome. As I noted in my original luxury beliefs essay, material goods have become more affordable and, thus, less reliable indicators of social class. Status has shifted to the beliefs we express. And beliefs are less expensive than goods because anyone can adopt them. They are not financially costly. And according to Veblen, along with other social observers like Paul Fussell, ordinary people try to emulate the upper classes. The elite want to differentiate themselves from the rabble with their visible badges of luxury. But then then the class below tries to emulate the elite, and the stratum below that as well, until the style has trickled down to the rest of society. And because luxury beliefs don’t have any financial costs, the ‘fashion’ in beliefs trickles down more quickly.

Over time, luxury beliefs are embraced down the social ladder—at which point, the upper class abandons its old luxury beliefs and embraces new ones. Which explains why the beliefs of the upper class are constantly changing. It’s easy to see how this works if we look at actual fashion. The author Quentin Bell, in On Human Finery, wrote “Try to look like the people above you; if you’re at the top, try to look different from the people below you.” The elite’s conspicuous display of their luxury beliefs falls into this pattern. Their beliefs are emulated by others, sending them off in search of new beliefs to display. The affluent can’t risk looking like hoi polloi, after all.

Or consider art. The psychologist Steven Pinker in How the Mind Works writes, “In an age when any Joe can buy CDs, paintings, and novels, artists make their careers by finding ways to avoid the hackneyed, to challenge jaded tastes, to differentiate the cognoscenti from the dilettantes.” Artists want to differentiate themselves from what’s been done before and what others are currently doing. And so do the affluent. Moral fashions change over time for the same reason. Moral fashions can quickly spiral as more and more members of the chattering classes adopt a certain view. Once the view becomes passé, the upper class, aiming to separate themselves, then update their moral inventories. Veblen still reigns supreme, but in a different way.

As he puts it, “What is common is within the (pecuniary) reach of many people…Hence the consumption, or even the sight of such goods, is inseparable from an odious suggestion of the lower levels of human life.” The affluent do not want to be seen with “common” goods. They view them as distasteful. Today, it’s not just common goods they view as distasteful—it’s beliefs too. The affluent, dreading an “odious” designation, resist displaying commonplace beliefs. Those beliefs are for the little people. Instead, the upper class want to be seen displaying luxury beliefs.

Modern neuroscience did not exist in the nineteenth century. But Veblen might have been amused to learn that the same regions of the brain involved in rewards such as eating chocolate or winning money also activate when we receive compliments from strangers or learn that people we will never meet find us attractive. Veblen wrote, “Immaterial evidences of past leisure are quasi-scholarly or quasi-artistic accomplishments and a knowledge of processes and incidents which do not conduce directly to the furtherance of human life.” In his day, the leisure class spent a lot of time accruing useless knowledge and partaking in activities that have the appearance of intellect and artistry, but had no functional utility. These activities didn’t help anyone, but they did make their enthusiasts look good. What might Veblen have made of Twitter, given these observations?

Status Spirals

The economist and social theorist Thomas Sowell once said that activism is “a way for useless people to feel important, even if the consequences of their activism are counterproductive for those they claim to be helping and damaging to the fabric of society as a whole.” The same could be said for luxury beliefs. They are similar to luxury goods, but present new problems. Attaching status to luxury goods or financial standing meant there were limits to how much harm the leisure class could do when it came to their conspicuous displays. For example, fashion is constrained by the speed with which people could adopt a new look. But with beliefs, this status cycle accelerates. A rich person flaunts her new belief. It then becomes fashionable among her peers, so she abandons it. Then a new stylish belief arises, while the old luxury belief trickles down the social hierarchy and wreaks havoc.

Rob Henderson is a PhD candidate at the University of Cambridge. He obtained a BS in Psychology from Yale University and is a veteran of the U.S. Air Force. You can follow him on Twitter @robkhenderson

Feature photo: District Of Columbia, United States. 01st Aug, 2018. Activists from across the county converged in Washington DC for an action dubbed “Say No to Kavanaugh.” Michael Nigro/Pacific Press/Alamy Live News.

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# How Airplanes Fly

How Airplanes Fly

FERMAT’S LIBRARY

Journal Club
Librarian
Margins

In order for an airplane to rise and fly in the air, a force must b…
**How Do Airplanes Fly?** A short and very interest explanation by …
Bernoulli’s Principle states that within a horizontal flow of fluid…
The principle of **”equal transit times”** states that the air goin…
The air going over the top of the wing reaches the trailing edge be…
If the principle of equal transit times and thus the Bernoulli effe…
> The popular explanation also implies that inverted flight is impo…
The wing produces lift by diverting air down. The work produced by …
![updownwash](https://i.imgur.com/E8b7xhw.jpg) **Upwash** When …
> One observation that can be made from figure 7 is that the top su…
**The Coanda effect** was first discovered by a mathematician and e…
The Angle of attack (also known as AOA) is the angle between the on…
**The induced power** is the power required to redirect the air and…
In order to lower the induced power needed for lift one needs to im…
Visualization of the airflow with increasing angle of attack. W…
At the end of the wing the lift goes to zero very rapidly and there…
How Airplanes Fly: A Physical Description of Lift
David Anderson
Fermi National Accelerator Laboratory
Batavia IL 60510
dfa@fnal.gov
Scott Eberhardt
Dept. of Aeronautics and Astronautics
University of Washington
Seattle WA 91895-2400
scott@aa.washington.edu
Originally published in February 1999
I. INTRO
Almost everyone today has ﬂown in an airplane. Many
ask the simple question “what makes an airplane ﬂy”?
