Paper Boomerangs
Use paper to make several different types of boomerangs that will return to you when thrown.
A boomerang is a flying tool that returns to its owner after being thrown. Historically, boomerangs have been used for hunting, but in modern times they are primarily used for sports and entertainment. Boomerangs come in a variety of shapes and sizes and can be made of many different materials including wood, plastic and paper. Paper is cheap and readily available, so this page will discuss the various ways to make boomerangs from paper.
In this article you will learn how to fold several different styles of paper boomerangs that are easy to fold, throw, and catch when they come back to you. You will also learn how to turn a regular paper airplane into boomerang paper plane that flies a loop right back to you.
How Boomerangs Work
The standard boomerang shape consists of two arms connected at an angle, forming a shallow V shape. Some boomerangs have 3, 4 or more arms, but the science behind them is the same. Each arm of the boomerang is flat on the bottom and rounded on the top. The leading edge is the rounded part of each arm that is in front and hitting the air as it spins. The trailing edge, or back part of each arm, tapers to a sharper point. The cross section of this shape is called an airfoil and it is the same shape that engineers use for airplane wings and propellers. This airfoil shape produces lift as air moves over it. As a result, each arm of a boomerang produces lift as it spins through the air. You can think of a boomerang as a helicopter rotor flying through the air all by itself. The faster the air moves (the faster the boomerang spins), the more lift it produces.
If the boomerang was magically spinning in place, hovering parallel to the ground, then the lift on both arms would be equal and the boomerang would rise upwards, just like a helicopter. However, boomerangs don't spin in place - you throw them! As a boomerang is spinning and moving forwards at the same time, something interesting happens. Try to picture the motion of one arm relative to the ground as the boomerang spins and flies forward. During one half of the spin, that arm will be moving in the direction of travel and it will be moving through the air slightly faster (forward speed plus arm spinning speed). Then half a rotation later, that same arm will be moving backwards relative to the direction of travel and it will be moving through the air slightly slower (forward speed minus arm spinning speed). During the forwards part of the spin the arm will produce more lift and during the backwards part of the spin the arm will produce less lift. This difference in lift will tend to cause the boomerang to tilt to one side. If you are a right handed thrower and give the boomerang a counter-clockwise spin (looking down), then the right side of the boomerang will have more lift and it will want to tilt left.
If this was all that was going on then the boomerang would just flip over and continue to fly straight ahead. So, there must be something else happening here, right? There is! And that something is called gyroscopic precession. If you have ever played with a gyroscope, or a spinning top, then you may remember that it has a unique behavior. Spinning gyroscopes always resist forces that would change the orientation of the axis of rotation. They do this by moving in a direction that is perpendicular to the force that was applied. It may sound confusing, but that's physics!
A spinning boomerang is basically a gyroscope. So, let's go back to our prior example of a counter-clockwise spinning boomerang that is flying away from you. The difference in lift between the two arms is applying a force that is trying to tilt the boomerang to the left, but the gyroscopic effect instead redirects this force 90 degrees and actually causes the boomerang to tilt upwards. If you throw a boomerang horizontally to the ground, this is exactly what you will see. The boomerang will fly away from you and then go straight upwards. Try it out with one of the boomerang designs lower on this page.
Throwing a Boomerang
So now it all comes together. Instead of throwing the boomerang level with the ground, you generally throw the boomerang at an angle. This means that the gyroscopic force will be at an angle too, causing the boomerang to tilt a little up and a little to the side. The "little up" will counteract gravity and keep the boomerang aloft and the "little to the side" will cause the boomerang to curve. Continuing with our prior example, the boomerang will curve to the left and fly in a counter-clockwise loop, hopefully coming right back to you.
If the angle that you throw the boomerang is too flat, then it will fly upwards too much and won't make the complete loop. If you throw the boomerang at too steep an angle, then it will curve sharply but will not have enough upward force to counteract gravity and it will crash into the ground before completing the loop. Perfecting the angle is an important skill to learn, and it is different for each boomerang so you will need to experiment to find the best technique.
In addition to the tilt angle, there is also the angle that you throw the boomerang up or down in a direction away from you. Generally you want to throw the boomerang towards or slightly above the horizon. If you aim for a spot below the horizon, the boomerang wont have enough time to make a full loop before hitting the ground. If you aim too high into the air, the boomerang may have too much time and will fly too far and land far away from you. If your boomerang isn't making the complete loop back to you, and adjusting the tilt angle isn't working, try throwing it slightly more upwards into the air and see if that helps.
Besides the angle, two other variables that you can control are the velocity/speed that you throw the boomerang forward and the amount of spin that you impart on the boomerang when you release it. These two variables are intertwined and must be carefully considered. The optimal spin for a boomerang is directly proportional to the velocity that you throw it. In other words, if you throw the boomerang harder, you also need to spin it faster. A gently thrown boomerang will need a slower spin. Getting a feel for the relationship between spin and speed is another skill that you will need to develop.
