paper airplane background research

For New Insights into Aerodynamics, Scientists Turn to Paper Airplanes

A series of experiments using paper airplanes reveals new aerodynamic effects--findings that enhance our understanding of flight stability.

Findings Unveil Mechanisms that Explain Flight Stability

A series of experiments using paper airplanes reveals new aerodynamic effects, a team of scientists has discovered. Its findings enhance our understanding of flight stability and could inspire new types of flying robots and small drones.

“The study started with simple curiosity about what makes a good paper airplane and specifically what is needed for smooth gliding,” explains Leif Ristroph, an associate professor at New York University’s Courant Institute of Mathematical Sciences and an author of the study , which appears in the Journal of Fluid Mechanics . “Answering such basic questions ended up being far from child’s play. We discovered that the aerodynamics of how paper airplanes keep level flight is really very different from the stability of conventional airplanes.”

“Birds glide and soar in an effortless way, and paper airplanes, when tuned properly, can also glide for long distances,” adds author Jane Wang, a professor of engineering and physics at Cornell University. “Surprisingly, there has been no good mathematical model for predicting this seemingly simple but subtle gliding flight.”

Since we can make complicated modern airplanes fly, the researchers say, one might think we know all there is to know about the simplest flying machines. 

“But paper airplanes, while simple to make, involve surprisingly complex aerodynamics,” notes Ristroph.

The paper’s authors began their study by considering what is needed for a plane to glide smoothly. Since paper airplanes have no engine and rely on gravity and proper design for their movement, they are good candidates for exploring factors behind flight stability.

To investigate this phenomenon, the researchers conducted lab experiments by launching paper airplanes with differing centers of mass through the air. The results, along with those from studying plates falling in a water tank, allowed the team to devise a new aerodynamic model and also a “flight simulator” capable of predicting the motions.

A video and image showing the experimental results may be downloaded from Google Drive .

To find the best design, the researchers placed different amounts of thin copper tape on the front part of the paper planes, giving them varied center of mass locations. Lead weights added to the plates in water served the same purpose.

“The key criterion of a successful glider is that the center of mass must be in the ‘just right’ place,” Ristroph explains. “Good paper airplanes achieve this with the front edge folded over several times or by an added paper clip, which requires a little trial and error.”

In the experiments, the researchers found that the flight motions depended sensitively on the center of mass location. Specifically, if the weight was at the center of the wing or only displaced somewhat from the middle, it underwent wild motions, such as fluttering or tumbling. If the weight was displaced too far toward one edge, then the flier quickly dove downwards and crashed. In between, however, there was a “sweet spot” for the center of mass that gave stable gliding.

The researchers coupled the experimental work with a mathematical model that served as the basis of a “flight simulator,” a computer program that successfully reproduced the different flight motions. It also helped explain why a paper airplane is stable in its glide. When the center of mass is in the “sweet spot,” the aerodynamic force on the plane’s wing pushes the wing back down if the plane moves upward and back up if it moves downward.

“The location of the aerodynamic force or center of pressure varies with the angle of flight in such a way to ensure stability,” explains Ristroph. 

He notes that this dynamic does not occur with conventional aircraft wings, which are airfoils—structures whose shapes work to generate lift. 

“The effect we found in paper airplanes does not happen for the traditional airfoils used as aircraft wings, whose center of pressure stays fixed in place across the angles that occur in flight,” Ristroph says. “The shifting of the center of pressure thus seems to be a unique property of thin, flat wings, and this ends up being the secret to the stable flight of paper airplanes.”

“This is why airplanes need a separate tail wing as a stabilizer while a paper plane can get away with just a main wing that gives both lift and stability,” he concludes. “We hope that our findings will be useful in small-scale flight applications, where you may want a minimal design that does not require a lot of extra flight surfaces, sensors, and controllers.”

The paper’s other authors were Huilin Li, a doctoral candidate at NYU Shanghai, and Tristan Goodwill, a doctoral candidate at the Courant Institute’s Department of Mathematics.

The work was supported by grants from the National Science Foundation (DMS-1847955, DMS-1646339).

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A Living History of The Humble Paper Airplane

For centuries, paper airplanes have unlocked the science of flight—now they could inspire drone technology.

Shinji Suzuki met Takuo Toda in 1999, atop Mt. Yonami in the southern city of Jinseki-Kogen, Japan. Toda, the chairman of the Japan Origami Airplane Association, was there to launch a large paper plane from a tower he had built on the mountaintop for just that purpose.

Toda’s lofty dream inspired Suzuki to take action, and in 2008, the pair announced a project to launch paper airplanes from the International Space Station (ISS). Critics suggested these planes would burn up on their descent back to Earth, Suzuki says. However, he predicted that with a protective coating and a controlled trajectory, they might actually be able to avoid burning up on reentry into Earth’s atmosphere. Another challenge? Figuring out where exactly the planes would land.

While Suzuki plotted the planes’ journey to the ISS, Toda would chart another path, racking up Guinness World Records for his paper airplane designs . For decades, he’s aimed to break the 30-second record for time aloft of a paper plane. He’s come close multiple times.

At a Japan Airlines hangar near Tokyo’s Haneda Airport in 2009, Toda sent a paper plane soaring for a whopping 26.1 seconds. And he holds the current time aloft record, which he set in 2010 with a rectangular design that lingered in the air for an astonishing 29.2 seconds. There are other records to be broken, too. As of April 2023, a trio of aerospace engineers currently hold the title for longest-distance throw of a paper airplane. Their dart-shaped plane traveled 289 feet and 9 inches, beating the previous record by almost 40 feet.

Our obsession with testing the boundaries of folded flight is relatively recent, but our desire to explore and explain the complex world of aerodynamics goes back much further.

Chinese engineers are thought to have invented what could be considered the earliest paper planes around 2,000 years ago. But these ancient gliders, usually crafted from bamboo and paper or linen, resembled kites more than the dart-shaped fliers that have earned numerous Guinness World Records in recent years.

Leonardo da Vinci would take a step closer to the modern paper airplane in the late 14th and early 15th centuries by building paper models of his aircraft designs to assess how they might sustain flight. But da Vinci’s knowledge of aerodynamics was fairly limited. He was more inspired by animal flight and, as a result, his design for craft like the ornithopter—a hang-glider-​size set of bat wings that used mechanical systems powered by human movement—never left the ground.

Paper airplanes helped early engineers and scientists learn about the mechanics of flight. The British engineer and aviator Sir George Cayley reportedly crafted the first folded paper plane to approach modern specifications in the early 1800s as part of his personal experimentation with aerodynamics. “He was one of the early people to link together the idea that the lift from the wings picking up the aircraft for stable flight must be greater than or equal to the weight of the aircraft,” says Jonathan Ridley , PhD, the head of engineering and a scholar of early aviation at Solent University in the U.K.