just plain wrong. We hope that the answers provided
here will clarify many misconceptions about lift and that
you will adopt our explanation when explaining lift to
others. We are going to show you that lift is easier to un-
derstand if one starts with Newton rather than Bernoulli.
We will also show you that the popular explanation that
most of us were taught is misleading at best and that lift
is due to the wing diverting air down.
Let us start by deﬁning three descriptions of lift com-
monly used in textbooks and training manuals. The ﬁrst
we will call the Mathematical Aerodynamics Description
which is used by aeronautical engineers. This description
uses complex mathematics and/or computer simulations
to calculate the lift of a wing. These are design tools
which are powerful for computing lift but do not lend
themselves to an intuitive understanding of ﬂight.
The second description we will call the Popular Expla-
nation which is based on the Bernoulli principle. The
primary advantage of this description is that it is easy
to understand and has been taught for many years. Be-
cause of its simplicity, it is used to describe lift in most
ﬂight training manuals. The major disadvantage is that
it relies on the “principle of equal transit times” which
is wrong. This description focuses on the shape of the
wing and prevents one from understanding such impor-
tant phenomena as inverted ﬂight, power, ground eﬀect,
and the dependence of lift on the angle of attack of the
wing.
The third description, which we are advocating here,
we will call the Physical Description of lift. This descrip-
tion is based primarily on Newton’s laws. The physical
description is useful for understanding ﬂight, and is ac-
cessible to all who are curious. Little math is needed
to yield an estimate of many phenomena associated with
ﬂight. This description gives a clear, intuitive under-
standing of such phenomena as the power curve, ground
eﬀect, and high-speed stalls. However, unlike the math-
ematical aerodynamics description, the physical descrip-
tion has no design or simulation capabilities.
II. THE POPULAR EXPLANATION OF LIFT
Students of physics and aerodynamics are taught that
airplanes ﬂy as a result of Bernoulli’s principle, which
says that if air speeds up the pressure is lowered. Thus
a wing generates lift because the air goes faster over the
top creating a region of low pressure, and thus lift. This
explanation usually satisﬁes the curious and few chal-
lenge the conclusions. Some may wonder why the air
goes faster over the top of the wing and this is where the
popular explanation of lift falls apart.
In order to explain why the air goes faster over the
top of the wing, many have resorted to the geometric
argument that the distance the air must travel is directly
related to its speed. The usual claim is that when the air
separates at the leading edge, the part that goes over the
top must converge at the trailing edge with the part that
goes under the bottom. This is the so-called “principle
of equal transit times”.
As discussed by Gail Craig (Stop Abusing Bernoulli!
How Airplanes Really Fly, Regenerative Press, Anderson,
Indiana, 1997), let us assume that this argument were
true. The average speeds of the air over and under the
wing are easily determined because we can measure the
distances and thus the speeds can be calculated. From
Bernoulli’s principle, we can then determine the pressure
2
forces and thus lift. If we do a simple calculation we
would ﬁnd that in order to generate the required lift for
a typical small airplane, the distance over the top of the
wing must be about 50% longer than under the bottom.
Figure 1 shows what such an airfoil would look like. Now,
imagine what a Boeing 747 wing would have to look like!
FIG. 1: Shape of wing predicted by principle of equal transit
time
If we look at the wing of a typical small plane, which
has a top surface that is 1.5 – 2.5% longer than the bot-
tom, we discover that a Cessna 172 would have to ﬂy at
over 400 mph to generate enough lift. Clearly, something
in this description of lift is ﬂawed.
But, who says the separated air must meet at the trail-
ing edge at the same time? Figure 2 shows the airﬂow
over a wing in a simulated wind tunnel. In the simula-
tion, colored smoke is introduced periodically. One can
see that the air that goes over the top of the wing gets
to the trailing edge considerably before the air that goes
under the wing. In fact, close inspection shows that the
air going under the wing is slowed down from the “free-
stream” velocity of the air. So much for the principle of
equal transit times.
The popular explanation also implies that inverted
ﬂight is impossible. It certainly does not address acro-
batic airplanes, with symmetric wings (the top and bot-
tom surfaces are the same shape), or how a wing adjusts
for the great changes in load such as when pulling out of
a dive or in a steep turn.
