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Scientists experiment with paper planes to study aerodynamics, flight stability
The properties that make a paper airplane fly have much to tell scientists about aerodynamics and flight stability, according to U.S. National Science Foundation grantee researchers at New York University . They conducted a series of experiments using paper planes to make their conclusions.
The research could influence the development of airborne vehicles like drones. The team's research was 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 Leif Ristroph, an author of the study. "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 very different from the stability of conventional airplanes."
Paper planes rely on gravity and proper design to successfully glide.
"Birds glide and soar in an effortless way, and paper airplanes, when tuned properly, can also glide for long distances," added co-author Jane Wang. "Surprisingly, there has been no good mathematical model for predicting this seemingly simple but subtle gliding flight."
Paper planes appear unassuming in design and composition, "But paper airplanes, while simple to make, involve surprisingly complex aerodynamics," said Ristroph.
The researchers launched paper planes with different centers of mass, observed paper planes descending into a water tank, and used the data to develop a new aerodynamic model and flight simulator that successfully replicates flight motions.
"The key criterion of a successful glider is that the center of mass must be in the 'just right' place," Ristroph said. "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 location of the aerodynamic force or center of pressure varies with the angle of flight to ensure stability."
The effect the team found in paper airplanes doesn't happen in the traditional airfoils used as aircraft wings, whose center of pressure stays fixed in place across the angles that occur in flight, according to Ristroph. "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."
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).
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.
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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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Learn about the science of flight and then experiment with your own paper airplane models.
Four forces act on an airplane: weight, lift, thrust and drag.
Try these paper airplanes and share creations with #AFRLPaperAirplane on social media.
Right click an image below and select “Save image as” to download and print.
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Paper Airplanes: Why Flaps and Folds Matter
- Sheet of paper, standard 8 ½ inch by 11 inch size
- Large open area in which to fly a paper plane, such as a long hallway, school gym, baseball field, or basketball court. If you are flying your paper plane outside, try to do it when there is not any wind.
- Something to make at least a one foot line with, such as a long string, another ruler, masking tape, rocks, or sticks.
- Follow the instructions for the Intermediate design to build a paper airplane .
- Go to a large area to fly your paper plane. Make sure that there is no foot or car traffic at the area. A long hallway or your school gym is a good location. If you are flying your plane outside, like in a baseball field or on a basketball court, do your experiment on a day when there is no wind.
- Use a string, a ruler, masking tape, rocks, or sticks, to make a line in front of you that is at least 30 centimeters (cm) (or one foot) long, going from left to right. This will be the starting line from which you will fly the paper plane.
- Place your toe on the line you prepared and practice throwing your paper air plane a couple of times.
Paper airplanes are fun and easy to make. Just fold a piece of paper into a simple plane and send it soaring into the sky with a flick of your wrist. Watching it float and glide in the air gives you a very satisfying and happy feeling.
But what allows the paper plane to glide through the air? And why does a paper plane finally land? To find out, we will talk about the science behind flying a paper plane and the different forces that get a paper plane to fly and land. These same forces apply to real airplanes, too. 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 is moving over and under the wings and is providing a force called lift to the plane. If the paper plane has enough thrust and the wings are properly designed, the plane will have a nice long flight.
But there is more than lack of thrust and poor wing design that gets a paper plane to come back to Earth. 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 outside of the window. The force of the air pushing your hand back as you move forward is drag. Finally, the weight of the paper plane affects its flight and brings it to a landing. Weight is the force of Earth's gravity acting on the paper plane. Figure 1 below shows how all four of these forces, thrust, lift, drag, and weight, act upon a paper plane.
A paper airplane in flight will experience an initial thrust forward which begins its flight and lift from air which will help push it upward. These forces are counteracted by drag that acts in the opposite direction as thrust and gravity which will constantly pull the plane towards the ground.
Well, what do you think? Would you like to start experimenting with these forces? In this activity, you increase how much drag a paper plane experiences and see if this changes how far the plane flies. How will adding drag affect your plane's flight? You can answer this question with just a flick of your wrist.
Ask an Expert
For further exploration.
- Make paper planes that are different sizes and compare how well they fly. Do bigger planes fly further?
- 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?
- Some people like to add paperclips to their paper planes to make them fly better. Try adding a paperclip (or multiple paperclips) to different places on 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 paperclips somewhere make the paper plane's flight better, or much worse?
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