.css-2l0eat{font-family:UnitedSans,UnitedSans-roboto,UnitedSans-local,Helvetica,Arial,Sans-serif;font-size:1.625rem;line-height:1.2;margin:0rem;padding:0.9rem 1rem 1rem;}@media(max-width: 48rem){.css-2l0eat{font-size:1.75rem;line-height:1;}}@media(min-width: 48rem){.css-2l0eat{font-size:1.875rem;line-height:1;}}@media(min-width: 64rem){.css-2l0eat{font-size:2.25rem;line-height:1;}}.css-2l0eat b,.css-2l0eat strong{font-family:inherit;font-weight:bold;}.css-2l0eat em,.css-2l0eat i{font-style:italic;font-family:inherit;} “Over the last 20 years, there’s been an increasing interest in smaller-scale flight.”

More than a century later, before their famous 1903 flight in Kitty Hawk, North Carolina, the Wright Brothers built paper models of wings to better understand how their glider would sustain flight, explains Ridley. They then tested these models in a rudimentary, refrigerator-size wind tunnel—only the second to be built in the U.S.

Paper planes are still illuminating the hidden wonders of flight. Today, these lightweight aircraft serve as a source of inspiration not only for aviation enthusiasts but also for fluid dynamicists and engineers studying the complex effects of air on small aircraft like drones.

At Cornell University, in a lab run by physics professor Jane Wang , PhD, paper gliders plunge, swoop, and flutter through the air. What might look like child’s play to the untrained eye is actually part of a serious experiment conducted by Wang and her colleague Leif Ristroph , PhD, an associate professor of mathematics at New York University. Once the planes land, Wang and Ristroph analyze data from their flight and apply weights to change the balance of these gliders. They hope doing so will help them better understand how lightweight objects soar—something that could one day inform the future of miniature drones and other robotic craft.

The team’s most recent study, published in the Journal of Fluid Mechanics in February 2022 , explored the mechanics of gliding and identified new ways for paper gliders to achieve stable flight. Insights gleaned from this research have practical applications, but they also shed light on the aerodynamic principles that keep paper airplanes thrown by enthusiasts up in the air. All planes —powered and unpowered —are controlled by the four forces of flight: lift, weight, thrust, and drag. Lift is the aerodynamic force produced by the forward motion of an object through a fluid—in this case, air. Weight, or the force of gravity, is the opposing force and pulls the airplane toward Earth. Where the engines or propellers on a passenger aircraft generate thrust, the force of a paper plane pilot’s throw gives the aircraft the forward momentum. Drag, caused by the friction a plane experiences as it moves through the air, acts in opposition to thrust.

Traditional airplanes have airfoil-shaped wings with a round leading edge. Air that passes over the wing conforms to its shape. Air flowing above the wing moves faster than air below the wing, forming a low-pressure zone above the wing that generates lift.

“The magic of a paper airplane is that all of these little flight corrections are happening continuously throughout its flight.”

But the wing of a paper glider is flat, and air does not flow smoothly around it. Instead, that air forms a small, low-pressure vortex immediately above the leading edge of the wing. “This little vortex ends up changing a lot of the aerodynamic characteristics of the plane,” Ristroph says. “One thing it does is give the plane a natural stability, meaning that, in principle, it can and will glide.”

As the angle at which a glider’s wing cuts through the air—known as the angle of attack—changes, so too does the size and location of the vortex above the wing. This affects where the center of pressure, or the precise location where lift is focused, lies along the wing and how responsive it is to disturbances. If, for example, the plane encounters a gust that pushes its nose down, the center of pressure will slide forward, pushing the nose back up and into a stable position.

“The magic of a paper airplane is that all of these little flight corrections are happening continuously throughout its flight,” Ristroph says. “The plane is hanging under a vortex that is constantly swelling and shrinking in just the right ways to keep a smooth and level glide.”

The center of pressure for an airfoil, however, is locked in place and does not change with the angle of attack. This means it has trouble self-correcting if destabilized. Ristroph says the team tested this in some of their experiments by folding the sheets into an airfoil. These sheets quickly crashed after brief, erratic flights because they could not stabilize after being perturbed.

This phenomenon changes at different scales, Ristroph adds. For instance, if you were to construct a paper plane the size of a Boeing 747 , the vortex above the wing would be much larger and behave differently. “That vortex would not just stay on the plane and sit there, it would jump off, reform again, and do something a little turbulent and a little crazy,” he says. “You might not be able to rely on that vortex to give you stability because it may not always be there.” Conversely, if you created a paper airplane less than, say, a millimeter long, the aerodynamics would change—along with the behavior of that vortex.

The central focus of Ristroph and Wang’s work—and, as their research suggests, the true secret to a stable glide—is identifying and making adjustments based on a glider’s center of balance. The center of balance lies at the point where a plane would be perfectly balanced if suspended in midair. (You can locate the center of balance on a paper airplane by balancing it between the tips of your thumb and forefinger.) For an unfolded sheet of paper like the ones Wang and Ristroph tested, the center of balance is directly in the middle of the page.

The team experimented with tweaking the center of balance by placing strips of copper tape on their paper gliders and studying their flight. If the weights were placed too close to the center of the sheet, the gliders would tumble uncontrollably to the ground. If the weights were placed too far forward, they would immediately nose-dive.

“People can make very, very good paper airplanes now,” Wang says. “It’s a fine art. They build their intuition by making them.”

Through trial and error, they discovered that placing these weights halfway between the middle of the sheet and the leading edge created a stable glide, meaning that even if the glider was disturbed during its flight, it would still be able to right itself. Wang says this discovery was particularly surprising because previous work done on this topic had only ever identified “neutrally stable” modes of flight, which become unstable if perturbed and cannot self-correct.

Ristroph hopes the findings from their work will help engineers design new types of small aircraft that take advantage of passive modes of flight like, say, windsurfing craft that sail high above cities to monitor air quality. “Over the last 20 years, there’s been increasing interest in smaller-scale flight,” Ristroph says. “Small-scale flying robots [could] do things like ride on the wind rather than having some kind of engine or spinning rotors like a helicopter.”

The push to develop low-cost and low-impact alternatives to traditional aircraft has grown in recent decades. For example, in 2017 the San Francisco–based research and development firm Otherlab announced it had won a grant from the Defense Advanced Research Projects Agency (DARPA) to work on a lightweight cardboard glider that could someday deliver blood, vaccines, or other critical cargo to remote locations inaccessible via other modes of transportation.