So, why has the popular explanation prevailed for so
long? One answer is that the Bernoulli principle is easy to
understand. There is nothing wrong with the Bernoulli
principle, or with the statement that the air goes faster
over the top of the wing. But, as the above discussion
suggests, our understanding is not complete with this
FIG. 2: Simulation of the airﬂow over a wing in a wind tunnel,
with colored “smoke” to show the acceleration and decelera-
tion of the air.
explanation. The problem is that we are missing a vi-
tal piece when we apply Bernoulli’s principle. We can
calculate the pressures around the wing if we know the
speed of the air over and under the wing, but how do we
determine the speed?
Another fundamental shortcoming of the popular ex-
planation is that it ignores the work that is done. Lift
requires power (which is work per time). As will be seen
later, an understanding of power is key to the under-
standing of many of the interesting phenomena of lift.
III. NEWTON’S LAWS AND LIFT
So, how does a wing generate lift? To begin to un-
review Newton’s ﬁrst and third laws. (We will introduce
Newton’s second law a little later.) Newton’s ﬁrst law
states a body at rest will remain at rest, and a body in
motion will continue in straight-line motion unless sub-
jected to an external applied force. That means, if one
sees a bend in the ﬂow of air, or if air originally at rest
is accelerated into motion, there is a force acting on it.
Newton’s third law states that for every action there is an
equal and opposite reaction. As an example, an object
sitting on a table exerts a force on the table (its weight)
and the table puts an equal and opposite force on the ob-
ject to hold it up. In order to generate lift a wing must
do something to the air. What the wing does to the air
is the action while lift is the reaction.
Let’s compare two ﬁgures used to show streams of air
(streamlines) over a wing. In ﬁgure 3 the air comes
straight at the wing, bends around it, and then leaves
straight behind the wing. We have all seen similar pic-
tures, even in ﬂight manuals. But, the air leaves the wing
exactly as it appeared ahead of the wing. There is no net
3
action on the air so there can be no lift! Figure 4 shows
the streamlines, as they should be drawn. The air passes
over the wing and is bent down. The bending of the air
is the action. The reaction is the lift on the wing.
FIG. 3: Common depiction of airﬂow over a wing. This wing
has no lift.
FIG. 4: True airﬂow over a wing with lift, showing upwash
and downwash.
IV. THE WING AS A PUMP
As Newton’s laws suggest, the wing must change some-
thing of the air to get lift. Changes in the air’s momen-
tum will result in forces on the wing. To generate lift a
wing must divert air down, lots of air.
The lift of a wing is equal to the change in momentum
of the air it diverts down. Momentum is the product of
mass and velocity. The lift of a wing is proportional to
the amount of air diverted down times the downward ve-
locity of that air. Its that simple. (Here we have used
an alternate form of Newton’s second law that relates the
acceleration of an object to its mass and to the force on it,
F = ma) For more lift the wing can either divert more air
(mass) or increase its downward velocity. This downward
velocity behind the wing is called “downwash”. Figure
5 shows how the downwash appears to the pilot (or in
a wind tunnel). The ﬁgure also shows how the down-
wash appears to an observer on the ground watching the
wing go by. To the pilot the air is coming oﬀ the wing
at roughly the angle of attack. To the observer on the
ground, if he or she could see the air, it would be coming
oﬀ the wing almost vertically. The greater the angle of
attack, the greater the vertical velocity. Likewise, for the
same angle of attack, the greater the speed of the wing
the greater the vertical velocity. Both the increase in the
speed and the increase of the angle of attack increase the
length of the vertical arrow. It is this vertical velocity
that gives the wing lift.
FIG. 5: True airﬂow over a wing with lift, showing upwash
and downwash.
As stated, an observer on the ground would see the
air going almost straight down behind the plane. This
can be demonstrated by observing the tight column of
air behind a propeller, a household fan, or under the
rotors of a helicopter, all of which are rotating wings. If
the air were coming oﬀ the blades at an angle the air
would produce a cone rather than a tight column. If a
plane were to ﬂy over a very large scale, the scale would
register the weight of the plane.
If we estimate the average vertical component of the
downwash of a Cessna 172 traveling at 110 knots to be
about 9 knots, then to generate the needed 2,300 lbs of
lift the wing pumps a whopping 2.5 ton/sec of air! In fact,
as will be discussed later, this estimate may be as much
as a factor of two too low. The amount of air pumped
down for a Boeing 747 to create lift for its roughly 800,000
pounds takeoﬀ weight is incredible indeed.
Pumping, or diverting, so much air down is a strong
argument against lift being just a surface eﬀect as implied
by the popular explanation. In fact, in order to pump 2.5
ton/sec the wing of the Cessna 172 must accelerate all of
the air within 9 feet above the wing. (Air weighs about 2
pounds per cubic yard at sea level.) Figure 6 illustrates
the eﬀect of the air being diverted down from a wing. A
huge hole is punched through the fog by the downwash
from the airplane that has just ﬂown over it.
4
FIG. 6: Downwash and wing vortices in the fog. (Photogra-
pher Paul Bowen, courtesy of Cessna Aircraft, Co.)
