Section 1: How does a boomerang work? This is a simplified explanation, but it hits the important points: 1. A boomerang has arms shaped like airplane wings they create lift. 2. The boomerang is moving forward and the boomerang is spinning creating an uneven lift. 3. The uneven lift created by the spinning boomerang makes it turn (like leaning on a bicycle) and keep turning until it makes a circle and comes back to you. Let s start with number 1: the boomerang arms are shaped like wings. Notice the crosssection of the boomerang. The wing has a flat side and a curved side. Notice also that it has a rounded, more blunt edge and a tapered, sharper edge, like an airplane wing. The blunt edge is called the leading edge and the tapered one is called the trailing edge.
A properly built boomerang is made so that, as it s spinning, the leading edge of each wing cuts through the air first. Because of this, there really is such a thing as a left-handed or right-handed boomerang and, if you don t throw it correctly, with the leading edge cutting through the air first as it spins, a boomerang won t work. A two-winged boomerang (it s possible to make boomerangs with 3, 4 or 5 wings even more, but I m sticking with the traditional 2-winged version for this book) has a control wing and a dingle wing. This is another thing that s great about Australians they not only have a lot of weird animals, they have a lot of weird words! Talk like an Australian berk: a bad person quokka: a kind of marsupial ocker: an Australian redneck galah: rosy breasted jumbuck: a sheep hooly-dooly: holy cow! molly-dooker: lefty bludger: a do-nothing stoush: a brawl starkers: naked argy-bargy: argumentative jaffle: sandwich ripper: terrific dinkum: honest From Kangaroo s Comments and Wallaby s Words, by Helen Jonsen, Hippocrene Books, NY, 1988.
It is possible to make a boomerang that doesn t have one edge more rounded; some have a symmetrical, lens-shaped, cross section. The purpose of the airfoil shape is to create lift, so if the boomerang doesn t have a strong airfoil shape, the tip of the control wing is often twisted, or it has a bevel cut into the tip on the flat side. Carving the bevel or twisting the wing tip helps the boomerang create more lift. It s the same effect as when you re cruising down the freeway, put your arm out the car window and tilt your hand. When you tilt your hand up, your hand flies up. You created lift. Your hand was acting like an airfoil.
We ll see why that lift is important but for now, just hang on to this: boomerang wings, like airplane wings, create lift (by the way, you can call them the wings of the boomerang or the arms of the boomerang, either word is OK although the fact that they re shaped like wings is a big part of why they work, and wings is the term most commonly used).
2. The boomerang is moving forward and the boomerang is spinning creating uneven lift (torque). When you throw the boomerang correctly, it s almost vertical when it leaves your hand, not lying flat like a frisbee. The boomerang is both moving forward and spinning, so you ve got two speeds. As the rotating wing is spinning forward, the rotation speed is added to the forward speed. As the rotating wing is spinning in the opposite direction to the forward motion, the rotation speed is subtracted from the forward speed. See the diagram below: Greater speed means greater lift. That means, as the spinning boomerang moves forward, more lift is being created on the upper half of the spin than the lower half. This puts a twisting force, or torque, on the spinning boomerang.
Imagine looking at the same diagram from behind. The forward speed plus the spinning speed in the top area, the white area of the diagram, creates more lift than the spinning speed minus the forward speed in the bottom area, the gray area of the diagram. The end result on the boomerang is a kind of twisting force, or torque. The top area of the spinning boomerang is being tugged by the lift more than the bottom area of the spinning boomerang. This is important because of the physics of how spinning objects react to twisting forces. Because it s spinning the boomerang acts like a gyroscope or a spinning top. When you throw a boomerang, flicking or snapping your wrist like you d snap a whip, you apply a torque, a force that makes the boomerang spin on its axis. For our imaginary top, that spinning torque is A in the diagram. Now suppose we apply pressure, (another torque) at the upper end of the top that is torque B. The result is that the top tilts in the direction C. If I keep applying pressure, B, the upper end of the spinning top will make a small, circular motion that is a combination of the spinning force, A and the applied force, B. This resulting circular motion is called precession. A little pressure makes the upper end of the top move in a small circle, a lot of pressure makes it move in a bigger circle. Torque: a twisting force that tends to cause rotation.