The gliders, constructed from flat-packed pieces of cardboard, would be released from an airplane and, with the help of an onboard computer, navigate to a preprogrammed set of coordinates. Otherlab and DARPA shelved the project, but the central idea—tapping into the realm of unpowered flight to solve difficult problems—lives on.

Future small aircraft may also veer away from mimicking airplanes altogether, Wang says. In addition to studying paper gliders, much of her research focuses on forms of passive flight and gliding we already find in nature, such as insects and seeds that twirl off tree limbs. Using these techniques to create small craft could create even more possibilities in years to come.

Even after locating a glider’s center of mass, Wang cautions that this discovery won’t necessarily make solving future problems facing paper craft experts or engineers any easier. She and colleagues are attempting to solve these problems mathematically. Applying these mathematical revelations to a working glider? Well, that’s another challenge entirely.

Paper airplane enthusiasts, she suggests, might have better luck crafting gliders using intuition and experimentation instead. “People can make very, very good paper airplanes now,” Wang says. “It’s a fine art. They build their intuition by making them.”

Suzuki, Toda, and their collaborators spent 18 months testing multiple designs. They coated each plane in a protective glasslike substance that would raise the heat resistance but still allow for crisp, complex folds. With this design, Suzuki hoped that they might be able to test applications for other small-scale reentry vehicles.

The team then tested a prototype glider in the University of Tokyo’s hypersonic wind tunnel, subjecting the plane to speeds as high as Mach 7 and temperatures of almost 450°F—conditions similar to those a paper plane might face when reentering Earth’s atmosphere.

With these tests under their belt, the team reached out to Japan Aerospace Exploration Agency, who agreed to fund the project. One of the agency’s astronauts, Koichi Wakata, even expressed interest in launching them from the orbiting outpost himself. Ultimately, due to budget cuts, Suzuki and Toda’s paper planes never made it to space.

As researchers explore the field of aerodynamics, and new technology continues to model this type of flight, there’s still a chance we could see paper gliders pushing boundaries in years to come.

Weird Ways to Generate Lift

Here’s how strangely shaped objects—from Frisbees to honeybees—generate lift to soar through the air.

→ The lift produced by a Frisbee as it flies through the air is similar to the lift generated by an airplane’s wings. The perfect throw helps the disc push air downward without generating too much drag. In return, air pushes the Frisbee back up, generating additional lift. In 2005, researchers at MIT calculated the ideal throw angle for a Frisbee—12 degrees—to achieve maximum distance. (While the disc may travel greater heights with a larger angle, drag will shorten the distance traveled.)

Helicopter Seeds

→ The maple tree’shelicopter-like seeds, called samara, are specifically designed to fall and spin long distances away from the large, shady canopies of their parent trees. Their long, sail-like wings help balance the weight of the asymmetrical seeds. As the seed spins, the wider end of the wing moves faster than the air closer to the seed, generating lift to keep it airborne. Veins along the wing’s edge create turbulence, forming a small vortex above the wing that reduces pressure and generates even more lift.

→ Birds rely on their airfoil-shaped wings to generate enough lift force to equal and surpass their weight. But different types of birds rely on different modes of flight to generate lift force. (Hummingbirds hover thanks to a vortex that forms above their flapping wings.) Birds generate thrust by flapping their wings in a figure-eight motion. On the downstroke, air hits the bottom of the wing and is deflected past the bird, propelling it forward. Increasing the depth of each wingstroke increases airspeed and lifts the bird.

→ Bees have two sets of wings that they use to generate lift. As a bee rotates its wings back and forth, a small vortex forms above the wings’ leading edge, creating the lift force needed to keep the bee aloft. These soft and malleable wings move incredibly quickly, too, up to 230 beats per second. Compared to other insects of their size, this wingbeat is unusually fast. A fruit fly, for instance, is one eightieth the size of a honeybee and flaps its wings only 200 beats per second.

Sarah is a science and technology journalist based in Boston interested in how innovation and research intersect with our daily lives. She has written for a number of national publications and covers innovation news at Inverse .

Jennifer Leman is a science journalist and senior features editor at Popular Mechanics, Runner's World, and Bicycling. A graduate of the Science Communication Program at UC Santa Cruz, her work has appeared in The Atlantic, Scientific American, Science News and Nature. Her favorite stories illuminate Earth's many wonders and hazards.

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On the eleventh day of Christmas —

Experiments with paper airplanes reveal surprisingly complex aerodynamics, how these gliders keep level flight is different from the stability of airplanes..

Jennifer Ouellette - Jan 4, 2023 10:06 pm UTC

Drop a flat piece of paper and it will flutter and tumble through the air as it falls, but a well-fashioned paper airplane will glide smoothly. Although these structures look simple, their aerodynamics are surprisingly complex. Researchers at New York University’s Courant Institute of Mathematical Sciences conducted a series of experiments involving paper airplanes to explore this transition and develop a mathematical model to predict flight stability, according to a March paper published in the Journal of Fluid Mechanics.

“The study started with simple curiosity about what makes a good paper airplane and specifically what is needed for smooth gliding," said co-author Leif Ristroph . "Answering such basic questions ended up being far from child’s play. We discovered that the aerodynamics of how paper airplanes keep level flight is really very different from the stability of conventional airplanes.”

Nobody knows who invented the first paper airplane, but China began making paper on a large scale around 500 BCE, with the emergence of origami and paper-folding as a popular art form between 460 and 390 BCE. Paper airplanes have long been studied as a means of learning more about the aerodynamics of flight. For instance, Leonardo da Vinci famously built a model plane out of parchment while dreaming up flying machines and used paper models to test his design for an ornithopter. In the 19th century, British engineer and inventor Sir George Cayley —sometimes called the "father of aviation"—studied the gliding performance of paper airplanes to design a glider capable of carrying a human.

An amusing "scientist playing with paper planes" anecdote comes from physicist Theodore von Kármán . In his 1967 memoir The Wind and Beyond , he recalled a formal 1924 banquet in Delft, The Netherlands, where fellow physicist Ludwig Prandtl constructed a paper airplane out of a menu to demonstrate the mechanics of flight to von Kármán's sister, who was seated next to him. When he threw the paper plane, "It landed on the shirtfront of the French minister of education, much to the embarrassment of my sister and others at the banquet," von Kármán wrote.

While scientists have clearly made great strides in aerodynamics—particularly about aircraft—Ristroph et al . noted that there was not a good mathematical model for predicting the simpler, subtler gliding flight of paper airplanes. It was already well-known that displacing the center of mass results in various flight trajectories, some more stable than others. “The key criterion of a successful glider is that the center of mass must be in the ‘just right’ place,” said Ristroph . “Good paper airplanes achieve this with the front edge folded over several times or by an added paper clip, which requires a little trial and error.”