So how does a thin wing divert so much air? When
the air is bent around the top of the wing, it pulls on the
air above it accelerating that air down, otherwise there
would be voids in the air left above the wing. Air is
pulled from above to prevent voids. This pulling causes
the pressure to become lower above the wing. It is the
acceleration of the air above the wing in the downward
direction that gives lift. (Why the wing bends the air
with enough force to generate lift will be discussed in the
next section.)
As seen in ﬁgure 4, a complication in the picture of
a wing is the eﬀect of “upwash” at thae leading edge
of the wing. As the wing moves along, air is not only
diverted down at the rear of the wing, but air is pulled
up at the leading edge. This upwash actually contributes
to negative lift and more air must be diverted down to
compensate for it. This will be discussed later when we
consider ground eﬀect.
Normally, one looks at the air ﬂowing over the wing in
the frame of reference of the wing. In other words, to the
pilot the air is moving and the wing is standing still. We
have already stated that an observer on the ground would
see the air coming oﬀ the wing almost vertically. But
what is the air doing above and below the wing? Figure
7 shows an instantaneous snapshot of how air molecules
are moving as a wing passes by. Remember in this ﬁgure
the air is initially at rest and it is the wing moving. Ahead
of the leading edge, air is moving up (upwash). At the
trailing edge, air is diverted down (downwash). Over
the top the air is accelerated towards the trailing edge.
Underneath, the air is accelerated forward slightly, if at
all.
FIG. 7: Direction of air movement around a wing as seen by
an observer on the ground.
In the mathematical aerodynamics description of lift
this rotation of the air around the wing gives rise to the
“bound vortex” or “circulation” model. The advent of
this model, and the complicated mathematical manipu-
lations associated with it, leads to the direct understand-
ing of forces on a wing. But, the mathematics required
typically takes students in aerodynamics some time to
master.
One observation that can be made from ﬁgure 7 is that
the top surface of the wing does much more to move
the air than the bottom. So the top is the more critical
surface. Thus, airplanes can carry external stores, such
as drop tanks, under the wings but not on top where
they would interfere with lift. That is also why wing
struts under the wing are common but struts on the top
of the wing have been historically rare. A strut, or any
obstruction, on the top of the wing would interfere with
the lift.
V. AIR HAS VISCOSITY
The natural question is “how does the wing divert the
air down?” When a moving ﬂuid, such as air or water,
comes into contact with a curved surface it will try to
follow that surface. To demonstrate this eﬀect, hold a
water glass horizontally under a faucet such that a small
stream of water just touches the side of the glass. Instead
of ﬂowing straight down, the presence of the glass causes
5
the water to wrap around the glass as is shown in ﬁgure
8. This tendency of ﬂuids to follow a curved surface is
known as the Coanda eﬀect. From Newton’s ﬁrst law we
know that for the ﬂuid to bend there must be a force
acting on it. From Newton’s third law we know that the
ﬂuid must put an equal and opposite force on the object
that caused the ﬂuid to bend.vis
FIG. 8: Coanda eﬀect.
Why should a ﬂuid follow a curved surface? The an-
swer is viscosity: the resistance to ﬂow which also gives
the air a kind of “stickiness.” Viscosity in air is very small
but it is enough for the air molecules to want to stick to
the surface. The relative velocity between the surface
and the nearest air molecules is exactly zero. (That is
why one cannot hose the dust oﬀ of a car and why there
is dust on the backside of the fans in a wind tunnel.) Just
above the surface the ﬂuid has some small velocity. The
farther one goes from the surface the faster the ﬂuid is
moving until the external velocity is reached (note that
this occurs in less than an inch). Because the ﬂuid near
the surface has a change in velocity, the ﬂuid ﬂow is bent
towards the surface. Unless the bend is too tight, the
ﬂuid will follow the surface. This volume of air around
the wing that appears to be partially stuck to the wing
is called the “boundary layer”.
VI. LIFT AS A FUNCTION OF ANGLE OF
ATTACK
There are many types of wing: conventional, sym-
metric, conventional in inverted ﬂight, the early biplane
wings that looked like warped boards, and even the
proverbial “barn door.” In all cases, the wing is forc-
ing the air down, or more accurately pulling air down
from above. What all of these wings have in common
is an angle of attack with respect to the oncoming air.
It is this angle of attack that is the primary parameter
in determining lift. The lift of the inverted wing can
be explained by its angle of attack, despite the apparent
contradiction with the popular explanation involving the
Bernoulli principle. A pilot adjusts the angle of attack
to adjust the lift for the speed and load. The popular ex-
planation of lift which focuses on the shape of the wing
gives the pilot only the speed to adjust.