To summarize, when throwing a boomerang you can control three variables. Each boomerang will have a sweet spot that you will need to figure out based on experimentation.
- Forwards Speed - This is how hard you throw the boomerang. This force generally comes from your shoulder and arm.
- Spin Speed - This is how fast you spin the boomerang. This force generally comes from your wrist as you flick the boomerang at the end of the throw.
- Angle - There are three angles to consider. One is the amount of tilt that the boomerang has in your hand side to side. Another is the angle that the boomerang travels relative to the horizon, up or down. The third is the angle that the boomerang has relative to the wind as you turn your body around and face different directions.
Here are some variables that you cannot control.
- Wind - Wind complicates things by adding an extra force to the boomerang. This extra force pushes the boomerang off its normal course and makes it appear to drift. You can compensate for the wind by adjusting the angle that you throw the boomerang. If you are throwing into the wind, you might use a shallower angle because the wind will be helping it return to you. If you are throwing with the wind, you might need a steeper angle of attack.
- Thermals - Thermals are pockets of warm rising air. This can be caused by the sun poking through clouds or by heat being reflected differently from grass, dirt or concrete. If you can get your boomerang into a thermal, it will give it an upwards force that can lift it into the air. Competitive boomerang throwers will try to get in thermals on purpose to get their boomerangs to stay up in the air for a long time. The world record for flight time of a boomerang is nearly 4 minutes!
Here is an interesting boomerang fact: A boomerang will always fly in a circle of the same size, regardless of how hard you throw it or how fast you spin it. That's right! The dimensions of the boomerang's flight path is determined by the physical design of the boomerang and has nothing to do with how you throw it. This strange characteristic is based on some complicated physics, but here is a simple explanation. The size of the boomerang, its mass and the distribution of that mass throughout the boomerang can be turned into a number called the "moment of inertia". This is a measurement of how much the boomerang resists changes in acceleration in the spin direction. A boomerang with a bigger moment of inertia will fly in a larger circle. Additionally, the shape of the airfoil that is designed into the boomerang effects how much lift it produces. A flat boomerang will produce little lift and will have a wide flight path. A boomerang with a strong airfoil will produce a lot of lift and will have a tighter flight path.
If you want your boomerang to fly in a wider angle, throwing it harder wont help. Instead, add weights to the outside of the boomerang arms. This will increase the moment of inertia and therefore the flight radius of the boomerang will increase as well.
Paper V Boomerangs
The V shape is the traditional shape of a boomerang and it is still the most recognizable and historically significant style. It only has 2 arms, so it is easier and quicker to carve out of a single piece of wood. Boomerangs made with more arms would have required multiple pieces of wood joined together and this would have introduced weak points where the arms intersect. The same engineering limitation applies to paper boomerangs as well. This V shaped paper boomerang can be made with a single piece of paper. Click through to the instructions and give it a try!
We have made instructions and a printable template that you can use to fold the perfect paper boomerang in the traditional V shape. It has some tricky folds, but if you follow along carefully you should be able to produce this sleek shape. Hold it relatively level to the ground (5-10°) and give it a gentle toss with the flick of your wrist to make it spin away from you at a slightly upwards angle. It should glide up about 15-20 feet away, turn around and then come right back.
Learn to Fold the Paper BoomerangPaper Y Boomerangs
Adding a 3rd arm makes the boomerang rotationally symmetrical which can improve balance and performance, but it makes it harder to build because it cannot be made from a single piece of folded paper. You will need to use scissors and a fastener (tape, glue, staples, etc). The best way to make a three armed paper boomerang is to make 3 individual arms and then attach them in the middle. We'll be using some overlapping folds to give each arm an airfoil shape.
Fold a piece of paper in half from top to bottom and then cut along that crease to make two pieces of half sized paper. Each piece will make one arm, so you'll need three total.
Orient the paper so it's taller than it is wide and then fold the paper in half again from top to bottom. Unfold and fold both edges to the middle crease that you just made and press it flat.
Take both inner flaps and fold them back to the outside edge. Then take the new inner flaps and fold them to the outside edge again, making a thick strip on both sides. Then, take only one side and fold it one more time, making a thick skinny strip on one side. Press as flat as you can.
Now fold both thick edges to the middle. Leave them each about 1mm shy of the middle crease. Then using that middle crease fold the whole bundle in half. You should end up with a strip that has one rounded thick side and one thin side that tapers to a point. This is our airfoil shape. The curved thick edge will be our "Leading Edge". The thin edge will be the "Trailing Edge". Use some tape on the trailing edge to keep it held together. Notice which side of the piece is flat and which side is curved. The flat side will be the "Bottom". Label these with pencil to help in the next step.
Make three of these pieces and place them on the table so the flat bottom side is touching the table. Arrange the three pieces so they make a Y shape with an equal angle on all three sides. Make sure that the curved thick leading edges are pointing counter-clockwise around the circle for each piece. If you are left handed, reverse this. Use two pieces of tape on each side of the middle section to hold it all together. If you haven't already, put some tape on the trailing edge, near the tips to keep it together.