Or consider what might be a more familiar example of spinning object physics: the bicycle. 3. The uneven lift of the spinning boomerang makes it turn (like leaning on a bicycle) and keep turning until it makes a circle. It s like riding a bicycle no-handed. Even though you don t have your hands on the handlebars, you can make the bike turn just by leaning. It s the same principle. Think of the spinning bicycle wheels as if they are gyroscopes, spinning on one rotational axis, and when you lean, you are applying a torque (or force, or twisting pressure) on those spinning wheels. The result is that the whole bicycle turns. On a bicycle, you pedal to make the wheels spin, and you lean to make the bike turn. With a boomerang, you throw it to make it spin and the uneven lift (or torque) created by the combination of the spinning and forward speed of the wings makes the boomerang lean which makes the boomerang turn. 10
Lift not only helps the boomerang stay in the air, it also puts that twisting force on the spinning boomerang, which makes the boomerang turn slightly. The boomerang keeps spinning, the wings keep making lift, putting a torque on the spinning boomerang which makes it turn, and keep turning, until it makes a big circle. Imagine you re riding that bicycle on a big empty parking lot. You re riding no-handed, you lean slightly to the left, so you gradually turn left. If you keep leaning you ll go in a circle. If you lean just a little bit, you ll go in a big circle. If you lean a lot, you ll go in a smaller, tighter circle. That s essentially what happens when a boomerang returns. When you throw a boomerang, you ve got two torques or twisting, rotational forces: the first one is the spinning force you give the boomerang when you throw it. It s spinning on its axis. 11
The other torque is created by the uneven lift created by the spinning boomerang as it moves forward through the air. So you ve got one force moving in one direction (spinning forward) and another force pressing in a different direction (the uneven lift on the top area of the spinning boomerang). These two forces keep working together as the boomerang flies and create a change in direction which makes the boomerang move in a curved path. 12
Let s get some familiar Aussie critters to demonstrate this. Andrew and Bruce are pulling Carl, who is sitting on an Australian toboggan called a Wallabillumjumbaooladooker. Not really. I made that up. There is no such thing as an Australian toboggan. Anyway, Andrew and Bruce are pulling Carl. Andrew is pulling in one direction, Bruce is pulling in a different direction. The result is that Carl moves in a third direction. 13
Here s a diagram, Showing Andrew, Bruce and Carl from above. With the boomerang, a diagram showing two torques ( spinning and uneven lift) and the result they create might look like this: 14
WARNING: Complicated Math Stuff Ahead! (Skip this part if math gives you a headache.) If it s enough for you to just know that a boomerang creates lift the same way an airplane wing creates lift, great. You ve got an idea about how boomerangs work. If that s not enough for you, if you want to understand how a wing creates lift...well, that means you need to read lots of books by people much smarter than me. It means digging into the physics of aerodynamics, and it gets complicated. The common explanation of how a wing creates lift is based on something called the Bernoulli effect. A good example of this explanation is in The Way Things Work [Macaulay 1988]. The cross-section of a wing has a shape called an airfoil. As the wing moves through the air, the air divides to pass around the wing. The airfoil is curved so that air passing above the wing moves faster than air passing beneath. Fast-moving air has a lower pressure than slow-moving air. The pressure of the air is therefore greater Aerodynamics: Even Einstein got it wrong! Don t feel bad if you have a hard time getting your head around explanations of aerodynamics. It has confused some very smart people. Even Albert Einstein got it wrong. Before his E=MC2 days, he once tried to design a new wing shape, based on the commonly held principles of aerodynamics. It didn t work. Jörgen Skogh wrote, During the First World War Albert Einstein was for a time hired by the LVG (Luft-Verkehrs-Gesellshaft) as a consultant. At LVG he designed an airfoil with a pronounced mid-chord hump, an innovation intended to enhance lift. The airfoil was tested in the Göttingen wind tunnel and also on an actual aircraft and found, in both cases, to be a flop. In 1954 Einstein wrote Although it is probably true that the principle of flight can be most simply explained in this [Bernoullian] way it by no means is wise to construct a wing in such a manner! Skogh, Jörgen. Einstein s Folly and The Area of a Rectangle. 15