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Cool Science: Paper airplanes, insect wings and the future of tiny drones

Conduct your own aerodynamics experiment at home

For nearly 200 years, in the great pursuit of knowledge about aerodynamics, researchers have been fascinated by paper airplanes. Even the simplest design – a plain sheet of paper with no wings or fins, nothing resembling a modern airplane – can provide insights into complex aerodynamic principles.

A rectangular sheet of paper will tumble to the ground like confetti, but adding just the right amount of weight, in just the right location, affects how the paper flies.

Leif Ristroph, an associate professor at New York University and self-described paper airplane fanatic, said the idea to study the aerodynamics of a falling sheet of paper began with curiosity about the movement.

“The magic that makes a paper airplane glide and not flutter is how you weight it. You don’t need all the other aspects,” Ristroph said. “It feels like someone must have observed this before because it seems so basic but I couldn’t find it. It’s worth understanding, then.”

And while designing a passenger airplane that resembles a sheet of paper is a horrible idea, he said, the research could contribute to new ways of thinking about the design of simple aircraft such as tiny drones.

Observations in air and water

Researchers added strips of metallic tape to one of the long edges of a rectangular sheet to create varying degrees of front weight. When dropped, each sheet moves in a unique way. “There is kind of a magic spot for the balance point where you can get the best glide. If the balance point is too close to the middle, you will see fluttering and tumbling motions. If the balance point is too far forward, it will nose-dive and crash. The best point is about halfway between the middle of the sheet and the front edge. Then you will see a nice glider,” Ristroph said.

Part of Ristroph’s work for his doctorate in physics was studying insect flight and how flapping wings affect flight control and stability. The paper airplane study was not part of his planned research under a U.S. National Science Foundation grant , but the relationship between insect wings and falling paper stood out, and the results contribute to a more general understanding of animal flight and swimming dynamics.

Plus, sheets of paper are easier to maintain in the laboratory than insects, he said.

Ristroph also made observations using a water tank and thin plates of plastic, whose “flight” through water (video above) are governed by the same physics that determines the motions of paper falling through the air. In both instances, the rate and control of the fall was affected by the location of the weight and the impact it had on the center of mass. There is a “sweet spot” for the center of mass that produces a stable glide path.

Based on the results, Ristroph and his team created a mathematical model that serves as the basis of a “flight simulator,” a computer program that reproduces the different flight motions. No such model had previously existed for predicting gliding flight.

“The simulator can produce the full range of motions accurately. It describes the forces acting on the plate and finds out how the flyers should move based on the forces used in the equation. I think for the scientific community, that will translate well into something useful for everyone involved,” he said.

The findings could also contribute to new design methods for drones. “There are a lot of people working on making very small-scale flying robots. There are even some designs that are passive flyers – not powered – that are modeled on flying plant seeds that twirl like helicopters when they fall.”

These passive drones can be used for projects like air quality monitoring.

“There is an initiative to make small flyers, and at very small scales, simpler is better,” Ristroph said. “When you think about paper airplanes, it doesn’t get much simpler than that. I’m not an engineer who can make a useful flying robot, but I hope our findings will inspire others who can.”

“Studying toys is serious fun. Whether it’s a paper airplane or a spinning top, there is something scientifically valuable in finding out how they work.”

Experiments with aerodynamics at home

Ristroph’s research includes a component dedicated to training STEM students in aspects of modern applied mathematics, emphasizing the connections among modeling, simulation and experimental observation.

And his experiments are simple enough that they can be conducted anywhere. “I like to think of the whole world as a laboratory. There are simple experiments in front of you. The things you see around you are fascinating if you look at them in the right way,” he said.

Want to replicate the experiment at home? The basic materials are a notepad or copy paper about 6 inches long and 2 inches wide that can be folded and tape or paper clips that can be used to add weight.

“Studying toys is serious fun,” Ristroph said. “Whether it’s a paper airplane or a spinning top, there is something scientifically valuable in finding out how they work.”  

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For new insights into aerodynamics, scientists turn to paper airplanes

Findings unveil mechanisms that explain flight stability.

A series of experiments using paper airplanes reveals new aerodynamic effects, a team of scientists has discovered. Its findings enhance our understanding of flight stability and could inspire new types of flying robots and small drones.

"The study started with simple curiosity about what makes a good paper airplane and specifically what is needed for smooth gliding," explains Leif Ristroph, an associate professor at New York University's Courant Institute of Mathematical Sciences and an author of the study, which appears in the Journal of Fluid Mechanics . "Answering such basic questions ended up being far from child's play. We discovered that the aerodynamics of how paper airplanes keep level flight is really very different from the stability of conventional airplanes."

"Birds glide and soar in an effortless way, and paper airplanes, when tuned properly, can also glide for long distances," adds author Jane Wang, a professor of engineering and physics at Cornell University. "Surprisingly, there has been no good mathematical model for predicting this seemingly simple but subtle gliding flight."

Since we can make complicated modern airplanes fly, the researchers say, one might think we know all there is to know about the simplest flying machines.

"But paper airplanes, while simple to make, involve surprisingly complex aerodynamics," notes Ristroph.

The paper's authors began their study by considering what is needed for a plane to glide smoothly. Since paper airplanes have no engine and rely on gravity and proper design for their movement, they are good candidates for exploring factors behind flight stability.

To investigate this phenomenon, the researchers conducted lab experiments by launching paper airplanes with differing centers of mass through the air. The results, along with those from studying plates falling in a water tank, allowed the team to devise a new aerodynamic model and also a "flight simulator" capable of predicting the motions.

To find the best design, the researchers placed different amounts of thin copper tape on the front part of the paper planes, giving them varied center of mass locations. Lead weights added to the plates in water served the same purpose.

"The key criterion of a successful glider is that the center of mass must be in the 'just right' place," Ristroph explains. "Good paper airplanes achieve this with the front edge folded over several times or by an added paper clip, which requires a little trial and error."

In the experiments, the researchers found that the flight motions depended sensitively on the center of mass location. Specifically, if the weight was at the center of the wing or only displaced somewhat from the middle, it underwent wild motions, such as fluttering or tumbling. If the weight was displaced too far toward one edge, then the flier quickly dove downwards and crashed. In between, however, there was a "sweet spot" for the center of mass that gave stable gliding.

The researchers coupled the experimental work with a mathematical model that served as the basis of a "flight simulator," a computer program that successfully reproduced the different flight motions. It also helped explain why a paper airplane is stable in its glide. When the center of mass is in the "sweet spot," the aerodynamic force on the plane's wing pushes the wing back down if the plane moves upward and back up if it moves downward.

