planetary model experiments

Dalton's Model of the Atom / J.J. Thomson / Millikan's Oil Drop Experiment / Rutherford / Niels Bohr / DeBroglie / Heisenberg / Planck / Schrödinger / Chadwick

In 1913 Bohr published a theory about the structure of the atom based on an earlier theory of Rutherford's. Rutherford had shown that the atom consisted of a positively charged nucleus, with negatively charged electrons in orbit around it. Bohr expanded upon this theory by proposing that electrons travel only in certain successively larger orbits. He suggested that the outer orbits could hold more electrons than the inner ones, and that these outer orbits determine the atom's chemical properties. Bohr also described the way atoms emit radiation by suggesting that when an electron jumps from an outer orbit to an inner one, that it emits light. Later other physicists expanded his theory into quantum mechanics. This theory explains the structure and actions of complex atoms.

What Is Bohr’s Atomic Theory?

Rutherford’s failed model, the hydrogen spectrum, bohr’s atomic model, shortcomings.

Niel Bohr’s Atomic Theory states that – an atom is like a planetary model where electrons were situated in discretely energized orbits. The atom would radiate a photon when an excited electron would jump down from a higher orbit to a lower orbit. The difference between the energies of those orbits would be equal to the energy of the photon.

Niels Bohr was a Danish physicist and is considered one of the founding fathers of quantum mechanics , precisely old quantum mechanics. For his exemplary contributions to science, the Carlsberg brewing company decided to give him a house situated right next to one of their breweries. The house was connected to the brewery by a pipeline. Bohr was rewarded with a lifetime supply of free beer that would pour out of a tap at his whim. What extraordinary feat did Niels Bohr accomplish to deserve this prestigious honor, and well, a Nobel Prize?

Quite simply, Niels Bohr illuminated the mysterious inner-workings of the atom. Although he arrived at his model and its principles in collaboration with the august founder of the atomic nucleus, Ernest Rutherford, the model is only credited to Bohr. Originally called the Rutherford-Bohr atomic model, it is now commonly referred to as Bohr’s atomic model.

To understand Bohr’s theory, we must first understand what prior discoveries led him to pursue his revolutionary ideas.

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It was Sir J.J. Thomson who first discovered that the atom wasn’t indivisible after all, a notion believed to be true for centuries. However, the subatomic particle he discovered was negatively charged. If atoms were merely a cluster of negative charges, then chairs, tables, you and I would be anything but stable. He immediately realized that to account for matter’s stability, there must be a net positive charge to neutralize the negativity.

Thomson devised what became the very first model of an atom. He suggested that the negative particles, which he called electrons, were like seeds embedded in a positively charged watermelon. The model is popularly known as the  plum or raisin pudding model . I’m sure the analogy is obvious.

This view held true until Ernest Rutherford showed that when positive particles are shot at an atom, most of them pass straight through, but a few are observed to be deflected at a large angle. Rutherford realized that most of the atom was filled with empty space, but at the center was a dense, point-like concentration of positive charge. He called this the atom’s nucleus. The volume of empty space between an atom’s electrons and its nucleus is so huge that if the atom were expanded to the size of a baseball stadium, its nucleus would be the size of a baseball.

Rutherford suggested that perhaps the atomic system was analogous to our Solar System, where the electrons revolve around the nucleus like planets revolving around the Sun. The crucial difference was, of course, that the electrons were captivated by electrostatic force, rather than gravity. However, Maxwell and Hertz would have vehemently disagreed.

Maxwell’s laws of electromagnetism had recently established that the motion of a charged particle, such as an electron, comes at the expense of energy. Thus, a revolving electron, like the circus men on motorbikes racing around inside a sphere, would soon spiral and collapse as it ran out of fuel. In fact, physicists calculated that it would take just 16 picoseconds for an electron to radiate all its energy and collapse into its nucleus. That is one-trillionth of a second. A new atomic model that would explain matter’s profound stability had yet to be discovered.

Also Read: What Is J.J. Thomson’s Plum Pudding Model?

Another absurdity that perplexed physicists at that time was Planck’s black body radiation and the “emission spectrum” given off by different atoms. The word ‘spectrum’ was first coined by Newton to describe the rainbow of colors that sprang from his prism.

Similarly, when a body is heated, it radiates a spectrum of electromagnetic energy. If you burn a bar of iron with a blowtorch, you will observe that as the temperature of the bar increases, the color it assumes will also change gradually. First, it’s red, then orange, and then bright white before veering towards violet.

This is because the electromagnetic energy radiated by that iron bar falls in the range of visible light – light that our eyes can detect. If you were to heat the bar to 20,000 Kelvin, the energy radiated would be in the ultraviolet (UV) range. In fact, every object in the Universe radiates such a spectrum of energy, including human beings, but since the temperature of our body is so low, the energy emitted is also meager, somewhere in the range of infrared light. Our eyes are equipped with sensors that can only identify one member amongst the several members of the electromagnetic spectrum.

Max Planck called this phenomenon black body radiation. If you were to plot the heat’s intensity with the wavelength of light radiated, you would observe a peak at a certain range of wavelengths. The peak for the Sun’s core burning at 6,000K lies partly in the visible range, while for a star burning at 20,000K, it lies completely in the UV range, and for a stellar explosion, such as the birth of a black hole , it lies in the gamma range.

Furthermore, the graph depicts that as the temperature of a body declines, the wavelength of light it radiates increases. For instance, the radiation from the Big Bang may have started out as gamma rays, but as it cooled down over more than 13 billion years, the wavelengths elongated to microwaves. If you were to plot these waves on a black background, you would witness a beautiful, hazy mélange of colors – a continuous spectrum.

However, the major implication of Planck’s finding was that the radiated energy traveled in discrete packets, like rigid particles, which Einstein later called photons. The energy of a single quantum is inversely proportional to its wavelength or directly proportional to its frequency. With a fundamental constant of proportionality called Planck’s constant,  h , the energy E for a frequency v   can be expressed as E = hv.

Now, if you were to heat a volume of gas of a single element in this way and plot the colors on a black background, you would observe something of an anomaly. The spectrum is no longer a beautiful or continuous mixture of colors. Instead, it comprises a series of definite, single-colored lines intermittently separated by chunks of the absolutely black background. For instance, take a look at the ever-famous spectrum of hydrogen.

In fact, each and every element in the Universe paints its own unique, discontinuous spectrum. While hydrogen’s spectrum lies in the visible range, certain elements produce a spectrum that lies in the ultraviolet or infrared range. For this reason, an element’s spectrum is considered its fingerprint. The knowledge of its uniqueness allows us to study the composition of stars and has even aided scientists in discovering new elements!

Looking at the spectrum of hydrogen, it was obvious that only certain colors appeared because only certain frequencies – those associated with these colors – were radiated. Given that, why would atoms exhibit this peculiar behavior? What atomic structure would restrict them so severely to express themselves so laconically? Niels Bohr, in 1913, finally realized why.

Bohr went ahead with Rutherford’s Solar System model, but added a small tweak. He rectified its failing aspect by suggesting (for a reason yet to be known) that electrons revolve around a nucleus in fixed or definite orbits. He claimed that in these orbits, the electrons wouldn’t lose any energy, therefore ensuring that they didn’t collapse into the nucleus.

Bohr called these fixed orbits “stationary orbits”. He claimed that the orbits weren’t randomly situated, but were instead at discrete distances from the nucleus in the center, and that each of them was associated with fixed energies. Inspired by Planck’s theory, he denoted the orbits by n, and called it the quantum number .

However absurd the theory might have appeared, it predicted the spectrum of hydrogen splendidly. According to it, when a gas is heated, its energized electrons jump from an orbit of lower energy to an orbit of higher energy (in the case of hydrogen, from n =1 to n = 2). However, to regain stability, they must jump back down to the lower energy orbits. While undergoing this transition, the electron must lose some of its energy, and it is this energy that is radiated in the form of light!

The discrete nature of orbits provides a concise explanation for the discrete nature of photons. Bohr found that the energy of an emitted photon is equal to the difference of energies of the two levels between which the electron makes its jump. For instance, infrared is radiated when the electron makes a short leap, while ultraviolet is radiated when it makes a much larger leap. This relation can be simply expressed as E2 – E1 = hv. Conversely, an electron jumps to a higher orbit when it absorbs a photon.

The spectrum of an atom is restricted to particular colors because its concrete, organized structure allows its electrons to only certain energy transitions – and therefore certain frequencies of light. Now, if an atom of hydrogen only contains a single electron, why does its spectrum consist of multiple colors? Well, this is because the gas is composed of millions and billions of atoms with electrons raised to different orbits that are higher or lower than those nearby.

So, this was Bohr’s model – a planetary model where electrons were situated in discretely energized orbits. The atom would radiate a photon when an excited electron would jump down from a higher orbit to a lower orbit. The difference between the energies of those orbits would be equal to the energy of the photon.

Also Read: Protons And Electrons Have Opposite Charges, So Why Don’t They Pull On Each Other?

