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How Far Will It Fly? Build & Test Paper Planes with Different Drag
Michelle Maranowski, PhD, Science Buddies Teisha Rowland, PhD, Science Buddies

Determine whether the distance a paper plane flies is affected by increasing how much drag it experiences.
Introduction
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 aerodynamics science project, you will make a basic paper plane and then slightly alter its shape to increase how much drag is acting on it. You will investigate how far the basic paper plane flies and compare that to how far it flies when the drag is increased. How will adding drag affect your plane's flight? You can answer this question with just a flick of your wrist.
Terms and Concepts
- Wind Tunnel
- Computer Simulation
- Streamlines
- What is drag and how does it affect airplane flight?
- How do you think you could change how much drag a paper plane has?
- What provides thrust to a real airplane?
Bibliography
These sites explain how paper planes and airplanes fly.
- Shaw, R. (2010, September 10). Dynamics of Flight . Retrieved November 24, 2010.
- Doherty, P. (1999). Paper Airplanes . Exploratorium Magazine Online. Vol. 23, Number 2. Retrieved November 24, 2010.
The following resource can be used to convert inches and feet to metric units (i.e., centimeters and meters):
- Science Made Simple, Inc. (n.d.). Length conversion using online length converted by Science Made Simple . Retrieved February 13, 2013.
For help creating graphs, try this website:
- National Center for Education Statistics, (n.d.). Create a Graph . Retrieved June 25, 2020.
Materials and Equipment
- Paper (3 sheets)
- Metric ruler
- Masking tape (1 roll). Alternatively, if you are testing this project outside, you can use sticks or rocks.
- Tape measure
- Lab notebook
Experimental Procedure
Flying the planes.
- Follow the paper airplane template for the "intermediate" design instructions to build a paper airplane.
- Build two more so that you have a total of three paper planes. They should all look identical.
- Make a data table in your lab notebook, like Table 1 below, where you can record the data you get from your experiment.
- 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.
- Tear off a 5-foot-long piece of masking tape and tape it to the ground in front of you, going from left to right. This will be the starting line from which you will fly the paper planes. If you are doing this science project outside, you could use a line of sticks or rocks to mark the starting point.
- Practice throwing or launching the paper planes. You will want to launch the planes in exactly the same way every time. Hold the planes at exactly the same spot on the plane every time you launch a plane.
- Once you have finished practicing, it is time to start the experiment. Place your toe on the starting line you prepared earlier and then throw one of your planes.
- This will be "Flight 1" for "Plane 1."
- Science Made Simple, Inc. (n.d.). Length conversion using online length converter by Science Made Simple. Retrieved February 13, 2013.
- Before you fly the plane, make sure that it is in good condition and that the folds and points are still sharp.
- Record the distances in the data table in your lab notebook all in the same row as "Plane 1," as "Flight 2," Flight 3," "Flight 4," or "Flight 5."
- Cut four slits that are each roughly 2.5 cm long along the back edge of the wings. One in the center of each wing, and one where each wing meets the central fold.
- This will result in four tabs (two on each wing). Fold two of the tabs up 90 degrees, and two of the tabs down 90 degrees, as shown in Figure 2.
- How do you think this increases the plane's drag?

- Record the distances the plane flies in your data table in the row titled "Plane 1 with Added Drag."
- In your lab notebook, record any observations about how this plane appears to fly compared to how plane 1 flew before you added drag.
- Record the distances the plane flies in the row titled "Plane 2" and then "Plane 2 with Added Drag."
- In your lab notebook, record any observations you make.
- Record the distances the plane flies in the row titled "Plane 3" and then "Plane 3 with Added Drag."
Analyzing Your Data
- For example, if plane 1 traveled 4.60, 4.14, 5.00, 5.33, and 3.86 meters on flight 1, 2, 3, 4, and 5, respectively, to figure out its average distance you would first add these five distances together (which gives you 22.93 m) and then divide this number by five, which gives you an average distance of 4.59 meters.
- You can plot your data by hand or you can plot your data online at Create A Graph .
- Label the x-axis (the horizontal axis) "Paper Plane" and label the y-axis (the vertical axis) "Average Flight Distance." You will have six bars, one for each of the planes without added drag, and one for each of the planes with added drag. Make each bar go up to the average distance that plane traveled.
- Can you explain your results in terms of how forces allow a plane to fly? Hint: Re-read the Introduction in the Background tab.