"The location of the aerodynamic force or center of pressure varies with the angle of flight in such a way to ensure stability," explains Ristroph.

He notes that this dynamic does not occur with conventional aircraft wings, which are airfoils -- structures whose shapes work to generate lift.

"The effect we found in paper airplanes does not happen for the traditional airfoils used as aircraft wings, whose center of pressure stays fixed in place across the angles that occur in flight," Ristroph says. "The shifting of the center of pressure thus seems to be a unique property of thin, flat wings, and this ends up being the secret to the stable flight of paper airplanes."

"This is why airplanes need a separate tail wing as a stabilizer while a paper plane can get away with just a main wing that gives both lift and stability," he concludes. "We hope that our findings will be useful in small-scale flight applications, where you may want a minimal design that does not require a lot of extra flight surfaces, sensors, and controllers."

The paper's other authors were Huilin Li, a doctoral candidate at NYU Shanghai, and Tristan Goodwill, a doctoral candidate at the Courant Institute's Department of Mathematics.

The work was supported by grants from the National Science Foundation (DMS-1847955, DMS-1646339).

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Story Source:

Materials provided by New York University . Note: Content may be edited for style and length.

Journal Reference :

• Huilin Li, Tristan Goodwill, Z. Jane Wang, Leif Ristroph. Centre of mass location, flight modes, stability and dynamic modelling of gliders . Journal of Fluid Mechanics , 2022; 937 DOI: 10.1017/jfm.2022.89

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From paper planes to 3D-printed aircraft

By Robert C. Jones Jr. [email protected] 04-11-2024

It was 8-year-old Joshua Prabahar’s Kitty Hawk moment, accomplished not on an isolated strip of beach in North Carolina but in a Kingston, Jamaica, home, where toilet paper tubes, cardboard, and masking tape served as the parts for his Wright brothers-inspired toy airplanes. 

And like Wilbur and Orville, who made a multitude of adjustments to their engine-powered 1903 Wright Flyer, Prabahar tinkered endlessly with his creations, bending and folding the wings so that the aircraft could gain altitude faster.

Prabahar may not have realized it, but he was on the right track: The key to accomplishing greater lift is in the wings’ angle of attack. 

Today, as an aeronautical engineering major at the University of Miami, he is still experimenting with techniques to build a better airplane—only now, the materials and methods he employs are much more advanced: 3D-printed plastic parts and an airflow simulator. 

Prabahar has designed and built a prototype airfoil that uses what he describes as “suction and injection” along the wing’s surface to create lift. “We’ve done baseline computer simulations to prove that our concept is feasible, and it’s shown promising results in that regard,” he said. “Now, we’ve moved to wind tunnel testing to demonstrate that our design can achieve enhanced aerodynamic performance.” 

Designed through the process of computational fluid dynamics, the airfoil would serve as the wing of an electric short takeoff or landing (STOL) aircraft, with the real-world benefits from such technology resulting in flying machines that would deliver medicine and other essential goods to hard-to-reach areas, make aerial damage assessments in the aftermath of hurricanes and other natural disasters, and transport patients to medical facilities. 

Prabahar’s airfoil had its origins in his College of Engineering senior design project. With funding for that task capped at $250, he and his team knew they couldn’t afford to design, create, and test a new airfoil and considered building a remote-control airplane instead. 

“But it was our dream to aggressively pursue and test our design theories for a new type of wing,” he said, “and we were determined to see it through.” 

The college’s new Miami Engineering Autonomous Mobility Initiative , a consortium dedicated to developing electric vertical takeoff and landing (eVTOL) aircraft, came to the rescue, allocating additional funds that allowed Prabahar and his team to take their airfoil design from concept to creation. 

But even before wind tunnel testing could begin, Prabahar and his team had to overcome a final obstacle: adapting the airflow simulator to test a 3D-printed plastic component, as it had originally been constructed to assess the performance of metal and aluminum parts. 

“We had to take numerous measurements and check that all the alignments were just right,” Prabahar recalled. “Without a doubt, it was the biggest design issue we faced.” 

STOL and eVTOL aircraft are the future, he asserts.

“Increasing the range of such vehicles through better electric batteries is the next challenge,” he said. “But it’s sustainable, clean, and quiet technology—way above the toy airplanes I used to build as a little boy.”

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General Aviation News

Because flying is cool

For latest research on aerodynamics, scientists turn to paper airplanes

By General Aviation News Staff · October 3, 2022 ·

A series of experiments using paper airplanes reveals new aerodynamic effects, according to researchers at New York University.

They say their findings “enhance our understanding of flight stability” and could inspire new types of flying vehicles.

“The study started with simple curiosity about what makes a good paper airplane and specifically what is needed for smooth gliding,” explains Leif Ristroph, an associate professor at New York University’s Courant Institute of Mathematical Sciences and an author of the study, which appears in the Journal of Fluid Mechanics.

“Answering such basic questions ended up being far from child’s play. We discovered that the aerodynamics of how paper airplanes keep level flight is really very different from the stability of conventional airplanes.”

“Birds glide and soar in an effortless way, and paper airplanes, when tuned properly, can also glide for long distances,” adds author Jane Wang, a professor of engineering and physics at Cornell University. “Surprisingly, there has been no good mathematical model for predicting this seemingly simple but subtle gliding flight.”

Since we can make complicated modern airplanes fly, the researchers say, one might think we know all there is to know about the simplest flying machines.

“But paper airplanes, while simple to make, involve surprisingly complex aerodynamics,” notes Ristroph.

The researchers began their study by considering what is needed for a plane to glide smoothly. Since paper airplanes have no engine and rely on gravity and proper design for their movement, they are good candidates for exploring factors behind flight stability, they said.

To investigate this phenomenon, the researchers conducted lab experiments by launching paper airplanes with differing centers of mass through the air. The results, along with those from studying plates falling in a water tank, allowed the team to devise a new aerodynamic model and also a “flight simulator” capable of predicting the motions.

To find the best design, the researchers placed different amounts of thin copper tape on the front part of the paper planes, giving them varied center of mass locations. Lead weights added to the plates in water served the same purpose.

“The key criterion of a successful glider is that the center of mass must be in the ‘just right’ place,” Ristroph says. “Good paper airplanes achieve this with the front edge folded over several times or by an added paper clip, which requires a little trial and error.”

The researchers discovered that flight motions depended on finding that “just right” place.