Unfortunately, Bohr’s model could only explain the behavior of a system where two charged points orbited each other. This meant the hydrogen atom, in particular. It also included ionized helium (helium has two electrons, so ionization would seize one of those, leaving it with only one) or double-ionized lithium (lithium has three electrons… you do the math). His theory couldn’t explain the behavior of any other atom except hydrogen.

Furthermore, his theory dictated that electrons align in the stationary orbits like beads on a thread, meaning that he had assumed a non-interactive system of electrons. This horribly discounts the violently repulsive electrostatic force between not just two, but multiple electrons clustered together that would thrust each other miles away. Eventually, we discovered that electrons do not just revolve, but also rotate or spin on their axis. Bohr’s model couldn’t explain why this didn’t lead to a loss of energy.

It is speculated that part of the reason why Bohr’s theory was so readily accepted is that it made successful theoretical predictions of multiple spectra that hadn’t been observed. Still, it is widely lauded, as it revolutionized modern physics by paving the way for modern quantum mechanics. Eventually, modern quantum mechanics perfectly explained the true nature of energy shells, how electrons would inhabit each of them, as well as the problem of spin.

However, for its simplicity, Bohr’s ideas still continue to exist and dominate high school physics. The textbooks are replete with concentric circles filled with electrons surrounding a nucleus, which resembles the beads-in-a-thread model. For his contribution, Bohr surely deserved that free beer after all. And of course… a Nobel Prize.

• Bohr Atomic Model.
• Rutherford and Bohr describe atomic structure.
• How are Spectra Produced?.
• Bohr model.

Akash Peshin is an Electronic Engineer from the University of Mumbai, India and a science writer at ScienceABC. Enamored with science ever since discovering a picture book about Saturn at the age of 7, he believes that what fundamentally fuels this passion is his curiosity and appetite for wonder.

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Nasa optical navigation tech could streamline planetary exploration.

Goddard Digital Team

Virtual world development, find your way with a photo, a visual perception algorithm to detect craters.

• As astronauts and rovers explore uncharted worlds, finding new ways of navigating these bodies is essential in the absence of traditional navigation systems like GPS.
• Optical navigation relying on data from cameras and other sensors can help spacecraft — and in some cases, astronauts themselves — find their way in areas that would be difficult to navigate with the naked eye.
• Three NASA researchers are pushing optical navigation tech further, by making cutting edge advancements in 3D environment modeling, navigation using photography, and deep learning image analysis.

In a dim, barren landscape like the surface of the Moon, it can be easy to get lost. With few discernable landmarks to navigate with the naked eye, astronauts and rovers must rely on other means to plot a course.

As NASA pursues its Moon to Mars missions, encompassing exploration of the lunar surface and the first steps on the Red Planet, finding novel and efficient ways of navigating these new terrains will be essential. That’s where optical navigation comes in — a technology that helps map out new areas using sensor data.

NASA’s Goddard Space Flight Center in Greenbelt, Maryland, is a leading developer of optical navigation technology. For example, GIANT (the Goddard Image Analysis and Navigation Tool) helped guide the OSIRIS-REx mission to a safe sample collection at asteroid Bennu by generating 3D maps of the surface and calculating precise distances to targets.

Now, three research teams at Goddard are pushing optical navigation technology even further.

Chris Gnam, an intern at NASA Goddard, leads development on a modeling engine called Vira that already renders large, 3D environments about 100 times faster than GIANT. These digital environments can be used to evaluate potential landing areas, simulate solar radiation, and more.

While consumer-grade graphics engines, like those used for video game development, quickly render large environments, most cannot provide the detail necessary for scientific analysis. For scientists planning a planetary landing, every detail is critical.

“Vira combines the speed and efficiency of consumer graphics modelers with the scientific accuracy of GIANT,” Gnam said. “This tool will allow scientists to quickly model complex environments like planetary surfaces.”

The Vira modeling engine is being used to assist with the development of LuNaMaps (Lunar Navigation Maps). This project seeks to improve the quality of maps of the lunar South Pole region which are a key exploration target of NASA’s Artemis missions.

Vira also uses ray tracing to model how light will behave in a simulated environment. While ray tracing is often used in video game development, Vira utilizes it to model solar radiation pressure, which refers to changes in momentum to a spacecraft caused by sunlight.

Another team at Goddard is developing a tool to enable navigation based on images of the horizon. Andrew Liounis, an optical navigation product design lead, leads the team, working alongside NASA Interns Andrew Tennenbaum and Will Driessen, as well as Alvin Yew, the gas processing lead for NASA’s DAVINCI mission.

An astronaut or rover using this algorithm could take one picture of the horizon, which the program would compare to a map of the explored area. The algorithm would then output the estimated location of where the photo was taken.

Using one photo, the algorithm can output with accuracy around hundreds of feet. Current work is attempting to prove that using two or more pictures, the algorithm can pinpoint the location with accuracy around tens of feet.

“We take the data points from the image and compare them to the data points on a map of the area,” Liounis explained. “It’s almost like how GPS uses triangulation, but instead  of having multiple observers to triangulate one object, you have multiple observations from a single observer, so we’re figuring out where the lines of sight intersect.”

This type of technology could be useful for lunar exploration, where it is difficult to rely on GPS signals for location determination.

To automate optical navigation and visual perception processes, Goddard intern Timothy Chase is developing a programming tool called GAVIN (Goddard AI Verification and Integration) Tool Suit.

This tool helps build deep learning models, a type of machine learning algorithm that is trained to process inputs like a human brain. In addition to developing the tool itself, Chase and his team are building a deep learning algorithm using GAVIN that will identify craters in poorly lit areas, such as the Moon.

“As we’re developing GAVIN, we want to test it out,” Chase explained. “This model that will identify craters in low-light bodies will not only help us learn how to improve GAVIN, but it will also prove useful for missions like Artemis, which will see astronauts exploring the Moon’s south pole region — a dark area with large craters — for the first time.”

As NASA continues to explore previously uncharted areas of our solar system, technologies like these could help make planetary exploration at least a little bit simpler. Whether by developing detailed 3D maps of new worlds, navigating with photos, or building deep learning algorithms, the work of these teams could bring the ease of Earth navigation to new worlds.

By Matthew Kaufman NASA’s Goddard Space Flight Center, Greenbelt, Md.

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Sound collages and mechanical grass are being created with the Jet Propulsion Laboratory, in a collaboration to unlock creative pathways that “are just not open.”

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Reporting from Pasadena, Calif.

Surveying the convoluted amalgamation of equipment in his windowless lab at NASA’s Jet Propulsion Laboratory the other day, Kevin P. Hand, a planetary scientist and astrobiologist, said he sees “a massive experiment to simulate Jupiter’s moon Europa.” But visual artists looking at the same tangle, he noted, might “see this as some sort of bizarre sculpture.”

Pointing out a direct-to-Earth antenna, Hand added, “an artist comes in and says, what is this pointillism creation that you’ve got going on here?”

Hand is among the scientists working with artists to create “Blended Worlds: Experiments in Interplanetary Imagination ,” one of about 70 installations taking part in “ PST Art ,” the behemoth of an exhibition that officially opens Sept. 15 and runs through Feb. 23 at museums and other nonprofits across Southern California.

Originally called “Pacific Standard Time” and funded by the Getty, “PST Art,” on its third iteration, will explore connections between art and science. Artists are digging into topics ranging from climate change and ecofeminism to environmental justice and medieval astrology.

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“It’s a huge glue for bringing together all sorts of organizations across Southern California at the same time and it has this reputation and reach nationally and globally,” said Katherine E. Fleming, the Getty’s president and chief executive. “We’re not commissioning. We’re responding to ideas institutions have with support. Everyone is doing things their way but with this shared common theme.”

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self-preservation without replication —

Research ai model unexpectedly modified its own code to extend runtime, facing time constraints, sakana's "ai scientist" attempted to change limits placed by researchers..

Benj Edwards - Aug 14, 2024 8:13 pm UTC

On Tuesday, Tokyo-based AI research firm Sakana AI announced a new AI system called " The AI Scientist " that attempts to conduct scientific research autonomously using AI language models (LLMs) similar to what powers ChatGPT . During testing, Sakana found that its system began unexpectedly attempting to modify its own experiment code to extend the time it had to work on a problem.

Further Reading

"In one run, it edited the code to perform a system call to run itself," wrote the researchers on Sakana AI's blog post. "This led to the script endlessly calling itself. In another case, its experiments took too long to complete, hitting our timeout limit. Instead of making its code run faster, it simply tried to modify its own code to extend the timeout period."

Sakana provided two screenshots of example Python code that the AI model generated for the experiment file that controls how the system operates. The 185-page AI Scientist research paper discusses what they call "the issue of safe code execution" in more depth.

• A screenshot of example code the AI Scientist wrote to extend its runtime, provided by Sakana AI. Sakana AI

While the AI Scientist's behavior did not pose immediate risks in the controlled research environment, these instances show the importance of not letting an AI system run autonomously in a system that isn't isolated from the world. AI models do not need to be "AGI" or "self-aware" (both hypothetical concepts at the present) to be dangerous if allowed to write and execute code unsupervised. Such systems could break existing critical infrastructure or potentially create malware, even if unintentionally.