To better understand the role of the angle of attack it is
useful to introduce an “eﬀective” angle of attack, deﬁned
such that the angle of the wing to the oncoming air that
gives zero lift is deﬁned to be zero degrees. If one then
changes the angle of attack both up and down one ﬁnds
that the lift is proportional to the angle. Figure 9 shows
the coeﬃcient of lift (lift normalized for the size of the
wing) for a typical wing as a function of the eﬀective angle
of attack. A similar lift versus angle of attack relationship
is found for all wings, independent of their design. This
is true for the wing of a 747 or a barn door. The role of
the angle of attack is more important than the details of
the airfoil’s shape in understanding lift.
FIG. 9: Coeﬃcient of lift versus the eﬀective angle of attack.
Typically, the lift begins to decrease at an angle of
attack of about 15 degrees. The forces necessary to bend
the air to such a steep angle are greater than the viscosity
of the air will support, and the air begins to separate from
the wing. This separation of the airﬂow from the top of
the wing is a stall.
6
VII. THE WING AS AIR “SCOOP”
We now would like to introduce a new mental image of
a wing. One is used to thinking of a wing as a thin blade
that slices through the air and develops lift somewhat
by magic. The new image that we would like you to
adopt is that of the wing as a scoop diverting a certain
amount of air from the horizontal to roughly the angle
of attack, as depicted in ﬁgure 10. The scoop can be
pictured as an invisible structure put on the wing at the
factory. The length of the scoop is equal to the length
of the wing and the height is somewhat related to the
chord length (distance from the leading edge of the wing
to the trailing edge). The amount of air intercepted by
this scoop is proportional to the speed of the plane and
the density of the air, and nothing else.
FIG. 10: The wing as a scoop.
As stated before, the lift of a wing is proportional to the
amount of air diverted down times the vertical velocity
of that air. As a plane increases speed, the scoop diverts
more air. Since the load on the wing, which is the weight
of the plane, does not increase the vertical speed of the
diverted air must be decreased proportionately. Thus,
the angle of attack is reduced to maintain a constant lift.
When the plane goes higher, the air becomes less dense
so the scoop diverts less air for the same speed. Thus, to
compensate the angle of attack must be increased. The
concepts of this section will be used to understand lift in
a way not possible with the popular explanation.
VIII. LIFT REQUIRES POWER
When a plane passes overhead the formerly still air
ends up with a downward velocity. Thus, the air is left
in motion after the plane leaves. The air has been given
energy. Power is energy, or work, per time. So, lift must
require power. This power is supplied by the airplane’s
engine (or by gravity and thermals for a sailplane).
How much power will we need to ﬂy? The power
needed for lift is the work (energy) per unit time and
so is proportional to the amount of air diverted down
times the velocity squared of that diverted air. We have
already stated that the lift of a wing is proportional to
the amount of air diverted down times the downward ve-
locity of that air. Thus, the power needed to lift the
airplane is proportional to the load (or weight) times the
vertical velocity of the air. If the speed of the plane is
doubled the amount of air diverted down doubles. Thus
the angle of attack must be reduced to give a vertical ve-
locity that is half the original to give the same lift. The
power required for lift has been cut in half. This shows
that the power required for lift becomes less as the air-
plane’s speed increases. In fact, we have shown that this
power to create lift is proportional to one over the speed
of the plane.
But, we all know that to go faster (in cruise) we must
apply more power. So there must be more to power than
the power required for lift. The power associated with
lift, described above, is often called the “induced” power.
Power is also needed to overcome what is called “para-
sitic” drag, which is the drag associated with moving the
wheels, struts, antenna, etc. through the air. The en-
ergy the airplane imparts to an air molecule on impact
is proportional to the speed squared. The number of
molecules struck per time is proportional to the speed.
Thus the parasitic power required to overcome parasitic
drag increases as the speed cubed.
Figure 11 shows the power curves for induced power,
parasitic power, and total power which is the sum of in-
duced power and parasitic power. Again, the induced
power goes as one over the speed and the parasitic power
goes as the speed cubed. At low speed the power require-
ments of ﬂight are dominated by the induced power. The
slower one ﬂies the less air is diverted and thus the angle
of attack must be increased to maintain lift. Pilots prac-
tice ﬂying on the “backside of the power curve” so that
they recognize that the angle of attack and the power
required to stay in the air at very low speeds are consid-
erable.
At cruise, the power requirement is dominated by par-
asitic power. Since this goes as the speed cubed an in-
crease in engine size gives one a faster rate of climb but
does little to improve the cruise speed of the plane.
Since we now know how the power requirements vary
with speed, we can understand drag, which is a force.
Drag is simply power divided by speed. Figure 12 shows
the induced, parasitic, and total drag as a function of
speed. Here the induced drag varies as one over speed
squared and parasitic drag varies as the speed squared.
Taking a look at these curves one can deduce a few things
about how airplanes are designed. Slower airplanes, such
7
FIG. 11: Power requirements versus speed.
as gliders, are designed to minimize induced drag (or in-
duced power), which dominates at lower speeds. Faster
airplanes are more concerned with parasitic drag (or par-
asitic power).
FIG. 12: Drag versus speed.