Ask an Expert
- Does size matter? Make planes of different sizes but keep the design and the type of paper you use the same. Do bigger planes fly further?
- Do more complicated planes fly further? In order words, does the number of folds that you use to make a paper plane affect the distance that it flies? Try this out using the same size and type of paper.
- Does the type of paper you use affect how far the paper plane flies? Try making paper planes out of different types of paper, such as printer paper, construction paper, and newspaper. Make all of the planes using the same design and fly them as similarly as you can. Does one type of paper seem to work best for making paper planes? Does one type work the worst? You may need to do several trials to see a trend.
- Some people like to add paperclips to their paper planes to make them fly better. But where should the paper clips be placed for the best flight? Try adding paperclips to the back, the front, the middle, or the wings. You can add one paper clip or several, but try to be consistent with how many you use. Take notes in your lab notebook so you know what you tested. Does adding paperclips somewhere make the paper plane's flight better, worse, or have no effect at all?
If you like this project, you might enjoy exploring these related careers:

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Paper Airplane Experiment
The paper airplane experiment, as well as being great fun, is a chance for us to study something called 'The Laws of Aerodynamics'.
This article is a part of the guide:
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When you throw a flimsy paper dart across a room, you might not realize that it follows the same laws of flight as a Jumbo Jet!
With just a few pieces of paper and a little patience, you can explore these laws and find out how a big piece of metal manages to stay in the air.
For this experiment, we are going to chose five different designs of plane. One place to look is www.paperairplanes.co.uk , for instructions on how to make these. You can use any design you like, as long as they are different and you don't use any scissors or tape to make them.
In the paper airplane experiment, we are going to test which designs fly the furthest. Some of the designs have a sharp point so do not throw them at anybody's face!

- Lots of copy paper to make your planes.
- Loads of space - if your school has a large gym or hall, then great. You can fly them outside but it must be on a day with no wind.
- A long tape measure - 50 or 100 meters long
- A chart to record your results in

- Make a chart to record your results, like in Figure 1.
- Next, make a lot of paper airplanes of each type. Take your time to make sure that the planes are as similar as possible. You should practice throwing each type to make sure that you are throwing with the same amount of force and speed.
- Do this five times for each type of plane and note the results on your chart.
- Try to use the same plane for all five throws, but if it gets damaged, use another.
You should work out an average distance flown for each type of plane in your paper airplane experiment.
However, we are going to use something called an adjusted average. Do not use the lowest and highest figures to work out your average, just the three in the middle. This is because; in an experiment like this, a gust of wind or a bad throw can make one or more of your results wrong. This is called an outlier-data .
After you have worked out the average for each, you can plot a bar chart and discuss the results with your class. Which planes flew the furthest? Why do you think they were the best fliers?
For some tips, please see the NASA site for some advice on the Laws of Aerodynamics.
There are many more experiments you can perform with paper airplanes. Maybe this is the first step on you journey to being an airplane engineer or designer!
Figure 1 - The distance flown by paper airplanes.
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Martyn Shuttleworth (Sep 21, 2008). Paper Airplane Experiment. Retrieved Mar 13, 2023 from Explorable.com: https://explorable.com/paper-airplane-experiment
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Science Experiment: Aerodynamics - Paper Airplanes
07/15/2021 | Science Experiments
Try some at Home! What You Need :
- Paper Clips
Do an experiment with three paper airplanes folding the exact same way with the exact same size of paper. Fly all three planes and measure how far they go. What happens if you add one paperclip to each? What happens of you add 2? Or 3? Record your results.
Websites, Printables & Activities:
- NASA: How to Make a Dart Airplane
- NASA: How to Build a Paper Jet Model
- NASA: How to Make a Blunt Nose Airplane
- NASA: Four Forces on an Airplane
- NASA: What Is Aerodynamics?
- Printable: PBS Kids Fetch Hang Time
- Exploratorium Try This! Paper Airplanes
- The Children's Museum of Indianapolis: Airplane Models & Toys