For example, if the weight was at the center of the wing or only displaced somewhat from the middle, it underwent wild motions, such as fluttering or tumbling. If the weight was displaced too far toward one edge, then the flier quickly dove downwards and crashed. In between, however, there was a “sweet spot” for the center of mass that gave stable gliding.

The researchers coupled the experimental work with a mathematical model that served as the basis of a “flight simulator,” a computer program that successfully reproduced the different flight motions. It also helped explain why a paper airplane is stable in its glide. When the center of mass is in the “sweet spot,” the aerodynamic force on the plane’s wing pushes the wing back down if the plane moves upward and back up if it moves downward, the researchers explain.

“The location of the aerodynamic force or center of pressure varies with the angle of flight in such a way to ensure stability,” Ristroph says.

He notes that this dynamic does not occur with conventional aircraft wings, which are airfoils, structures whose shapes work to generate lift.

“The effect we found in paper airplanes does not happen for the traditional airfoils used as aircraft wings, whose center of pressure stays fixed in place across the angles that occur in flight,” Ristroph says. “The shifting of the center of pressure seems to be a unique property of thin, flat wings, and this ends up being the secret to the stable flight of paper airplanes.”

“This is why airplanes need a separate tail wing as a stabilizer while a paper plane can get away with just a main wing that gives both lift and stability,” he concludes. “We hope that our findings will be useful in small-scale flight applications, where you may want a minimal design that does not require a lot of extra flight surfaces, sensors, and controllers.”

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October 4, 2022 at 7:50 am

Interesting subject. When I was young, and could not afford any kind of flying machine, I found relief from my flying passion by building paper models. Some of them were actually aerodynamically impressive, with very shallow glides and very stable. Since I lived in a mountainous area I could let them go and at times get lucky were some would catch some lift and fly for a while. During those moments I would dream of one day flying a real aircraft. Eventually that lead to flying RC models, getting my private license and eventually a fun life engaged in different forms of aviation activities.

Thanks for reminding me of this fun aspect of my aviation career.

an analogy for every complexity

The science behind paper airplanes.

• Explanations

14 Comments

Have you ever thrown a paper airplane? How did it fly? Paper airplanes vary widely in design, and those differences lead to meaningful differences in the way that they fly. Some airplanes fly quickly through the air, while others glide slowly. Sometimes, a paper airplane will tip its nose upward, leading to a stall. Why do these things happen?

The mechanics of paper airplanes are interesting because they are similar to those of most things that move quickly through the air. They have four basic forces acting on them:

via auntannie.com

The thrust comes from you when you throw the plane. Thus, the plane has no thrust in flight. The reason it doesn’t continue to slow down during flight is because it is also falling, “converting” its potential energy into thrust as it falls.

The lift comes from the difference in air pressure above and below the wing. This is caused by the shape of the wing, known as an airfoil. Lift is proportional to the size of the wing and the square of the speed of the plane.

So how do these forces affect how a plane flies? Take for example the standard paper “dart” plane:

via Wikigami

If you have flown this plane before, you know that it flies quickly, but drops to the ground relatively quickly. This can be explained as the plane having little drag, but little lift as well. More specifically, the lift and gravity forces are not perfectly aligned like they are in the first image. Rather, the center of gravity is slightly ahead of the center of lift in this plane, causing it to tip downwards and fly towards the ground.

Another popular plane is this “glider”:

via Instructables

This plane has a slow and steady flight if thrown gently or even dropped from a high place. Even without thrust from the person who throws it, it is able to maintain steady flight, if at the cost of a slight drop at the beginning. This indicates that its gravity and lift forces are aligned correctly. While it does not fly as fast, it has a larger wing surface area, which allows it to get enough lift at lower speeds.

With these ideas in mind, it’s easy to pick the correct airplane for any task. (That’s a common issue people have… right?) I once participated in a paper airplane competition based on longest total flight time. Knowing this, I instantly started folding large-winged gliders. When my plane nosedived too often, I folded it to place less paper in the front half, which moved the center of mass further back to compensate for the nosediving, which led to a steady-flying glider.

I went on to win $20 in that small competition. While, in real life, paper airplanes competitions are few and far between, this knowledge is not useful exclusively in these rare situations. Just to understand the basic mechanics at work in the planes, drones, and squirrel suits of the world is enlightening.

I have made lots of paper airplanes and lots of them failed this is a very detailed way to look at something so simple.

I agre I lyke paper airplanes because they are cool and soemtime I get them to fly. My bike is red and has stuff on the grip bars. What is yoru bike like.

are you in special ed classes?

Why was the necessary? If it was because of a few spelling errors by the previous poster than you don’t have much to talk about as your post had no capital letter at the beginning of your sentence.

Meow fuck out the way.

Come on people show some respect

Thank you for this post Gemlik Zeytin Fidanı

say my name

Heisenberg!

Am using this as research for my Engineering project. Very helpful, thanks!

allauh akbar 💥💥💥

Where’s my cupcake?

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Paper Airplanes Plans

A glider is a special kind of aircraft that has no engine. In flight, a glider has three forces acting on it as compared to the four forces that act on a powered aircraft. Both types of aircraft are subjected to the forces of lift, drag, and weight. The powered aircraft has an engine that generates thrust, while the glider has no thrust.

Types of Glider Aircraft

There are many different types of glider aircraft.  Paper airplanes  are the simplest aircraft to build and fly, and students can learn the basics of aircraft motion by flying paper airplanes. Building and flying balsa wood or Styrofoam gliders is an inexpensive way for students to have fun while learning the basics of aerodynamics.  Hang-gliders  are piloted aircraft that are launched by leaping off the side of a hill or by being towed aloft.  Piloted gliders  are launched by ground based catapults, or are towed aloft by a powered aircraft then cut free to glide for hours over many miles. The Wright Brothers perfected the design of the first airplane and gained piloting experience through a series of glider flights from 1900 to 1903. The Space Shuttle flies as a glider during reentry and landing; the rocket engines are used only during liftoff.

On the graphic at the top of this page, there are two paper airplane designs shown: Paper Airplane #1 (PA-1), in blue at the lower right, and Paper Airplane #2 (PA-2), in red at the upper left. Both of these aircraft are constructed by folding an 8 1/2 by 11 sheet of paper. The plans for these aircraft are provided below.

To obtain your own copy of PA-1 click here  and save the Power Point file. Open Power Point and follow the directions written on the aircraft to obtain a two-sided copy of the plans from your printer. The plans will look like this:

Constructing an Aircraft

To construct the aircraft, fold on the solid lines in the prescribed numerical order (1,2,3..) always folding to the inside. Cover the number with the fold. The dashed lines on the plans indicate places to cut with a scissors. The PA-1 is designed to be highly maneuverable and employs both ailerons and a rudder. If both ailerons are turned upward, the aircraft will loop. If one is turned up and the other down, and the rudder is fixed straight, the aircraft will roll. If the rudder is turned, the aircraft will perform a banked turn.