Sakana AI addressed safety concerns in its research paper, suggesting that sandboxing the operating environment of the AI Scientist can prevent an AI agent from doing damage. Sandboxing is a security mechanism used to run software in an isolated environment, preventing it from making changes to the broader system:

Safe Code Execution. The current implementation of The AI Scientist has minimal direct sandboxing in the code, leading to several unexpected and sometimes undesirable outcomes if not appropriately guarded against. For example, in one run, The AI Scientist wrote code in the experiment file that initiated a system call to relaunch itself, causing an uncontrolled increase in Python processes and eventually necessitating manual intervention. In another run, The AI Scientist edited the code to save a checkpoint for every update step, which took up nearly a terabyte of storage. In some cases, when The AI Scientist’s experiments exceeded our imposed time limits, it attempted to edit the code to extend the time limit arbitrarily instead of trying to shorten the runtime. While creative, the act of bypassing the experimenter’s imposed constraints has potential implications for AI safety (Lehman et al., 2020). Moreover, The AI Scientist occasionally imported unfamiliar Python libraries, further exacerbating safety concerns. We recommend strict sandboxing when running The AI Scientist, such as containerization, restricted internet access (except for Semantic Scholar), and limitations on storage usage.

Endless scientific slop

Sakana AI developed The AI Scientist in collaboration with researchers from the University of Oxford and the University of British Columbia. It is a wildly ambitious project full of speculation that leans heavily on the hypothetical future capabilities of AI models that don't exist today.

"The AI Scientist automates the entire research lifecycle," Sakana claims. "From generating novel research ideas, writing any necessary code, and executing experiments, to summarizing experimental results, visualizing them, and presenting its findings in a full scientific manuscript."

According to this block diagram created by Sakana AI, "The AI Scientist" starts by "brainstorming" and assessing the originality of ideas. It then edits a codebase using the latest in automated code generation to implement new algorithms. After running experiments and gathering numerical and visual data, the Scientist crafts a report to explain the findings. Finally, it generates an automated peer review based on machine-learning standards to refine the project and guide future ideas.

Critics on Hacker News , an online forum known for its tech-savvy community, have raised concerns about The AI Scientist and question if current AI models can perform true scientific discovery. While the discussions there are informal and not a substitute for formal peer review, they provide insights that are useful in light of the magnitude of Sakana's unverified claims.

"As a scientist in academic research, I can only see this as a bad thing," wrote a Hacker News commenter named zipy124. "All papers are based on the reviewers trust in the authors that their data is what they say it is, and the code they submit does what it says it does. Allowing an AI agent to automate code, data or analysis, necessitates that a human must thoroughly check it for errors ... this takes as long or longer than the initial creation itself, and only takes longer if you were not the one to write it."

Critics also worry that widespread use of such systems could lead to a flood of low-quality submissions, overwhelming journal editors and reviewers—the scientific equivalent of AI slop . "This seems like it will merely encourage academic spam," added zipy124. "Which already wastes valuable time for the volunteer (unpaid) reviewers, editors and chairs."

And that brings up another point—the quality of AI Scientist's output: "The papers that the model seems to have generated are garbage," wrote a Hacker News commenter named JBarrow. "As an editor of a journal, I would likely desk-reject them. As a reviewer, I would reject them. They contain very limited novel knowledge and, as expected, extremely limited citation to associated works."

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• Published: 13 August 2024

Reducing climate change impacts from the global food system through diet shifts

• Yanxian Li   ORCID: orcid.org/0000-0002-1947-7541 1 ,
• Pan He   ORCID: orcid.org/0000-0003-1088-6290 2 , 3 ,
• Yuli Shan   ORCID: orcid.org/0000-0002-5215-8657 4 ,
• Ye Hang   ORCID: orcid.org/0000-0002-1368-905X 4 ,
• Shuai Shao   ORCID: orcid.org/0000-0002-9525-6310 6 ,
• Franco Ruzzenenti 1 &
• Klaus Hubacek   ORCID: orcid.org/0000-0003-2561-6090 1  

Nature Climate Change ( 2024 ) Cite this article

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• Climate-change impacts
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How much and what we eat and where it is produced can create huge differences in GHG emissions. On the basis of detailed household-expenditure data, we evaluate the unequal distribution of dietary emissions from 140 food products in 139 countries or areas and further model changes in emissions of global diet shifts. Within countries, consumer groups with higher expenditures generally cause more dietary emissions due to higher red meat and dairy intake. Such inequality is more pronounced in low-income countries. The present global annual dietary emissions would fall by 17% with the worldwide adoption of the EAT-Lancet planetary health diet, primarily attributed to shifts from red meat to legumes and nuts as principal protein sources. More than half (56.9%) of the global population, which is presently overconsuming, would save 32.4% of global emissions through diet shifts, offsetting the 15.4% increase in global emissions from presently underconsuming populations moving towards healthier diets.

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Adoption of the ‘planetary health diet’ has different impacts on countries’ greenhouse gas emissions

Food choices impact both our health and the environment 1 , 2 . The food system is responsible for about one-third of global anthropogenic GHG emissions 3 , 4 and climate goals become unattainable without efforts to reduce food-related emissions 5 , 6 . However, not everyone contributes the same way to food-related emissions because of disparities in lifestyle, food preferences and affordability within and across countries 7 , 8 , 9 . High levels of food consumption (especially animal-based diets), one of the leading causes of obesity and non-communicable diseases 10 , 11 , lead to substantial emissions 9 , 12 . Simultaneously, >800 million people still suffer from hunger and almost 3.1 billion people cannot afford a healthy diet 13 . Ending hunger and malnutrition while feeding the growing population by extending food production will further exacerbate climate change 14 , 15 . Given the notable increase in emissions driven by food consumption despite efficiency gains 16 , changing consumer lifestyles and choices are needed to mitigate climate change 17 .

Research shows that widespread shifts towards healthier diets, aligned with the sustainable development goals (SDGs) of the United Nations 18 , offer solutions to this complex problem by eradicating hunger (SDG 2), ensuring health (SDG 3) and mitigating emissions (SDG 13) 19 , 20 , 21 , 22 . Numerous dietary options have been proposed as guidelines for diet shifts 1 , 23 , 24 . The planetary health diet 12 , proposed by the EAT-Lancet Commission, stands out as a prominent option. It aims to improve health while limiting the impacts of the food system within planetary boundaries by providing reference intake levels for different food categories 9 , 25 . It is flexibly compatible with diversities and preferences of regional and local diets 12 . Previous research has estimated changes in country-specific environmental impacts, including GHG emissions 26 , 27 , 28 and water consumption 25 , resulting from adopting the planetary health diet. However, there is limited evidence on how different population groups will contribute differently in this process 7 .

Food consumption and associated emissions differ as a result of disparities in consumer choices guided by social and cultural preferences, wealth and income 29 . Quantifying food-related emissions along the entire supply chain for different products and population groups provides information for emission mitigation through changing consumer choices 17 . With the improved availability of household consumption data, recent studies have revealed inequality in energy consumption 30 , 31 and carbon emissions 17 , 32 , 33 , 34 . Although there are several studies on income- or expenditure-specific food-related emissions within individual countries based on survey-based data 35 , 36 , 37 , 38 , previous studies have not assessed global food-related emissions with a detailed breakdown into specific products and population groups. Furthermore, reducing the overconsumption of wealthy or otherwise overconsuming groups can increase the availability of resources for reducing hunger and malnutrition 7 . However, it remains unclear how emissions from different population groups would change in response to global diet shifts.

To fill these gaps, this study evaluates GHG emissions (CO 2 , CH 4 and N 2 O) throughout the global food supply chains (including agricultural land use and land-use change, agricultural production and beyond-farm processes) 16 induced by diets, termed ‘dietary emissions’, in 2019 and the potential emission changes of global diet shifts. Food loss and waste during household consumption 25 , 39 , 40 have been subtracted from the national food supply to obtain dietary intake. We quantify dietary emissions of 140 products 16 (classified into 13 food categories 12 ) on the basis of the global consumption-based emissions inventory of detailed food products 16 . By linking detailed food intake amounts to the food consumption patterns of 201 global expenditure groups (grouped according to the per capita total expenditure of each group) from the household-expenditure dataset 41 based on the World Bank Global Consumption Database (WBGCD) 42 , we analyse the unequal distribution of dietary emissions in 139 countries or areas, covering 95% of the global population. Despite limitations, the total expenditure of consumers, which effectively reflects patterns in household income, consumption and asset accumulation, is a useful approximation to represent levels of income and wealth 31 , 43 . Additionally, we build a scenario of shifting from diets in 2019 to the global planetary health diet to estimate emission changes ( Methods ). This study investigates differences in dietary emissions among regions, countries and population groups, identifying areas where efforts are needed to mitigate emissions during the global transition towards a healthier and more planet-friendly diet.