You can also ask a math and science expert for homework help by calling the Ask Rose Homework Hotline . They provide FREE math and science homework help to Indiana students in grades 6-12.
Use your indyPL Library Card to check out books about Paper Airplanes at any of our locations , or check out e-books and e-audiobooks from home right to your device. If you have never used Axis 360 or OverDrive before, you can learn how to use them for both e-books and audiobooks .
- e-Books and audiobooks about Paper Airplanes from Axis 360 Kids
- e-Books and audiobooks about Paper Airplanes from Overdrive Kids
Need help? Ask a Library staff member at any of our locations or call, text, or email Ask-a-Librarian . The Tinker Station helpline at (317) 275-4500 is also available. It is staffed by device experts who can answer questions about how to read, watch and listen on a PC, tablet or phone.
Aerodynamic for Kids
A group of lively, highly creative third graders visited the Learning Curve recently to explore aerodynamics. They built, tested, and tweaked glider designs using strips of paper, straws, and tape. Their intense focus during construction and delight as they launched the gliders along the designated indoor flight path inspired me to create this list of kid friendly books about flight. I hope it encourages the young flight enthusiasts in your life to explore the mechanics of aerodynamics!
Riveting Reads for Curious Kids
Grant, R. G.
From the early days of flight up through the space program, this book shares interesting tidbits about the evolution of human flight. It features "Weird World" highlights and includes a reference section with historic moments in flight, aviation heroes, glossary, great aircraft and websites where eager learners can discover even more about flight.
Birds, Bees, Biplanes, and Other Things With Wings
Turner, Tracey
From insects (the first creatures on Earth to have wings) all the way to spacecraft, this colorfully illustrated book shares a wealth of information about flight and how it works in nature and in human made machines.
Wood, Wire, Wings
Emma lilian todd invents an airplane.
Larson, Kirsten W.
This illustrated biography shares the story of Emma Lilian Todd's innovations in the early days of aviation. Some of her inventions continue to be part of airplane design today! Also available as an eBook.

FREE K-12 standards-aligned STEM
curriculum for educators everywhere!
Find more at TeachEngineering.org .
- TeachEngineering
- Paper Airplanes: Building, Testing, & Improving. Heads Up!
Hands-on Activity Paper Airplanes: Building, Testing, & Improving. Heads Up!
Grade Level: 6 (5-7)
Time Required: 45 minutes
Expendable Cost/Group: US $1.00
Group Size: 1
Activity Dependency: None
Subject Areas: Physical Science
NGSS Performance Expectations:

Curriculum in this Unit Units serve as guides to a particular content or subject area. Nested under units are lessons (in purple) and hands-on activities (in blue). Note that not all lessons and activities will exist under a unit, and instead may exist as "standalone" curriculum.
- Fun with Bernoulli
- Air Pressure
- Windy Tunnel
- Bend That Bar
- Physics Tug of War
- Equal & Opposite Thrust in Aircraft: You’re a Pushover!
- What a Drag!
- Better By Design
- Let's Get It There Fast
- Balsa Glider Competition
- Design a Flying Machine
TE Newsletter
Engineering connection, learning objectives, materials list, worksheets and attachments, more curriculum like this, introduction/motivation, troubleshooting tips, activity extensions, activity scaling, additional multimedia support, user comments & tips.


Engineers often create small-size models of a new product to test its design. This is especially true with airplanes. Model testing tells engineers how a design responds to different air conditions and aircraft shapes, and lets them experiment with the control surfaces that are used to steer the aircraft. Using small models guides engineers to discard prototypes that do not work, which is a smarter option than than throwing away full-size (large and expensive to build) aircraft that do not work.
After this activity, students should be able to:
- Create a paper model of an airplane to use in experiments.
- Use their observations of paper airplane flight to explain flight.
- Find the average distance of flight trials.
- Explain how engineers often create small-size models of new products to test designs.
Educational Standards Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards. All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN) , a project of D2L (www.achievementstandards.org). In the ASN, standards are hierarchically structured: first by source; e.g. , by state; within source by type; e.g. , science or mathematics; within type by subtype, then by grade, etc .
Ngss: next generation science standards - science, common core state standards - math.
View aligned curriculum
Do you agree with this alignment? Thanks for your feedback!
International Technology and Engineering Educators Association - Technology
State standards, colorado - math, colorado - science.
Each student needs:
- 1 of the 4 paper airplane designs in the Plane Patterns Handout and its associated Plane Design Instructions ; vary designs among students
- Flight Distances Worksheet
- 1-2 sheets of 8.5 x 11" copy paper
For the class to share:
- tape measure and/or meter sticks, and/or use cones to mark every five feet
- stopwatch, or a watch with a second hand
- completed examples of each of the 4 paper airplane designs
- overhead projector to show the Plane Overhead Transparency and Distance/Time Table .
- (optional) calculators