Look down each arm towards the middle and make sure the arms are flat and not twisted in either direction. Then, with the boomerang resting on the table with the bottom flat side down, give each arm a slight upward bend so the tips of each arm are slightly elevated when the boomerang is resting on a table.
You are now ready to throw your paper boomerang. Hold it in your dominant hand by pinching the tip of one boomerang arm with your thumb and finger. Hold it at an angle of about 45° tipped away from you with the flat bottom side pointed out away from you. Give it a good throw straight ahead with a sharp flick of the wrist to give it a fast spin. It should fly away from you and curve to the left and then circle back towards you in a big circle. See if you can catch it! If the boomerang doesn't make it all the way back on the first try, don't worry. You will need to experiment with the power of your throw, the speed that it spins and the angle that you release it. Each boomerang is different and will require a slightly different throw.
If you want the boomerang to fly in a wider circle, add a staple or two to the tip of each arm. This will increase the "moment of inertia" as described above and make the boomerang go further away before returning.
Paper X Boomerangs
Not happy with the V or Y boomerangs? Try adding a fourth arm to make it an X shape. This can be easily achieved by taking two of our V boomerangs and stapling them together in the middle. You can use tape or glue if you prefer. When attaching the two boomerangs together, make sure that you orient both boomerangs the same direction with the angled parts of the tips pointed the same way for each arm.
Because of the symmetry, this design is more stable than one of the V boomerangs by itself. To throw it, hold by one of the tips and give it a flick with your wrist, spinning it clockwise. Throw it at a slight upward angle with as much spin as you can. Don't throw it too hard; aim for a spot on the ceiling about 15-20 feet (4-6 meters) away. It should spin away from you, curve up towards the ceiling and then turn around and come back. See if you can catch it!
Another way to make a four armed paper boomerang is to follow the directions for the Y boomerang above, but just add another arm. You can use this technique to make 5, 6 or even 7 armed boomerangs, but that might be going a bit too far.
Turn Paper Airplanes Into A Boomerangs
A boomerang is a rigid object with 2 or more arms that you throw with a spinning motion. A traditional paper airplane doesn't "technically" meet this definition, but if you allow a loose interpretation of the word, we can make a paper airplane boomerang. If you prefer, you can call it a "Returning Paper Airplane".
Many different paper airplane designs can be made to boomerang back to you. You do this by making some simple adjustments that will make the airplane fly in a flat loop. These adjustments are explained in detail on our How to Steer a Paper Airplane article, but we will explain the specific adjustments that you need to make here.
- Airplane Style - First, choose a glider style of paper airplane. Our Hunting Flight, Lock-Bottom, V-Wing, and Stealth Glider designs will all work, as will other designs that have wide wings and a shorter body.
- Wingtip Stabilizers - Fold up some small stabilizers at the ends of each wing tip. This will help keep the airplane from spiraling into the ground. Some of our designs have this already built in, but if your design doesn't, you'll need to add it. Make sure they are pointing up.
- Positive Dihedral Angle - Tilt the wings up at their intersection with the fuselage so the wings are not parallel with the ground. This positive dihedral will give your airplane the necessary stability that it will need to avoid flipping over. If the airplane unfolds a little during flight, you may need to use a staple or tape to keep this angle positive.
- Up Elevator - Make a small upward bend to the back edges of both wings. You can crimp the paper, or you can cut little slits to make elevators or elevons. This upward bend will cause the airplane to pitch upwards, which will be necessary to accomplish the loop. You can control the radius of the loop by giving your airplane more or less up elevator.
- Banked Launch - Normally you throw a paper airplane so the wings are level with the ground. However, to get your modified airplane to fly in a loop, you'll instead need to throw and release your airplane with a significantly banked angle. The exact angle will depend on the design, but you can start with a 45° angle and adjust it from there. The airplane should be banked into the turn, so if you are a right handed thrower, it will look like this diagram. If you are left handed, reverse this.
With these adjustments, your paper airplane should fly in a loop to the left (counter-clockwise when looking down from the ceiling) and come right back to you. See if you can catch it! If it doesn't make the complete loop, try giving it a little more bank, or a little more up elevator. If the loop is too tight, reduce some of the elevator. Figuring out the optimal adjustments will take a little trial and error for each new paper airplane design, but once you get a little practice you'll be able to make these tweaks in only a few minutes.
Conclusion
If this article has sparked your interest in boomerangs, you may be interested in purchasing a boomerang made out of something other than paper. Paper is a good material because it is cheap, disposable and safe, but it isn't very durable. There are many different styles of boomerangs made out of more durable materials if you want something that will last for awhile. Foam boomerangs are safe and can be thrown indoors. Wooden boomerangs fly further but can only be used outdoors away from other people. All of the styles are fun to throw and catch. Take a look at the different Boomerangs that are available.