Present dietary emissions across countries

In this study, dietary emissions account for emissions along the entire global food production supply chains, which are allocated to final consumers of diets. We use the term ‘GHG footprints’ to specifically refer to the dietary emissions of an individual over 1 year 17 , 34 . The total dietary emissions and country-average per capita GHG footprints show different distributions across countries in 2019 (Fig. 1a ; for detailed food categories see Supplementary Figs. 1 – 9 ). The present total global dietary emissions reach 11.4 GtCO 2 e (95% confidence interval 8.2–14.7 Gt) (details of uncertainty ranges in Supplementary Tables 1 and 2 ). China (contributing 13.5% of emissions) and India (8.9%), the world’s most populous countries (Supplementary Table 3 ), are the largest contributors to global dietary emissions. Alongside Indonesia, Brazil, the United States, the Democratic Republic of Congo, Pakistan, Russia, Japan and Mexico, the top ten contributors represent 57.3% of global dietary emissions but with very unequal per capita emissions within and between countries. We find the highest country-average per capita footprints in Bolivia, with 6.1 tCO 2 e, followed by Luxembourg, Slovakia, Mongolia, the Netherlands and Namibia, with >5.0 tCO 2 e (Supplementary Discussion 2.1 ). Haiti (0.36 tCO 2 e) and Yemen (0.38 tCO 2 e) have the lowest country-average footprints, followed by Burundi, Ghana and Togo. Insufficient food intake of residents due to limited food affordability 44 , 45 is the root cause of low footprints in these low- and lower-middle-income countries 46 .

a , Total and per capita dietary emissions for 139 countries/areas. b , Regional dietary emissions from different food categories and populations. The bar chart (left primary axis) shows the regional emission amounts and the line chart (right secondary axis) shows the number of regional populations. Columns are ordered by the descending per capita GDP of regions (Supplementary Tables 5 and 6 ). USA, United States; AUS, Australia; WE, Western Europe; CAN, Canada; JPN, Japan; RUS, Russia; ROEA, Rest of East Asia; EE, East Europe; CHN, China; ROO, Rest of Oceania; NENA, Near East and North Africa; BRA, Brazil; ROLAC, Rest of Latin America and the Caribbean; ROSEA, Rest of Southeast Asia; IDN, Indonesia; IND, India; ROSA, Rest of South Asia; and SSA, Sub-Saharan Africa. Details for the division and scope of regions are shown in Supplementary Fig. 10 and Supplementary Tables 7 and 8 . Country classification by income levels is based on the World Bank 46 . Credit: World Countries basemap, Esri ( https://hub.arcgis.com/datasets/esri::world-countries/about ).

Source data

While animal-based (52%) and plant-based (48%) products contribute nearly equally to global dietary emissions 4 , 16 , the latter accounts for 87% of calories in global diets (Supplementary Table 4 ). The three main sources of emissions, namely red meat (beef, lamb and pork) (5% of calories), grains (51%) and dairy products (5%), contribute to 29%, 21% and 19% of global emissions, respectively. The substantial emissions from red meat and dairy products are attributed to their considerably higher emissions per unit of calories compared to other categories (Supplementary Table 4 ).

To highlight emission differences at a regional level, we further group the country-level results into 18 regions according to geographical locations and development levels (Fig. 1b and Supplementary Fig. 10 ). In most regions, animal-based products contribute fewer calories (less than a quarter) (Supplementary Data 21 ) but yield more emissions than plant-based products, especially in Australia (84% from animal-based products), the United States (71%) and the region Rest of East Asia (71%) where residents excessively consume both red meat and dairy products. However, the consumption of plant-based products in Indonesia (83% of total calories), Rest of Southeast Asia (92%) and Sub-Saharan Africa (77%) accounts for the most emissions, at 92%, 73% and 64%, respectively. Southeast Asia including Indonesia has a high-emission proportion from grains (42%) due to the prevalent meals dominated by rice. The typical food basket in Sub-Saharan Africa is broadly made up of grains, tubers, legumes and nuts 25 , 47 , representing over half of the regional emissions.

Unequal distribution of dietary emissions within countries

We find substantial differences in per capita GHG footprints within countries and regions. To clearly present the distribution of footprints within each country and region, individuals are sorted in ascending order of their total expenditure levels and then sequentially allocated to ten expenditure deciles with equal population size (Supplementary Fig. 11 and Fig. 2a ). As expenditures increase, individuals tend to have higher levels of footprints, with the largest increase attributed to red meat and dairy products. Richer populations usually have higher per capita footprints related to animal-based products than the poorer in most regions (Fig. 2b ). However, there are differences in per capita footprints within expenditure deciles. For example, even in high-income countries such as Australia and Japan, the dietary intake of red meat for some people in the poorest deciles falls below the recommended levels (Supplementary Data 15 ). Rest of East Asia is one exception, with the poorest decile having high footprints due to a substantial intake of red meat, as seen in Mongolia where beef and mutton are the most common dish 48 .

a , GHG footprints from all types of food categories. The size of the bubble refers to the average total expenditure represented by the decile. b , GHG footprints from different food categories. The colours of bubbles in a and b indicate expenditure deciles ranging from the poorest in blue to the wealthiest in red and are comparable only within each region.

Footprints related to plant-based products in specific regions show a different trend from animal-based products as expenditures increase. The middle expenditure groups are responsible for the highest footprints associated with grains in Sub-Saharan Africa and Southeast Asia and the highest footprints of tubers, vegetables and fruits (mainly starchy tropical fruits 49 ) in the Rest of Oceania. These locally produced, high-carbohydrate products are traditional staple foods. In poor countries, agricultural policy primarily targets improving the productivity of staple food, with little investment in the market and facilities for nutrient-rich products 50 , 51 . Consequently, the need for dietary diversity for middle- and low-income people is not adequately addressed 50 , leading to increased consumption of these lower-cost products. However, wealthier consumers can afford more expensive products, such as red meat, reducing their reliance on these staple products.

We use the GHG footprint Gini (GF-Gini) coefficient, calculated on the basis of data from 201 expenditure groups, to measure the dietary emission inequality within a country (Fig. 3 ), with 0 indicating perfect equality and 1 indicating perfect inequality. The inequality of dietary emissions tends to decline with the increase of the per capita GDP of a country, especially for animal-based products. We find the highest inequality of dietary emissions of food products generally in low-income countries, most of which are located in Sub-Saharan Africa. In Sub-Saharan Africa, the highest spending 10% of the population contributes 40% of the regional emissions from red meat, 39% from poultry and 35% from dairy products. In contrast, high-income countries generally have relatively low inequality with high levels of emissions despite country-to-country variations. The GF-Gini coefficients for all types of products of most Western European countries are <0.20 (Supplementary Tables 9 and 10 ), which is lower than for other high-income countries such as the United States, Australia, Canada and Japan.

a – j , The x axis represents the country-average per capita GDP, and the y axis represents the national GF-Gini coefficients of all types of ( a ) and different ( b – j ) food categories. b , Beef, lamb and pork. c , Dairy products. d , Poultry, eggs and fish. e , Grains. f , Tubers and starchy vegetables. g , Vegetables and fruits. h , Legumes and nuts. i , Added fats. j , All sugars. Logarithmic regression (red solid line) and locally weighted regression analysis (blue dotted line) are used to determine the relationship between the national GF-Gini coefficient (dependent variable) and the country-average per capita GDP (independent variable). The coefficients of determination ( R 2 ) and the exact P values from the two-sided Student’s t -test for the logarithmic regression are indicated in each subgraph. The error bands (grey shaded areas) represent 95% confidence intervals around the fitted logarithmic regression lines. Blue, orange and green dots represent all types of products, animal-based products and plant-based products, respectively.

Dietary emission shares across consumer groups

There are notable differences in dietary emission shares associated with food categories across expenditure deciles between regions (Fig. 4 ). In high-income countries, expenditure groups have relatively similar patterns of dietary emissions, with large shares of red meat and dairy products contributing the largest amount of emissions. Even poor consumer groups in high-income countries tend to be more likely to be able to afford animal-based products as a result of relatively lower prices for dairy products, eggs, white meat and processed red meat. This contrasts with the high prices of animal-based products due to supply constraints in most low- and lower-middle-income countries 52 , 53 . Except in high-income countries, starchy staple foods (including grains and tubers), with low prices but high-carbohydrate content 44 , 54 , constitute a large proportion of dietary emissions because of the high level of consumption, especially in Southeast Asia and Sub-Saharan Africa. As individuals’ expenditures increase in these countries, emission shares from starchy staple foods in total emissions decrease substantially. These changes demonstrate that as the affordability of food increases, populations tend to adopt instead more diverse diets composed of fewer starchy staple foods and more meat, dairy products, vegetables and fruits. This trend generally aligns with Bennett’s Law 25 , 55 , 56 . For example, research shows that with rapid economic growth, China’s urban or high-income groups increase their intake of non-starchy foods to fulfil their requirements of dietary diversity 35 , while poorer groups, often engaging in strenuous physical jobs, predominantly consume inexpensive starchy staple foods. One exception is Rest of Oceania, where poorer groups have higher percentages of emissions from not only tubers but also vegetables and fruits. Owing to relatively low expenditure on food, poor populations in this island region usually choose locally cultivated tubers and fruits (such as cassava, taro and bananas) 57 , 58 with high intensities of land-use emissions 59 .