Students are introduced to the art of designing airplanes through paper airplane constructions. The goal is for students to learn important aircraft design considerations and how engineers must iterate their designs to achieve success.

Students learn about airplane control surfaces on tails and wings, and engineering testing wherein one variable is changed while others are held constant. Through the associated activity, they compare the performance of a single paper airplane design while changing its shape, size and flap positions...

Students act as if they are engineers designing gliders, aiming to improve the flight distance and time in the air. This activity brings together students' knowledge of engineering and airplanes, applying what they have previously learned about lift, weight, thrust and drag to glider models, as well...

Students learn about kites and gliders and how these models can help in understanding the concept of flight. Then students move on to conduct the associated activity, during which teams design and build their own balsa wood glider models and experiment with different control surfaces, competing for ...

Paper airplanes are gliders. They have a main body, and generally two wings. Some are more complex, with tails, rudders and flaps. The wings compress the air below the paper airplane, creating high pressure, and thus the airplane is able to "sit" and glide on the air. Moving the rudders, ailerons, or flaps up or down can change the flight path of an airplane. For example, folding down the wing flaps can result in a nosedive and folding up the flaps can point the airplane in an upward direction. (Show the class an overhead transparency of the Blank Plane Diagram and have students come up to the board and identify/label the various parts. See Figure 1 for the answers. For younger students, you may want to list the parts nearby from which they can choose.)
Engineers start with designing and testing several different models of an airplane before they get the approval to build a real one. They typically must work under specific constraints or limits, including the purpose of the airplane. By testing different models of planes, engineers can determine which one is best for distance, speed and other factors.
Today, we are going to learn how to design some simple gliders and airplanes using paper. The class is going to design and build a few different models and determine which paper airplane is the best for distance.