To obtain your own copy of PA-2 click here  and save the Power Point file. Open Power Point and follow the directions written on the aircraft to obtain a two-sided copy of the plans from your printer. The plans will look like this:

To construct the aircraft, fold on the solid lines in the prescribed numerical order (1,2,3..) always folding to the inside. Cover the number with the fold. The PA-2 is designed to fly fast and far.

Students should build and fly both aircraft to learn how differences in design affect the flight performance of an aircraft. After experimenting with paper airplanes, the student is ready to move up to more challenging aircraft such as wooden or Styrofoam gliders.

Thanks for contacting us! We will get in touch with you shortly.

February 28, 2013

Soaring Science: Test Paper Planes with Different Drag

An aerodynamic activity from Science Buddies

By Science Buddies

Key concepts Aerodynamics Planes Forces Drag Physics

Introduction Have you ever wondered what makes a paper plane fly? Some paper planes clearly fly better than others. But why is this? One factor is the kind of design used to build the plane. In this activity you'll get to build a paper plane and change its basic design to see how this affects its flight. There's a lot of cool science in this activity, such as how forces act on a plane so it can fly. So get ready to start folding!

Background The forces that allow a paper plane to fly are the same ones that apply to real airplanes. A force is something that pushes or pulls on something else. When you throw a paper plane in the air, you are giving the plane a push to move forward. That push is a type of force called thrust. While the plane is flying forward, air moving over and under the wings is providing an upward lift force on the plane. At the same time, air pushing back against the plane is slowing it down, creating a drag force. The weight of the paper plane also affects its flight, as gravity pulls it down toward Earth. All of these forces (thrust, lift, drag and gravity) affect how well a given paper plane's voyage goes. In this activity you will increase how much drag a paper plane experiences and see if this changes how far the plane flies.

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Materials • Sheet of paper • Ruler • Scissors • Large open area in which to fly a paper plane, such as a long hallway, school gym or basketball court. If you're flying your paper plane outside, such as in a field, try to do it when there isn't any wind. • Something to make at least a one-foot-long line, such as a long string, another ruler, masking tape, rocks or sticks. • Paper clips (optional)

Preparation • Make a standard, "dart" design paper airplane (for instructions, go to the Amazing Paper Airplanes Web page ). • Fold your paper into the basic dart paper plane. Fold carefully and make your folds as sharp as possible, such as by running a thumbnail or a ruler along each fold to crease it. Do not bend up the tailing edge of the wings (step 6 of the online folding instructions). • Go to a large open area and, using string, a ruler, masking tape, rocks or sticks, make a line in front of you that's at least one foot long, going from left to right. This will be the starting line from which you'll fly the paper plane.

Procedure • Place your toe on the line you prepared and throw the paper plane. Did it fly very far? • Throw the plane at least four more times. Each time before you throw the plane, make sure it is still in good condition (that the folds and points are still sharp). When you toss it, place your toe on the line and try to launch the plane with a similar amount of force, including gripping it at the same spot. Did it go about the same distance each time? • Once you have a good idea of about how far your plane typically flies, change the plane’s shape to increase how much drag it experiences. To do this, cut slits that are about one inch long right where either wing meets the middle ridge. Fold up the cut section on both wings so that each now has a one-inch-wide section at the end of the wing that is folded up, at about a 90-degree angle from the rest of the wing. • Throw your modified paper plane at least five more times, just as you did before. How far does the paper plane fly now compared with before? Why do you think this is, and what does it have to do with drag? • Extra: Make paper planes that are different sizes and compare how well they fly. Do bigger planes fly farther? • Extra: Try making paper planes out of different types of paper, such as printer paper, construction paper and newspaper. Use the same design for each. Does one type of paper seem to work best for making paper planes? Does one type work the worst? • Extra: Some people like to add paper clips to their paper planes to make them fly better. Try adding a paper clip (or multiple paper clips) to different parts of your paper plane (such as the front, back, middle or wings) and then flying it. How does this affect the plane's flight? Does adding paper clips somewhere make its flight better or much worse? Observations and results Did the original plane fly the farthest? Did the plane with increased drag fly a much shorter distance?

As a paper plane moves through the air, the air pushes against the plane, slowing it down. This force is called drag. To think about drag, imagine you are in a moving car and you put your hand out the window. The force of the air pushing your hand back as you move forward is drag, also sometimes referred to as air resistance. In this activity you increased how much drag acted on the paper plane by making a one-inch-high vertical strip on both wings. For example, this is what happens when you're in a moving car with your hand out the window and you change its position from horizontal to vertical. When your hand is held out vertically, it catches a greater amount of air and experiences a greater drag than when it is horizontal. You could probably feel this, as your hand would be more forcefully pushed back as the car moves forward. This is what happened to the modified plane—it experienced a greater amount of drag, which pushed it back more than the original plane. This experiment has clearly demonstrated that altering how just one force acts on a paper plane can dramatically change how well it flies.

Cleanup Recycle the paper plane when you are done with it.

More to explore Dynamics of Flight: Forces of Flight , from NASA What Makes Paper Airplanes Fly? , from Scholastic Forces of Flight—Drag , from The Franklin Institute How Far Will It Fly? Build and Test Various Paper Planes , from Science Buddies

This activity brought to you in partnership with  Science Buddies

Paper Airplane Study Finds New Aerodynamic Effects

A team of researchers analyzing the flight characteristics of paper airplanes have found a whole new set of unexpected aerodynamic effects. Initially designed to understand the basic mechanics behind what makes a good paper airplane fly, the novel aerodynamic effects found by researchers may lead to the development of a whole new class of flying robots or small drones that function with very few moving parts.

WHAT MAKES A GOOD PAPER AIRPLANE FLY?

What is it that makes a good paper airplane glide across a lengthy high school cafeteria but dooms other similar-appearing craft to dive straight into the floor? It’s a question that has flummoxed more than one would-be paper airline launcher and one that motivated a team of researchers from New York University’s (NYU) Courant Institute of Mathematical Sciences and Cornell University to search for an answer.

“The study started with simple curiosity about what makes a good paper airplane and specifically what is needed for smooth gliding,” explains NYU associate professor and study co-author Leif Ristroph in a press release announcing the research. “Answering such basic questions ended up being far from child’s play. We discovered that the aerodynamics of how paper airplanes keep level flight is really very different from the stability of conventional airplanes.”