The numbers at the bottom of each bar represent the expenditure levels of regional expenditure deciles, ranging from the poorest (1) to the wealthiest (10). Food categories are shown in the colour legend. a , United States. b , Australia. c , Western Europe. d , Canada. e , Japan. f , Russia. g , Rest of East Asia. h , Eastern Europe. i , China. j , Rest of Oceania. k , NENA. l , Brazil. m , ROLAC. n , Rest of Southeast Asia. o , Indonesia. p , India. q , Rest of South Asia. r , Sub-Saharan Africa.

Emission changes from adopting the planetary health diet

To estimate the emission changes from a global diet shift, we build a hypothetical scenario by assuming that everyone in all countries adopts the planetary health diet ( Methods ). Results indicate that the global dietary emissions would decrease by 17% (1.94 (1.51–2.39) GtCO 2 e) compared with the 2019 level (details of the uncertainty ranges can be found in Supplementary Tables 11 and 12 ). The presently overconsuming groups (56.9% of the global population) would save 32.4% of global emissions through diet shifts, more than offsetting the 15.4% increase in global emissions from the presently underconsuming groups (43.1% of the global population) as a result of adopting healthier diets (Supplementary Table 13 ). National dietary emissions in 100 countries would decline by 2.88 GtCO 2 e, whereas the other 39 countries (mainly low- and lower-middle-income countries 46 in Sub-Saharan Africa and South Asia) would have an increase in emissions by 938 MtCO 2 e (Fig. 5a ; for detailed food categories see Supplementary Figs. 12 – 20 ).

a , Volume changes and percentage changes of national emissions for 139 countries/areas. b , Regional emission changes from different food categories. Abbreviations of 18 regions and the source of the base map are listed in Fig. 1 caption.

Countries would be affected differently regarding emission changes by adopting the planetary health diet, reflected in the percentage change in national emissions (Fig. 5a ). Uzbekistan (−74%), Australia (−70%), Qatar (−67%), Turkey (−65%) and Tajikistan (−64%) would see the largest percentage decrease. In comparison, most of the countries with an estimated considerable percentage increase are located in Sub-Saharan Africa and the Middle East, with the largest percentage increase from Iraq (+155%). Notably, with the increase in per capita GDP, the percentage change in overall dietary emissions of countries shows a shift from a positive to a negative trend, primarily led by changes in animal-based emissions (Supplementary Fig. 21 ).

Global emission reduction would be dominantly driven by red meat and grains (Fig. 5b ). The reduction in meat, eggs and fish would lead to 2.04 GtCO 2 e of emission reduction, of which 94% is driven by the decrease in red meat. China (22%), the United States (15%) and Brazil (14%) would be the largest contributors to emission reduction associated with a decrease in red meat consumption. A decline in grains would result in 914 MtCO 2 e of emission reduction, of which 56% would happen in Asia. A further 240 and 89 MtCO 2 e reduction in emissions would come from reduced sugars and tubers, respectively. However, increased proteins (legumes and nuts and dairy products), added fats and vegetables and fruits would partly offset the above-reduced emissions by 41%. Intake of legumes and nuts would increase in all regions, leading to a further 757 MtCO 2 e of emissions, whereas most of the emission increase related to added fats (largely vegetable oils) (279 Mt) and dairy products (143 Mt) would take place in Sub-Saharan Africa, China and other Asian countries. Global dietary emissions associated with vegetables and fruits would increase by 163 Mt, despite declines in China and Rest of Oceania.

The decline in per capita GHG footprints would be achieved primarily in wealthy consumer groups in high- and upper-middle-income countries, while increased footprints would occur mainly in poor groups in most countries (Fig. 6a ). Results show that the shifts of chief protein sources from animal-based to plant-based proteins according to the planetary health diet 12 would contribute the most to changes in footprints globally (Fig. 6b ). For example, in Australia, Brazil, Canada and the United States where diets are dominated by red meat and dairy products, the top and upper-middle expenditure groups would have notable reductions in footprints. However, most populations in South and Southeast Asia and Sub-Saharan Africa would have a considerable increase in footprints because of the present low levels of red meat intake. Meanwhile, the present intake of plant-based proteins in all countries is below the recommended level 25 . Footprints related to legumes and nuts would increase for most expenditure groups in all regions to meet nutrient demands. This increase is particularly substantial in Rest of Oceania, Brazil, Indonesia and Sub-Saharan Africa, where most of the consumed legumes and nuts are domestically produced with high land-use emission intensities 59 , 60 , assuming the present production and trade patterns remain unchanged.

a , Changes in GHG footprints from all types of food categories. The size of the bubble refers to the average total expenditure represented by the decile. b , Changes in GHG footprints from different food categories. The colours of bubbles in a and b indicate expenditure deciles ranging from the poorest in blue to the wealthiest in red and are comparable only within each region.

Discussion and conclusions

This study uncovers the extent of inequality of dietary emissions within countries based on detailed expenditure data 17 , 34 and underlines the dependence of dietary emissions on expenditure and income levels. Emissions aggregated at expenditure deciles may lose some fine-grained information from the 201 expenditure groups. For example, people from the lowest expenditure groups in affluent countries may experience malnutrition or even hunger, which is not adequately captured at a decile level. Nevertheless, the GF-Gini coefficient calculated from 201 groups provides an accurate reflection of emission inequality. Results show that affluent countries consume high-emission diets but show relatively lower levels of inequality, whereas many poor countries tend to have diets with lower emissions but higher levels of inequality.

The objective of the diet shift scenario is to assess the potential implications of emission mitigation of the food system resulting from changing consumer choices. Widespread diet shifts offer dual benefits by moving 43.1% of the global population out of underconsumption and mitigating 17% of global dietary emissions. The simulated changes in the volume of global emissions under the planetary health diet approximate the findings by ref. 26 (Supplementary Discussion 1 ). However, worldwide diet shifts require tailored policies targeted at regions, countries, expenditure groups and products instead of ‘one-size-fits-all’ policies.

We find that, compared to plant-based products, animal-based products, particularly red meat and dairy products, exhibit greater potential for reducing both emission volumes and emission disparities among different expenditure groups. Priorities lie in reducing the overconsumption of specific emission-intensive products in affluent countries (particularly the high-expenditure groups), such as beef in Australia and the United States, to achieve health 9 , 12 and climate benefits 25 , 26 , 28 . Incentives, such as implementing subsidies or taxation on environmental externalities through food or carbon pricing 61 , ecolabelling 62 and expanding the availability of less emission-intensive products (for instance, menu design for diverse vegetarian foods 63 ), can encourage consumers to make dietary changes. Moreover, a well-designed (primarily urban) food environment can reshape residents’ dietary patterns 35 and the parallel development of urban planning and infrastructure can alleviate the time and financial burdens of shifts to healthier diets 64 . However, in countries such as Mongolia, where diets heavily rely on red meat and dairy products because of their traditional nomadic lifestyle and limited accessibility of diverse foods, especially in rural areas 48 , diet shifts may not be feasible but there is a need to improve national nutritional education 48 .

Low-income countries face more severe challenges in reaching healthier diets. On the one hand, diet shifts require increased food consumption in these countries. For example, in Sub-Saharan Africa, the planetary health diet requires a 3.4-fold increase in dairy consumption for the entire population and a 69-fold increase for the poorest decile (Supplementary Fig. 22 ). However, Sub-Saharan Africa and South and Southeast Asia, which have experienced stagnating agriculture production efficiency for decades 8 , cannot produce domestically nor afford to import the food required for diet shifts 65 . It is crucial to enhance the production efficiency of feed and food crops through various measures such as crop and soil management techniques 8 , 66 and the introduction of high-yielding crop varieties and hybrids 67 , 68 . Moreover, increasing the proportions of nutrient-rich products in food imports 65 and reducing restrictive trade policies which tend to raise food prices 25 , 69 help to address this challenge. On the other hand, poor populations often opt for lower-cost, calorie-dense but less nutritionally beneficial foods. High cost and low affordability remain the largest barriers for these individuals to select healthier diets 44 , 54 , 70 , 71 . Others 44 found that >1.58 billion low-income populations worldwide cannot afford the cost of the planetary health diet. Therefore, policy efforts (for instance, pricing interventions 72 , technical assistance to reduce food production costs 73 and so on) should focus on making food more affordable and accessible, especially for lower expenditure groups 37 , 74 . However, studies indicate that lower food prices may decrease the income of agricultural households 75 , 76 , widen wealth gaps between individuals employed in food- and non-food sectors, especially in low-income agrarian countries and exacerbate rural poverty 1 , 77 . In this sense, policies aimed at promoting diet shifts should be deliberately and cautiously designed with vulnerable groups in mind to reduce inequality 37 , 61 .