Before the Activity
- Gather materials and make copies of the Flight Distances Worksheet .
- Make enough copies of the four different types of paper airplanes in the Plane Patterns Handout , and their instructions in the Plane Design Instructions , one design per student.
- Make a few models of the four airplane designs to get a feel for how to make them and how they fly.
- Prepare an indoor (hallway, gym) or outdoor plane testing area—an unobstructed area to throw the planes and measure flight time and distances.
- Become familiar with the activity vocabulary. List new terms, such as "aileron" and "rudder," on a chart or the classroom board.
- Prepare overhead transparencies to show the class: Blank Plane Diagram and Distance/Time Table .
With the Students
- Conduct the pre-activity assessment brainstorming, as described in the Assessment section.
- Present the Introduction/Motivation content to the class.
- Demonstrate one or two paper airplanes. Discuss and list on the board the airplane parts they may know about, and add any terms they do not know, such as "elevator" and "rudder."
- Then list factors they may know about that would affect flight (for example, plane shape, wing shape, weight, weight at the nose, tails, flaps, rudders, etc.).
- Explain that they will get to try several designs and see how they work. Hand out a variety of plane designs and their instructions, so each table/general area has an assortment. Give students time to work on the airplanes.
- Inform students on the method to measure flight distance and flight time, such as the following:
- Set out cones every five feet and have students estimate their flight distance based on the cones.
- Have students individually measure their flight distances using tape measures or meter sticks.
- Have students use a stopwatch to time how long their planes stay in the air.
- In the plane-testing area, have students test and gather data by performing three test flights with their first plane designs. Direct students to record all three flight distances on their worksheets.
- Hand out blank paper, and let students design and test a second airplane. Inform students that this second design should be their own, original design and entirely different from the first plane design that was provided to them.
- Have students test their second designs, again recording the distances and times.
- Have students compute on their worksheets the average flight times and distances for both plane designs.
- To conclude the activity, lead a class discussion. Make an effort to use the new airplane parts terminology. Question prompts:
- What did you learn?
- What changes did you make in your second airplane design and how did those changes affect the flight distance?
- Who's plane went farther than five feet? Farther than 10 feet? The farthest of all?
- Did certain designs go farther than others? Why?
- What were your flight times? What was the longest flight time?
- Did certain designs stay aloft longer than others? Why?
- Did you notice a relationship between average distance and average time? (Expect a weak relationship between time and distance since it is possible for a plane to fly straight up for a while but only travel a few feet forward.)
- To analyze the class data, first take a poll of the class to compile data counts to complete the Distance/Time Table as an overhead transparency. Direct students to use the larger of their two averages from design 1 or design 2.
- Using the class data, have students individually make bar graphs with number of students on the x-axis and distance on the y-axis. Which distance has the largest number of paper gliders that went that far?
- If time permits, as a class, determine who has the longest time average.
Pre-Activity Assessment
Brainstorming: Before starting the activity, have students generate a number of possible ideas about the activity topic. Encourage wild ideas and discourage criticism of any ideas. Ask:
- What are all the different ways you can design a paper airplane?
Activity Embedded Assessment
Worksheet: Have students record on the Flight Distances Worksheet their flight distances and times for both plane designs. Review their data to assess their engagement and comprehension of the experimental testing process.
Post-Activity Assessment
Class Discussion: Ask students to list factors that they noticed affected their airplane model test flights. Record their answers on the board. Ask how they would change their designs if they had more time to work on them. Have them list some of the variables that affect flight (such as the weight of the plane's parts, wing shape, wing length, rudders, ailerons, plane length, etc.)
Pass the Buck: In groups of four, have students brainstorm ideas to design the perfect paper airplane. First, assign one student in the group to be the recorder. Then have someone toss out an idea. Next, another person in the group provides an idea that builds on the first. Go around the group in this fashion until all students have put in enough ideas to put together a design. When they are done, have them share their ideas with the class.
Safety Issues
Provide a clear path for the airplanes to be thrown so that people are not be in the path of the paper airplanes.
Clarify to students when and where to fly the airplanes. Ideally, conduct the activity in a hallway, gym or outdoors. You may want to show them how to fold some of the trickier paper airplanes as a group before you let them try on their own.
If some students have dificulty folding the paper airplanes, ask other students who have mastered the process to help them.
Expect that some students already have experience with paper airplanes. Let them know that they will get a chance to demonstrate their favorite airplane design in a later lesson, but the purpose of this activity is to get some basic folding shapes down for the entire class. Or, ask them to do one of the provided patterns for their first trials and their own designs for the second trial. Then, have the students explain what changes were made to improve the plane for the second trial.
For extra math practice, have students create a line or bar graph of their individual plane trials.
Have students complete other challenges with their paper airplanes. Set up a mock landing pad, a target or a hoop to measure plane flight accuracy.
A company called Whitewings makes all sorts of kits for very cool paper airplanes; see https://www.acsupplyco.com/white-wings-model%20airplane-kits/whitewings-wwag5000-competition-glider-30-pack .
- For younger students, keep it simple by limiting the designs to one paper airplane prototype design. And, it may be easier if you do not introduce the concept of control surfaces such as rudders and elevators. Also, complete the bar graph as a class or in small groups.
- For older students, encourage more complex models and manipulate them more. Encourage students to come up with their own unique paper airplane designs (even for the first plane design), and have them explain their designs to the class in terms of what they changed to improve flight.
A helpful NASA diagram shows the basic ariplane parts and their functions; see https://www.grc.nasa.gov/www/k-12/airplane/airplane.html.
Paper Aircraft Association. Accessed 2004. http://www.topphotograph.dsl.pipex.com/paamain/index.html
Contributors
Supporting program, acknowledgements.
The contents of this digital library curriculum were developed under grants from the Fund for the Improvement of Postsecondary Education (FIPSE), U.S. Department of Education and National Science Foundation (GK-12 grant no. 0338326). However, these contents do not necessarily represent the policies of the Department of Education or National Science Foundation, and you should not assume endorsement by the federal government.
Last modified: December 9, 2022
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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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Channel Ars Technica
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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