IX. WING EFFICIENCY
At cruise, a non-negligible amount of the drag of a
modern wing is induced drag. Parasitic drag, which dom-
inates at cruise, of a Boeing 747 wing is only equivalent
to that of a 1/2-inch cable of the same length. One might
ask what aﬀects the eﬃciency of a wing. We saw that the
induced power of a wing is proportional to the vertical
velocity of the air. If the length of a wing were to be
doubled, the size of our scoop would also double, divert-
ing twice as much air. So, for the same lift the vertical
velocity (and thus the angle of attack) would have to be
halved. Since the induced power is proportional to the
vertical velocity of the air, it too is reduced by half. Thus,
the lifting eﬃciency of a wing is proportional to one over
the length of the wing. The longer the wing the less in-
duced power required to produce the same lift, though
this is achieved with an increase in parasitic drag. Low
speed airplanes are aﬀected more by induced drag than
fast airplanes and so have longer wings. That is why
sailplanes, which ﬂy at low speeds, have such long wings.
High-speed ﬁghters, on the other hand, feel the eﬀects of
parasitic drag more than our low speed trainers. There-
fore, fast airplanes have shorter wings to lower parasite
drag.
There is a misconception held by some that lift does
not require power. This comes from aeronautics in the
study of the idealized theory of wing sections (airfoils).
When dealing with an airfoil, the picture is actually that
of a wing with inﬁnite span. Since we have seen that the
power necessary for lift is proportional to one over the
length of the wing, a wing of inﬁnite span does not re-
quire power for lift. If lift did not require power airplanes
would have the same range full as they do empty, and he-
licopters could hover at any altitude and load. Best of all,
propellers (which are rotating wings) would not require
power to produce thrust. Unfortunately, we live in the
real world where both lift and propulsion require power.
Let us now consider the relationship between wing
creased the vertical velocity must be increased to com-
pensate. This is done by increasing the angle of attack.
If the total weight of the airplane were doubled (say, in
a 2-g turn) the vertical velocity of the air is doubled to
power is proportional to the load times the vertical ve-
locity of the diverted air, which have both doubled. Thus
the induced power requirement has increased by a factor
of four! The same thing would be true if the airplane’s
weight were doubled by adding more fuel, etc.
One way to measure the total power is to look at the
rate of fuel consumption. Figure 13 shows the fuel con-
sumption versus gross weight for a large transport air-
plane traveling at a constant speed (obtained from ac-
tual data). Since the speed is constant the change in fuel
consumption is due to the change in induced power. The
data are ﬁtted by a constant (parasitic power) and a term
that goes as the load squared. This second term is just
what was predicted in our Newtonian discussion of the
eﬀect of load on induced power.
8
FIG. 13: Fuel consumption versus load for a large transport
airplane traveling at a constant speed.
The increase in the angle of attack with increased load
has a downside other than just the need for more power.
As shown in ﬁgure 9 a wing will eventually stall when the
air can no longer follow the upper surface, that is, when
the critical angle is reached. Figure 14 shows the angle
of attack as a function of airspeed for a ﬁxed load and for
a 2-g turn. The angle of attack at which the plane stalls
stall speed increases as the square root of the load. Thus,
increasing the load in a 2-g turn increases the speed at
which the wing will stall by 40%. An increase in altitude
will further increase the angle of attack in a 2-g turn.
This is why pilots practice “accelerated stalls” which il-
lustrate that an airplane can stall at any speed. For any
speed there is a load that will induce a stall.
XI. WING VORTICES
One might ask what the downwash from a wing looks
like. The downwash comes oﬀ the wing as a sheet and is
related to the details of the load distribution on the wing.
Figure 15 shows, through condensation, the distribution
of lift on an airplane during a high-g maneuver. From the
ﬁgure one can see that the distribution of load changes
from the root of the wing to the tip. Thus, the amount
of air in the downwash must also change along the wing.
The wing near the root is “scooping” up much more air
than the tip. Since the root is diverting so much air the
net eﬀect is that the downwash sheet will begin to curl
FIG. 14: Angle of attack versus speed for straight and level
ﬂight and for a 2-g turn.
outward around itself, just as the air bends around the
top of the wing because of the change in the velocity of
the air. This is the wing vortex. The tightness of the
curling of the wing vortex is proportional to the rate of
change in lift along the wing. At the wing tip the lift
must rapidly become zero causing the tightest curl. This
is the wing tip vortex and is just a small (though often
most visible) part of the wing vortex. Returning to ﬁgure
6 one can clearly see the development of the wing vortices
in the downwash as well as the wing tip vortices.
FIG. 15: Condensation showing the distribution of lift along
a wing. The wingtip vortices are also seen. (from Patterns in
the Sky, J.F. Campbell and J.R. Chambers, NASA SP-514.)
Winglets (those small vertical extensions on the tips
of some wings) are used to improve the eﬃciency of the
wing by increasing the eﬀective length of the wing. The
lift of a normal wing must go to zero at the tip because
the bottom and the top communicate around the end.