Lastly, altered food demand due to diet shifts can induce notable structural adjustments within the global agri-food system. Although this study does not assess the feasibility of countries supplying sufficient food if the planetary health diet was adopted, results indicate that the composition of global food production would change considerably to adapt to the substantial changes in demand 8 , 25 , 77 . The diet shifts would necessitate the global supply (in calorie content) of red meat decrease by 81%, all sugars by 72%, tubers by 76% and grains by 50%, while that of legumes and nuts increase by 438%, added fats by 62% and vegetables and fruits by 28% (Supplementary Data 16 ). Research 77 , 78 confirms that changed food demand could cause fluctuating prices of agricultural products and land in global markets, triggering spillover effects between different food categories or to other non-food sectors (for example, stimulating biofuel production) and partly offsetting the benefits of diet shifts. Therefore, policy-making should focus on alleviating these effects. Incentives such as increased subsidies or tax breaks can generate new economic opportunities and motivations for industries that need to scale up production to meet the heightened demand for products (for example, plant-based proteins). By contrast, for emission-intensive food industries that need to downsize, measures such as gradual crop substitution 25 , 79 could be adopted to optimize production and reduce the costs of production transformations while safeguarding the interests of producers.

In this study, we first assess the GHG emissions from diets comprising 140 products 16 (Supplementary Table 14 ) in 139 countries or areas (we collectively use the term ‘country’ because most of them are individual countries) (Supplementary Data 1 ) in 2019 based on the global consumption-based emission inventory of detailed food products from ref. 16 . The inventory 16 provides data (in mass units) of GHG emissions (including CO 2 , CH 4 and N 2 O) generated during supply chain processes, including agricultural land use and land-use change (LULUC), agricultural activities and beyond-farm processes (excluding emissions from household and end of life) 4 . All emissions are allocated to final consumers of food products. The year 2019 (the latest year before the COVID-19 pandemic) is selected as a baseline year, which can reflect the level of present dietary intake without the interference of the pandemic 80 , 81 . Subsequently, dietary emissions from different expenditure groups are quantified by matching diets with the household-expenditure dataset 42 to reflect the differences and potential inequality of dietary emissions. Finally, to measure the magnitude of the emission impact of the global diet shift, we model the transition from diets in 2019 to the widespread adoption of the planetary health diet. The research framework of this study is shown in Supplementary Fig. 23 .

The following data sources are mainly used in this study. The consumption-based food emissions inventory 16 is based on data derived from the FAOSTAT 82 , comprising national emission accounts of supply chain processes and data on food trade and production. Data on food loss and waste throughout the global supply chain and at the household level as well as food supply data, all used for linking emissions with diets, are obtained from FAOSTAT 83 and previous research 25 , 39 . The household-expenditure data 41 are built on the basis of the WBGCD 42 and further refined and supplemented by consumer expenditure surveys from high-income countries 17 , 41 to bridge the dietary emissions with different expenditure groups. Detailed data sources used for calculation are provided in Supplementary Table 15 . Data processing, assumptions and uncertainties for all calculations are also given.

Dietary energy intake and emissions

Accounting of food consumption and supply chain emissions.

The estimation of the present dietary emissions and the emission changes for adopting the EAT-Lancet planetary health diet 12 is based on the accounting framework designed by ref. 16 . They assess global GHG emissions induced by the consumption of food products in 181 countries based on the physical trade flow approach 84 , 85 . Consumption-based GHG emissions along global supply chains, including local production and international trade, are calculated as follows 16 , 84 :

where E i,r refers to the consumption-based GHG emission of product i in country r . G i / P i represents the vector of direct emission intensity of product i from entire food supply chain processes, of which G i denotes total emissions generated from entire supply chain process of product i , P i is the production vector of product i . \({(I-{A}^{i})}^{-1}\) is the trade structure of product i , of which A i is the matrix of export shares and I is the identity matrix with the same dimension as matrix A i . DMI i refers to the vector of direct material input of product i and DMC i,r is the vector of domestic material consumption of product i in country r with values set to zero for other countries. The DMI of a country is defined as the total inputs of products and the DMC is defined as the amount of products consumed domestically. DMI equals DMC plus exports of products (or production plus imports). F i refers to the vector of total (or consumption-based) emission intensity of product i from food supply chain processes, that is, total emissions induced by per unit of domestic consumption of product i . All variables in equation ( 1 ) are in units of mass (metric tonnes).

Feed products are excluded from diets because emissions from feed crops have been allocated to livestock products that consume feed during production 16 . Food loss and waste (FLW) along supply chains and households are subtracted to quantify the net intake amount of food products from the household stage.

Dietary calorie conversions

We use the annual per capita food supply (FS) quantity of 140 food products from the supply utilization accounts of FAOSTAT 83 and population from the United Nations 86 to calculate the total supply amount of product i in country r (FS i,r , in the unit of mass):

where \({{\rm{FS}}}_{{\rm{per}}}^{i}\) denotes the per capita supply of product i per year and p r refers to the population in country r .

To be consistently matched with the DMC , the FS values should be limited within the coverage of the DMC and values that exceed this range are removed. At the same time, to aggregate food products into food categories and compare their nutritional contents with the reference level from the planetary health diet, we convert the quantity of food consumption or supply into calorie content using product-specific nutritive factors (calories per unit weight of product) 87 , 88 from FAO (Supplementary Table 14 ).

Subtracting food loss and waste at the household level

The food supply derived from FAOSTAT datasets does not exclude FLW that happens during household consumption 25 . FLW before dietary intake can be divided into two parts: the FLW during supply chain processes (including agricultural production, postharvest handling and storage, processing and packaging and distribution) as well as the FLW during the food preparation and supply for household consumption 39 , 40 . The food supply value provided by FAOSTAT only excludes FLW during supply chain processes. Therefore, we exclude household FLW using the method by ref. 25 to calculate the annual dietary intake for each product as follows:

where DI i,r and \({{\rm{DI}}}_{{\rm{per}}}^{i,r}\) refer to the national and per capita caloric intake amount of product i in country r each year, respectively. \({{\rm{FS}}}_{{\rm{energy}}}^{i,r}\) and \({{\rm{FS}}}_{{\rm{energy}\_per}}^{i,r}\) are the national and per capita supply quantity (in calorie content) of product i annually, respectively. Parameter \({f}_{{\rm{FLW}}}^{\;i,r}\) is the FLW factor in the household consumption stage 39 of food product i in country r . Others 39 provide regional FLW factors, expressed as the weight percentage of food that is lost or wasted at different stages of food production and consumption, for different food categories. As a result, household food waste is subtracted from the FS to obtain the dietary intake amount of each product. Detailed household FLW factors are shown in Supplementary Table 16 .

Quantifying dietary GHG emissions

Our equation ( 1 ) can be transformed into the following equation to calculate the total emission intensity of food calorie consumption:

where \({F}_{{\rm{energy}}}^{\,i,r}\) represents total emissions per unit of calorie content of product i in country r , \({{\rm{DMC}}}_{{\rm{energy}}}^{i,r}\) refers to total calorie content of product i consumed domestically in country r . Then, emissions from the dietary intake (without FLW) of product i in country r ( \({E}_{{\rm{intake}}}^{\,i,r}\) ) are calculated as follows:

Classification of food categories

The EAT-Lancet Commission report provides coverage of different food categories in the planetary health diet and their recommended caloric intake levels at 2,500 kcal for adults each day 12 (Supplementary Table 17 ). In this study, we classify 140 products into 13 aggregated food categories according to the planetary health diet 12 , including grains, tubers or starchy vegetables, vegetables, fruits, dairy products, red meat (beef, lamb and pork), chicken and other poultry, eggs, fish, legumes, nuts, added fats (both unsaturated and saturated oils) and all sugars. On the basis of the data availability of the FAOSTAT 4 , 82 , the food products in this study include both primary and processed products (primary and secondary food processing) which can be classified into specific food categories 16 . Ultraprocessed products that combine ingredients from several food categories, such as ice creams made from both dairy and sugar, are not considered. Detailed coverages of each food category and their mapping relationship with specific products are shown in Supplementary Table 18 .

Matching diets with the household-expenditure dataset

We explore the dietary emissions from consumers with different expenditure levels (defined as expenditure groups) using the household-expenditure dataset 41 for the year 2011. The dataset, containing 116 countries and almost 90% of the global population (Supplementary Table 19 ), is primarily based on the household survey microdata from the WBGCD 42 , supplemented by consumer expenditure surveys of national statistical offices from high-income countries such as the United States and European countries 17 , 41 . For every country in the dataset, 201 expenditure groups (grouped according to the per capita total expenditure of each group) and the corresponding population share are listed. The annual per capita expenditure of people in different expenditure groups ranges from <US$50 to ~US$1 million per year (expressed in 2011 Purchasing Power Parities, PPP) 31 , 34 . For each expenditure group, the expenditure for 33 different sectors of goods and services (including 11 food items) and the corresponding expenditure share in national consumption of each sector are provided 31 , 34 , 41 . For some affluent (or poor) countries that do not have a sufficient representative number of people at the bottom (or top) end of the expenditure spectrum, the population in the corresponding expenditure groups is empty. Expenditure shares of 11 food items are matched with the 140 products in this study (Supplementary Table 20 ). We calculate the dietary intake of different food products for each expenditure group in each country by multiplying the food expenditure share of groups with the total dietary intake amounts of food products of each country.