beneath the wing than above it. This difference in air pressure forces the wing upward. The force is called lift. Be aware, though, that not everyone agrees with this widely accepted explanation. Jef Raskin, who among many other amazing accomplishments created the Macintosh computer project, was convinced that the commonly held theory for how wings create lift according to the Bernoulli principle is wrong. I won t even try to simplify his explanation because it s way over my head. I ll tell you this, though, the question that got him thinking there had to be more to the explanation than just the Bernoulli effect was this: If the Bernoulli effect explains lift, then how can a plane fly upside down? This bugged him as a kid, and when he got frustrated and pestered his teach about it, he was told, Shut up Raskin! Eventually he learned enough math to verify for himself that the Bernoulli effect doesn t cut it, that it doesn t account for all the lift needed to make a plane fly. Read this excerpt from one of his articles and you ll see it gets pretty complicated. It s a taste of his explanation for why the Bernoulli equation doesn t account for how a wing creates lift: 16
According to the common explanation which has two adjacent molecules separated at the leading edge mysteriously meeting at the trailing edge, the average air velocities on the top and bottom [of a wing] are in the ratio of 1.0074. A typical speed for a model plane of 1m span and 0.16m chord with a mass of 0.7 kg (a weight of 6.9 N) is 10 ms-1 which makes 10.074 ms-1. Given these numbers, we find a pressure difference from the equation of about 0.9 kgm-1-2. The area of the wing 2s is 0.16 m giving a total force of 0.14 N. This is not nearly enough it misses lifting the weight of 6.9 N by a factor of about 50. We would need an air velocity difference of about 3 ms-1 to lift the plane. The calculation is, of course, an approximation since Bernoulli s equation assumes non viscous, incompressible flow and air is both viscous and compressible. But the viscosity is small and at the speeds we are speaking of air does not compress significantly. Accounting for these details changes the outcome at most a percent or so. None of these details affect the conclusion that the common explanation of how a wing generates lift with its naïve application of the Bernoulli equation fails quantitatively. This quote is from the article, Model Airplanes, The Bernoulli Equation, And The Coanda Effect by Jef Raskin. Jef Raskin was a professor at the University of California at San Diego and originated the Macintosh computer at Apple Computer Inc. He was a widely-published writer, an avid model airplane builder, and an active musician and composer. (See the appendix for a brief explanation of the Coanda Effect) 17
Forget Bernoulli, the BIG Lift is in the Angle of Attack! There s a factor that some scientists think is actually more important in creating lift than the Bernoulli effect something called the angle of attack. Airplanes have a mechanism on their wings that can change the angle of attack. You ve probably heard pilots call them flaps. They re a section on the trailing edge of a wing that moves, changes angle, when the airplane is taking off or landing. The pilot is basically doing what you do when you stick your arm out the car window and you twist your wrist. He s changing the angle of attack to get more lift. Watch an airliner taking off and notice how the whole airplane is angled upward as it takes off and as it lands. It s angled more to get more lift at slower speeds. Once the jet builds up speed it flies horizontally. If you re up to a challenge and want to get into the deeper mathematics of lift, check out Raskin s article. He s also got a great bibliography of other material about aerodynamics and baseballs, soccer balls and spinning cylinders. Knock yourself out! Once you start digging into aerodynamics you re into all kinds of effects. Besides the Bernoulli effect, you ve got the Coanda effect and the Magnus rise effect. You start messing around with fluid dynamics, viscosity and all the math holy smokes, the MATH! Section 2: How do you make a boomerang? Let s start with the basic characteristics that a boomerang needs to have and then we ll talk about building materials and techniques. There s a lot of flexibility in the basic shape of a boomerang. The wings can be straight or curved. The angle of the wings can be anywhere from about 80 degrees to about 120 degrees. The twist in the wing tips of a boomerang are creating that same effect, to give increased lift (the twist also increases drag, so there s a trade-off on how much you increase that angle). 18