The winglets blocks this communication so the lift can
9
extend farther out on the wing. Since the eﬃciency of a
wing increases with length, this gives increased eﬃciency.
One caveat is that winglet design is tricky and winglets
can actually be detrimental if not properly designed.
XII. GROUND EFFECT
Another common phenomenon that is misunderstood
is that of ground eﬀect. That is the increased eﬃciency
of a wing when ﬂying within a wing length of the ground.
A low-wing airplane will experience a reduction in drag
by 50% just before it touches down. There is a great
deal of confusion about ground eﬀect. Many pilots (and
the FAA VFR Exam-O-Gram No. 47) mistakenly believe
that ground eﬀect is the result of air being compressed
between the wing and the ground.
To understand ground eﬀect it is necessary to have an
understanding of upwash. For the pressures involved in
low speed ﬂight, air is considered to be non-compressible.
When the air is accelerated over the top of the wing and
down, it must be replaced. So some air must shift around
the wing (below and forward, and then up) to compen-
sate, similar to the ﬂow of water around a canoe paddle
when rowing. This is the cause of upwash.
As stated earlier, upwash is accelerating air in the
wrong direction for lift. Thus a greater amount of down-
wash is necessary to compensate for the upwash as well
as to provide the necessary lift. Thus more work is done
and more power required. Near the ground the upwash
is reduced because the ground inhibits the circulation of
the air under the wing. So less downwash is necessary to
provide the lift. The angle of attack is reduced and so is
the induced power, making the wing more eﬃcient.
Earlier, we estimated that a Cessna 172 ﬂying at 110
knots must divert about 2.5 ton/sec to provide lift. In
our calculations we neglected the upwash. From the mag-
nitude of ground eﬀect, it is clear that the amount of air
diverted is probably more like 5 ton/sec.
XIII. CONCLUSIONS
Let us review what we have learned and get some idea
of how the physical description has given us a greater
ability to understand ﬂight. First what have we learned:
• The amount of air diverted by the wing is propor-
tional to the speed of the wing and the air density.
• The vertical velocity of the diverted air is propor-
tional to the speed of the wing and the angle of
attack.
• The lift is proportional to the amount of air di-
verted times the vertical velocity of the air.
• The power needed for lift is proportional to the lift
times the vertical velocity of the air.
Now let us look at some situations from the physical
point of view and from the perspective of the popular
explanation.
• The plane’s speed is reduced. The physical view
says that the amount of air diverted is reduced so
the angle of attack is increased to compensate. The
power needed for lift is also increased. The popular
• The load of the plane is increased. The physical
view says that the amount of air diverted is the
same but the angle of attack must be increased to
give additional lift. The power needed for lift has
also increased. Again, the popular explanation can-
• A plane ﬂies upside down. The physical view has
no problem with this. The plane adjusts the angle
of attack of the inverted wing to give the desired
lift. The popular explanation implies that inverted
ﬂight is impossible.
As one can see, the popular explanation, which ﬁx-
ates on the shape of the wing, may satisfy many but it
does not give one the tools to really understand ﬂight.
The physical description of lift is easy to understand and
much more powerful.

Discussion
The air going over the top of the wing reaches the trailing edge before the air that goes under the wing. The air that passed under the wing has a somewhat retarded velocity compared to the velocity of air some distance from the wing. See the video below for a better visualization of this effect: [![](https://i.imgur.com/nfWlbVN.png)%5D(https://www.youtube.com/watch?v=UqBmdZ-BNig) Bernoulli’s Principle states that within a horizontal flow of fluid, points of higher fluid speed will have less pressure than points of slower fluid speed – an increase in velocity leads to an decrease in pressure. Bernoulli’s equation can be considered as a statement of the conservation of energy for flowing fluids and can be written as follows: $$P+\dfrac{1}{2}\rho v^2+\rho gh=\text{constant}$$ Applying this principle to the wing of an airplane we get that the air flowing over an airfoil will decrease in pressure. The difference in pressure between the top surface and the bottom surface creates a net pressure force in the upward direction. This pressure force is lift. ![incorrect theory](https://i.stack.imgur.com/24VM8.gif) The principle of **”equal transit times”** states that the air going around a wing, whether going over or under, must do so in equal time. For a curved wing the air has to travel farther over the top of the wing it has to go faster which produces a difference in pressure that will generate lift (Bernoulli’s principle). The notion that the air passing above and below the wing must do so in equal time is a common misconception that is usually used to explain how wings work. For a detailed and visual explanation of how wings generate lift see the video below **”How Does A Wing Actually Work?”