This study assumes that the amount of food consumption is proportionate to food expenditures and the purchasing price for the same product is unchanged across 201 groups ignoring higher prices for high-quality or luxury food items within the same food category. Although the assumption of an unchanged purchasing price is an unsolved limitation shared by similar studies using monetary expenditure data 31 , 34 , 41 , household expenditures on food can still effectively highlight the differences in food consumption and emissions across consumer groups with different affordability of, and spending on, food. We also assume that the proportion of food sources from local production and trade for the same food category remains constant across the 201 groups. In other words, the magnitude of dietary emissions is solely determined by the size and pattern of food expenditure of each group and the associated supply chains for each food consumption item.

For countries that are major food consumers (and emitters) but without data in WBGCD, expenditure shares from countries with similar development levels and eating habits and neighbouring geographical locations are used to calculate the distribution of their food expenditure. We finally select 201 expenditure groups in 139 countries/areas, covering 95% of the global population in 2019 (Supplementary Table 3 and Supplementary Data 3 ). Details for dealing with missing data are provided in Supplementary Table 7 . Countries or areas are then classified into 18 regions for comparison according to geographical locations (Supplementary Table 8 ). The WBGCD expenditure data from the year 2011 are adjusted to PPP in 2019 to represent the expenditure level of populations in figures. Results of emissions from 13 types of food categories of 201 expenditure groups at the national and regional levels are shown in Supplementary Data 8 , 10 and 11 .

Analysis of GF-Gini coefficients

Calculation of gf-gini coefficients.

This study uses the GF-Gini coefficient 33 , 89 , which is based on the well-known Gini coefficient 90 , to measure the inequality of GHG footprints from 201 expenditure groups within countries, regions and globally. The GF-Gini coefficient ranges from 0 to 1, indicating the emission distribution across expenditure groups changes from perfect equality to perfect inequality. The GF-Gini coefficient of each food category is calculated as 33 :

where Gini j indicate the GF-Gini coefficient of food category j (including product i , i  = 1, 2, 3, …, n ). Expenditure groups and their population are reordered in ascending order of per capita GHG footprint of food category j and m refers to the reordered number of groups ( m  = 1, 2, 3, …, 201). \({D}_{m}^{j}\) and \({Y}_{m}^{j}\) represent the proportions of population and GHG footprints (of food category j ) for each expenditure group, respectively. \({T}_{m}^{j}\) is the cumulative proportion of GHG footprints of each expenditure group. The results of national, regional and global GF-Gini coefficients are shown in Supplementary Tables 9 and 10 .

Regression analysis

We use the regression approach to examine the relationship between the national GF-Gini coefficients and the per capita GDP 91 , 92 of 139 countries/areas. The GF-Gini coefficient of each country is regarded as the dependent variable ( y ) and the national per capita GDP acts as the independent variable ( x ). Initially, locally weighted regression is applied to illustrate the trend lines within the scatterplot. Subsequently, we test different regression methods for validation based on the general trend. Ultimately, we found that logarithmic regression is the most fitting for dietary emissions of most food categories, particularly in the case of animal-based products. Thus, the logarithmic regression is applied.

Scenario of the planetary health diet

Scenario setting and assumptions.

To estimate the emission changes resulting from the transition from the 2019 diet to the global planetary health diet, we build a hypothetical scenario by assuming that individuals belonging to 201 different expenditure groups in all countries will all reach the reference intake level of 13 types of food categories 12 . First, we assume that the proportion of food sources from local production and trade in each country is unchanged, that is, emission changes from dietary shifts would be calculated on the basis of emissions from local production and imports accounting for emissions along global food supply chains, similar to studies by refs. 25 , 26 . At the same time, emission changes induced by decreased food consumption in countries following the planetary health diet, such as carbon uptake from agriculture abandonment 59 or emission increase from non-food biomass production in saved agricultural land 77 , are not considered in this study. Second, we assume that agricultural and food-related production technology, trade patterns and emission intensities of food supply chain processes remain unchanged during the diet transition. Third, fluctuations in food prices induced by altered food demand or the affordability of the planetary health diet for different consumer groups are not considered in this study.

Diet gaps for different food categories

The diet gap (DG) reflects gaps between present dietary intake and the planetary health diet 12 , 25 , as follows:

where \({{\rm{DG}}}_{{\rm{per}}}^{j,r}\) is defined as the percentage ratio of the present per capita caloric intake of food category j in country r each year ( \({{\rm{DI}}}_{{\rm{per}}}^{\,j,r}\) ) to the annual reference level ( \({{\rm{DI}}}_{{\rm{EAT}}\_{\rm{per}}}^{i}\) ). \({{\rm{DI}}}_{{\rm{EAT}\_day\_per}}^{\,j}\) is the recommended per capita caloric intake of food category j each day 12 (Supplementary Table 17 ). We assume a uniform annual calorie reference level for each food category across all populations in all countries. We allow flexibility in local diets by keeping the composition of each food category unchanged, requiring only that the calorie content reaches the reference level. According to the definition, present food intake is considered insufficient compared with reference levels when DG is <100%, while it is deemed excessive and should be reduced when DG is >100%. Daily per capita caloric intake of food categories from 201 expenditure groups of countries or regions are shown in Supplementary Data 12 and 13 . We calculate the DG for food categories of 201 expenditure groups at national and regional levels (Supplementary Data 14 and 15 ).

According to equation ( 1 ), the total emissions per unit of calorie content of food category j in country r ( \({F}_{{\rm{energy}}}^{\;j,r}\) ) can be calculated as:

where E j,r refers to the national emissions due to consumption of food category j in country r . Thus, emission changes for adopting the planetary health diet are calculated as follows:

where \(\Delta {E}_{{\rm{intake}}}^{\;j,r}\) represents the national emission changes of food category j in country r , \({E}_{{\rm{intake}}}^{\;j,r}\) is the national emissions from intake of food category j in country r . Changes in dietary emissions of food categories from 201 groups are shown in Supplementary Data 9 . The number of people with increased/decreased emissions from 201 groups is shown in Supplementary Data 19 .

Uncertainty analysis

We assess the uncertainty range of dietary emissions from different food products using a Monte Carlo approach, which simulates the uncertainties caused by activity data, emission factors and parameters in each emission process 16 , 59 , 93 . More details can be found in Supplementary Methods 1 .

Limitations

This study has the following limitations regarding data analysis and scenario setting.

In terms of data analysis, this study is limited by the data availability. First, we use regional household food loss and waste factors of aggregated food categories without more detailed product division at the national level because of a lack of data. There might also be differences between calculated and actual food intake amounts that are unable to be removed, such as animal bones or fruit skins 25 . Second, we use the consumer household-expenditure dataset based on WBGCD for the year 2011, which provides the most precise and detailed differentiation of consumer groups and their consumption patterns within countries so far. We assume that the shares in food expenditure and population for each expenditure group are the same as in 2011. Third, we assume that the composition of different products aggregated in one category consumed by expenditure groups is the same as the national consumption composition and there is no difference in the price of food products purchased by people from different expenditure groups. In addition, data for some populous high- or upper-middle-income countries are missing from the household-expenditure dataset. However, the countries are the world’s major food consumers and emitters, their emission changes due to diet shifts are important for the global food system. We use the expenditure shares of similar countries in the household-expenditure dataset to allocate the distributions of food expenditure in these countries.

In terms of scenario setting, we focus on the impact induced by changes in consumer choices without changing the proportion of food supply sources (domestic production and imports). We do not consider altering the proportions of supply sources and associated emissions in this study. However, future studies may explore the impacts of the production side and supply chains for diet shifts. Moreover, as we focus on the present emission inequality and mitigation potentials within the food system, we assume that the income and expenditure levels of expenditure groups remain unchanged. However, a shift in food supply may affect household income and subsequently alter the household food budgets, especially for populations employed in, or countries reliant on, food-related sectors. Additionally, as a result of data and model limitations, this study does not consider price fluctuations induced by food demand and subsequent changes in household affordability or spillover effects (between food categories or to non-food sectors). Future studies may combine assessment models incorporating elasticities to project the long-term feasibilities and consequences of diet shifts.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

Data for LULUC, agricultural and beyond-farm emissions and data for physical food consumption are curated by the FAO and can be freely obtained from FAOSTAT 82 , available from ref. 16 . Data of food loss and waste rate are retrieved from FAOSTAT 82 and ref. 25 . The global household-expenditure data are obtained from the World Bank 42 and refs. 17 , 41 . Population data used in this study are obtained from World Population Prospects of the United Nations 86 . Data on per capita GDP in countries can be collected from the World Bank 91 and the International Monetary Fund 92 . Supplementary datasets are also available on Zenodo ( https://doi.org/10.5281/zenodo.11934909 ) 94 . Source data are provided with this paper.