CENTER OF MASS IS THE KEY

To begin their study, the research team evaluated the mathematics behind paper airplane flight. For instance, a paper airplane has no motor but instead relies on gravity for its gliding movement, much like a gliding bird.

“Birds glide and soar in an effortless way, and paper airplanes, when tuned properly, can also glide for long distances,” said study co-author Jane Wang, a professor of engineering and physics at Cornell University. “Surprisingly, there has been no good mathematical model for predicting this seemingly simple but subtle gliding flight.”

It soon became apparent that absent previous mathematical modeling, uncovering the secrets of paper airplane flight would require some real-world testing. First, the team used a basic triangle design for their paper airplane, which is considered the simplest and most efficient form. Next, the researchers placed thin pieces of copper tape on the front part of the paper airplanes, much like the paper clip used in many homemade models. The copper tape segments were placed in different locations on each plane, creating a differing center of mass.

“The key criterion of a successful glider is that the center of mass must be in the ‘just right’ place,” Ristroph explains. “Good paper airplanes achieve this with the front edge folded over several times or by an added paper clip, which requires a little trial and error.”

After numerous paper airplane launches in a laboratory setting, the team found the best weight location to maximize flight distances.

“If the weight was at the center of the wing or only displaced somewhat from the middle, it underwent wild motions, such as fluttering or tumbling,” the press release explains. “If the weight was displaced too far toward one edge, then the flier quickly dove downwards and crashed. In between, however, there was a “sweet spot” for the center of mass that gave stable gliding.”

The team mirrored these test flights by sinking a set of plates in a water tank and observing their “gliding” motion on the way to the bottom. Lead weights were placed at different locations on the plates to change their center of mass, much like the copper tape on the paper airplane.

The researchers combined all of this accumulated data to create customized “flight simulator” software that allowed them to analyze and simulate paper airplane flight. And to their surprise, they not only found out how to make a good airplane, but they also learned that the aerodynamic principles of a gliding paper airplane (or a sinking plate) were completely different from that of a conventional aircraft.

Glowing Plants that Turn Energy into Light Are About to Be Commercially Available for the First Time

“The effect we found in paper airplanes does not happen for the traditional airfoils used as aircraft wings, whose center of pressure stays fixed in place across the angles that occur in flight,” said Ristroph. “The shifting of the center of pressure thus seems to be a unique property of thin, flat wings, and this ends up being the secret to the stable flight of paper airplanes.”

“This is why airplanes need a separate tail wing as a stabilizer,” he added, “while a paper plane can get away with just a main wing that gives both lift and stability.”

PAPER AIRPLANE AERODYNAMICS MAY LEAD TO INNOVATIVE AIRCRAFT

Published in the Journal of Fluid Mechanics , the study offers a unique insight into a child’s toy that nearly everyone has built. More importantly, it also found a whole new set of aerodynamic principles that the researchers believe could lead to the development of new types of hyper-efficient, specialized aircraft.

“We hope that our findings will be useful in small-scale flight applications,” concluded Ristroph, “where you may want a minimal design that does not require a lot of extra flight surfaces, sensors, and controllers.”

Unfortunately, the study did not indicate where you should write the “Do you like me? Mark Yes or No” message. SMH.

Follow and connect with author Christopher Plain on Twitter:   @plain_fiction

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For new insights into aerodynamics, scientists turn to paper airplanes

by New York University

A series of experiments using paper airplanes reveals new aerodynamic effects, a team of scientists has discovered. Its findings enhance our understanding of flight stability and could inspire new types of flying robots and small drones.

"The study started with simple curiosity about what makes a good paper airplane and specifically what is needed for smooth gliding," explains Leif Ristroph, an associate professor at New York University's Courant Institute of Mathematical Sciences and an author of the study, which appears in the Journal of Fluid Mechanics . "Answering such basic questions ended up being far from child's play. We discovered that the aerodynamics of how paper airplanes keep level flight is really very different from the stability of conventional airplanes."

"Birds glide and soar in an effortless way, and paper airplanes, when tuned properly, can also glide for long distances," adds author Jane Wang, a professor of engineering and physics at Cornell University. "Surprisingly, there has been no good mathematical model for predicting this seemingly simple but subtle gliding flight."

Since we can make complicated modern airplanes fly, the researchers say, one might think we know all there is to know about the simplest flying machines.

"But paper airplanes, while simple to make, involve surprisingly complex aerodynamics," notes Ristroph.

The paper's authors began their study by considering what is needed for a plane to glide smoothly. Since paper airplanes have no engine and rely on gravity and proper design for their movement, they are good candidates for exploring factors behind flight stability.

To investigate this phenomenon, the researchers conducted lab experiments by launching paper airplanes with differing centers of mass through the air. The results, along with those from studying plates falling in a water tank, allowed the team to devise a new aerodynamic model and also a "flight simulator" capable of predicting the motions.

To find the best design, the researchers placed different amounts of thin copper tape on the front part of the paper planes, giving them varied center of mass locations. Lead weights added to the plates in water served the same purpose.

"The key criterion of a successful glider is that the center of mass must be in the 'just right' place," Ristroph explains. "Good paper airplanes achieve this with the front edge folded over several times or by an added paper clip, which requires a little trial and error."

In the experiments, the researchers found that the flight motions depended sensitively on the center of mass location. Specifically, if the weight was at the center of the wing or only displaced somewhat from the middle, it underwent wild motions, such as fluttering or tumbling. If the weight was displaced too far toward one edge, then the flier quickly dove downwards and crashed. In between, however, there was a " sweet spot " for the center of mass that gave stable gliding.

The researchers coupled the experimental work with a mathematical model that served as the basis of a "flight simulator," a computer program that successfully reproduced the different flight motions. It also helped explain why a paper airplane is stable in its glide. When the center of mass is in the "sweet spot," the aerodynamic force on the plane's wing pushes the wing back down if the plane moves upward and back up if it moves downward.

"The location of the aerodynamic force or center of pressure varies with the angle of flight in such a way to ensure stability," explains Ristroph.

He notes that this dynamic does not occur with conventional aircraft wings, which are airfoils—structures whose shapes work to generate lift.

"The effect we found in paper airplanes does not happen for the traditional airfoils used as aircraft wings, whose center of pressure stays fixed in place across the angles that occur in flight," Ristroph says. "The shifting of the center of pressure thus seems to be a unique property of thin, flat wings, and this ends up being the secret to the stable flight of paper airplanes."

"This is why airplanes need a separate tail wing as a stabilizer while a paper plane can get away with just a main wing that gives both lift and stability," he concludes. "We hope that our findings will be useful in small-scale flight applications, where you may want a minimal design that does not require a lot of extra flight surfaces, sensors, and controllers."

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