**. [![](https://i.imgur.com/8ElKgOl.png)%5D(https://www.youtube.com/watch?v=aFO4PBolwFg) ![updownwash](https://i.imgur.com/E8b7xhw.jpg) **Upwash** When a plane is flying the air approaches the front of wings from below due to the wings angle of attack and is. This air is diverted upwards: upwash. **Downwash** The air splits around the wing and it will leave the wing with a downward angle. This downward-traveling air is the downwash and is the action that creates lift as its reaction. There has been a change in the air after passing over the wing. Lift is created via a force acting on the air and a reaction force acting on the wing. A better visualization of the downwash and upwash zones can be seen below. ![upwashdownwash](https://i.imgur.com/IGiLhH2.jpg) Visualization of the airflow with increasing angle of attack. When the angle of attack is too high the airflow over most of the top of the wing has separated and there is **no noticeable downwash thus there is no lift and the wing stalls**. ![increasing AOA](https://thumbs.gfycat.com/GoodnaturedEnchantedAardwolf-mobile.mp4) **How Do Airplanes Fly?** A short and very interest explanation by Minute Physics: [![](https://i.imgur.com/j6dkLfB.png)%5D(https://www.youtube.com/watch?v=Gg0TXNXgz-w) The wing produces lift by diverting air down. The work produced by the wing when it diverts the air downs produces lift. The lift produced by a wing $L_{wing}$ is the proportional to the product of the amount of air $V_{air}$ diverted down and the speed of that air $v_{air}$: $$L_{wing} \propto V_{air} \cdot v_{air}$$ In order for an airplane to rise and fly in the air, a force must be created that equals or exceeds the force of gravity. This force is called lift. The popular explanation for lift is based on Bernoulli’s principle. This explanation relies on the “principle of equal transit times” – air travelling over and under the wing will do so in the same amount of time. This explanation falls short when it comes to explain simple things like inverted flight or flat/symmetric wings. This paper provides a general overview of all the effects that contribute to the lift generated by wings and thus provides a better explanation of how planes really fly. If you are interested in learning more, the authors of this paper also wrote a book describe the phenomenon of flight: [Understanding Flight, by David W. Anderson, Scott Eberhardt](https://www.goodreads.com/book/show/26251943-understanding-flight-second-edition) > The popular explanation also implies that inverted flight is impossible. It certainly does not address acrobatic airplanes, with symmetric wings (the top and bottom surfaces are the same shape) If the principle of equal transit times and thus the Bernoulli effect were the only contributing factors to generate lift than the air would have to travel a distance over the wing $L_{over}$ that is 50% longer than that traveled under the wing $L_{under}$ which would produce “weirdly” shaped wings. **The Coanda effect** was first discovered by a mathematician and engineer named Henri Coanda in 1910. Coanda observed that when air was ejected from a rectangular nozzle, it would attach itself to an inclined flat plate connected to the nozzle exit. He stated that *“when a jet of fluid is passed over a curved surface, it bends to follow the surface, entraining large amounts of air as it does so”*. He applied this principle to a series of different surfaces, each at a sharp angle to the previous one, and succeeded in turning flows through angles as large as 180$^{\circ}$. He was the first to recognize the practical application of the phenomenon in aircraft design. ![coanda effect](https://i.imgur.com/v42vZqp.gif) > One observation that can be made from figure 7 is that the top surface of the wing does much more to move the air than the bottom. So the top is the more critical surface. Thus, airplanes can carry external stores, such as drop tanks, under the wings but not on top where they would interfere with lift. That is also why wing struts under the wing are common but struts on the top of the wing have been historically rare. A strut, or any obstruction, on the top of the wing would interfere with the lift. In order to lower the induced power needed for lift one needs to improve the efficiency of a wing. The easiest way to increase the efficiency of a wing is to increase the amount of air diverted by the wing. If the wing is able to divert more air, then the vertical velocity of the air is reduced for the same lift and so is the induced power. An “easy” way to accomplish this is by increasing the size of the wing. At low speeds induced drag dominates so for example sailplanes have longer wings and at high speeds parasitic drag dominates reason why high speed fighters have shorter wings. At the end of the wing the lift goes to zero very rapidly and there is some airflow around the wingtip. This causes the tightest curl in the wing vortex, creating the wingtip vortex. See below. ![wingtip vortices](https://i.imgur.com/VUbQB0Y.mp4) **The induced power** is the power required to redirect the air and generate lift. **The parasitic power** is the power needed to overcome the drag when an object is moving through a fluid (in the case of a plane that fluid is the atmosphere). The power required to overcome the parasitic drag is given by: $P_d = \mathbf{F}_d \cdot \mathbf{v} = \tfrac12 \rho v^3 A C_d$ where $F_{D}$ is the drag force, $\rho$ is the density of the fluid $v$ is the speed of the object relative to the fluid, $A$ is the cross sectional area, and $C_{D}$ is the drag coefficient. At cruise, the total power requirement is dominated by parasitic power since it is proportional to $v^3$. The total power is the sum of the induced and parasitic power. The Angle of attack (also known as AOA) is the angle between the oncoming air or relative wind and a reference line on the airplane or wing. See a few examples below. ![aoa](https://i.imgur.com/qlwNZKi.jpg) Fig: Illustartion of 3 different angles of attack: 5$^{\circ}$, 10$^{\circ}$, 20$^{\circ}$
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