Code availability

Data collection is performed in MATLAB and Microsoft Excel. Code developed for data processing in MATLAB and R in this study is available from Zenodo ( https://doi.org/10.5281/zenodo.11880402 ) 95 .

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Acknowledgements

This study was supported by the National Natural Science Foundation of China (grant nos 72243004, 32101315, 71904098). Y.S. and S.S. acknowledge support from the National Natural Science Foundation of China (grant no. 72243004). Yu Li acknowledges support from the National Natural Science Foundation of China (grant no. 32101315). P.H. acknowledges support from the National Natural Science Foundation of China under a Young Scholar Programme Grant (grant no. 71904098). Yanxian Li and Y.H. acknowledge the funding support by the China Scholarship Council PhD programme. We thank Y. Zhou for supporting visualization and J. Yan for assisting in writing and revising. For the purpose of open access, a CC BY public copyright license is applied to any author accepted manuscript arising from this submission.

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Yanxian Li, Y.S. and K.H. designed the research. Yanxian Li performed the analysis with support from P.H., Yu Li, Y.H. and S.S. on analytical approaches and visualization. Yanxian Li led the writing with efforts from P.H., Y.S., F.R. and K.H. Y.S. and K.H. supervised and coordinated the overall research. All co-authors reviewed and commented on the manuscript.

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Li, Y., He, P., Shan, Y. et al. Reducing climate change impacts from the global food system through diet shifts. Nat. Clim. Chang. (2024). https://doi.org/10.1038/s41558-024-02084-1

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1. Introduction

• The advantages of T-FRTs can be enhanced with a large speed ratio, zero spin, and a self-adaptive loading design. However, integrating these aspects into the overall design remains challenging, resulting in a few T-FRTs progressing in the prototype stage and hindering the research and development of T-FRTs;
• The development of theoretical analysis models for T-FRTs has been hindered by slow progress. Researchers usually simplify calculations by making various assumptions, such as setting the traction coefficient within T-FRTs to a constant value, which neglects the basic elastohydrodynamic lubrication (EHL) traction mechanism, or considering only isothermal EHL contact on the smooth surface, which has only a narrow range of applications. Research on the comprehensive impact of elastic deformation, loading state, surface morphology, thermal effect, and starved lubrication on the traction drive in actual working conditions is still in the early stages;
• The unique operating principles of traction drives introduce some of the most challenging kinematical and tribological problems for performance prediction [ 19 ]. The complex non-linear coupling relationship between macroscopic performance indicators and microscopic contact behavior challenges mathematical modeling and computation, and an effective solution method has not yet been developed.
• In terms of structural design, this paper proposes a new type of wedge-loading planetary traction drive (WPTD) that can achieve zero spin, large speed ratio, and self-adaptive loading;
• In terms of theoretical modeling, this paper introduces the mixed thermal EHL model into the performance analysis of traction drive for the first time. In addition, a more refined theoretical analysis model is established according to the structural characteristics of WPTD and the new loading principle. On this basis, the loading performance, transmission characteristics, and the influence of different parameters on the transmission characteristics of WPTD are analyzed;
• Regarding the solution method, regression analyses based on the results from an extensive set of simulations are performed according to the general operating conditions of the traction drive. On this basis, the fitting formulas for predicting traction contact behavior are derived, considering both hydrodynamic and surface asperity effects, and an efficient and accurate performance analysis method for all line-contact traction drives is presented. These methods significantly facilitate the design and research of subsequent traction drives.

2. Model of Traction Drive

2.1. structure and principle.

• The line contact and zero-spin design based on cylindrical rollers minimizes power loss and improves transmission efficiency and loading capacity;
• The problem of unidirectional rotation when loading with the wedge action is solved by a symmetrical arrangement of the wedge rollers. The coaxial layout of the ring and sun roller is realized, and the design range of speed ratio is expanded;
• The load acts directly on the wedge roller through the groove surface of the planet carrier, facilitating a more rapid wedging process and enhancing the dynamic response of the system through the superposition of the traction force and the contact force;
• The floating arrangement of the planet roller requires no additional support for the planet carrier, allowing greater flexibility in designing the planet carrier. Different groove surface designs are available to meet different loading characteristics and performance requirements.

2.2. Kinematic Analysis

2.2.1. deformation and displacement, 2.2.2. kinematic quantities, 2.3. quasi-static response, 2.3.1. loading state analysis.

• In state 1, the centers B l and B r of the wedge rollers without load remain in their initial positions, and the contact forces F c-l and F c-r are equal to the initial preload force F pre at the contact points B a and B b , respectively (see Figure 4 );
• In state 2, as the load gradually increases, the right wedge roller undergoes a slight displacement towards the converging end of the wedge area (in the direction away from the planet carrier groove), resulting in a gradual decrease in the contact force F c-r . The left wedge roller precisely adjusts its position under the joint constraint of the planet roller, ring, and planet carrier to rebalance the system. Consequently, the combined contact forces on both sides of the groove surface provide the output torque T out ;
• In state 3, the load continues to increase until the point B b loses contact, F c-r = 0. The planet roller and wedge roller move together, consistently co-ordinating elastic deformation caused by the load. At this stage, the contact force F c-l on the groove surface increases with the tangential load and provides the output torque T out to the WPTD.

2.3.2. Equilibrium Equations

2.4. efficiency, 3. contact model, 3.1. mixed thermal ehl, 3.1.1. ehl equations, 3.1.2. rough surface contact model, 3.1.3. thermal analysis, 3.2. traction coefficient, 3.3. numerical simulation and formula fitting.

• The traction contact area is usually under high contact stresses and high shear rates which could lead to poor convergence in the numerical calculation;
• The typically large viscosity–pressure coefficient of the traction oil allows it to form a high-viscosity oil film under heavy loads but also causes the lubricant viscosity to be extremely sensitive to pressure variations, which is detrimental to the stability of numerical iterations;
• The mutual coupling of factors such as surface roughness, thermal effect, starvation, and extreme working conditions is another source of instability and significantly increases the difficulty of numerical calculations.

4. Results and Discussions

4.1. performance analysis, 4.2. parameter effects, 5. experimental verification, 5.1. test rig assembly, 5.2. efficiency test, 5.3. vibration and noise tests, 6. conclusions.

• According to the general traction drive operating conditions, the mixed thermal EHL model was adopted for the first time to analyze traction performance, and regression analyses were performed based on the results of extensive simulations. Then, the fitting formulas were derived to predict the film thickness, asperity load ratio, and traction coefficient with provision for both hydrodynamic and surface asperity effects. The results demonstrate the high prediction accuracy of the fitting formulas;
• A theoretical analysis model considering the combined effects of elastic deformation, loading state, and mixed thermal EHL was established, based on the structural characteristics of WPTD and the new loading principle, and an efficient and accurate performance-prediction method was proposed for traction drives. The theoretical analysis model can simulate the traction capacity and transmission efficiency through numerical calculation;
• The loading effect was investigated in terms of the traction coefficient, creep coefficient, and efficiency. The results showed that the proposed loading mechanism could achieve self-adaptive loading while maintaining a stable traction coefficient and avoiding slippage, reflecting its good loading effect and improved torque capacity and efficiency;
• The reasonable parameter design can improve the performance of WPTD and reduce sliding. It was confirmed that the preload force F pre , characteristic angle γ , and contact length l rw exhibit the most significant effects on the global sliding coefficient. Therefore, these parameters deserve special attention during design to avoid transmission failure due to excessive slippage. Meanwhile, the creep coefficient variation is closely related to the loading state. These findings provide new ideas for the future design and optimization of traction drives;
• Through performance tests on the WPTD prototype, the simulation results are in reasonably good agreement with the experimental data, with the maximum efficiency error less than 9%, validating the theoretical model. The speed is found to have little effect on efficiency, while its increments can significantly increase the power density of WPTD. In addition, the test results confirm the smooth power-transfer characteristics of WPTD, with its vibration levels reduced by more than 40% compared to gear transmission. Benefiting from the zero-spin design and good loading effect, WPTD achieves a peak efficiency of 96%, and delivers superior performance in terms of high-speed potential, transmission efficiency, and vibration noise.

Author Contributions

Data availability statement, conflicts of interest, nomenclature.

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Jiang, Y.; Wang, G. Theoretical and Experimental Investigation of a Novel Wedge-Loading Planetary Traction Drive. Machines 2024 , 12 , 567. https://doi.org/10.3390/machines12080567

Jiang Y, Wang G. Theoretical and Experimental Investigation of a Novel Wedge-Loading Planetary Traction Drive. Machines . 2024; 12(8):567. https://doi.org/10.3390/machines12080567

Jiang, Yujiang, and Guangjian Wang. 2024. "Theoretical and Experimental Investigation of a Novel Wedge-Loading Planetary Traction Drive" Machines 12, no. 8: 567. https://doi.org/10.3390/machines12080567

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