# Boomerang Physics

## Making and Throwing a Boomerang

A Boomerang is a rather unique flying object. There are actually two somewhat distinct versions of throwing a Boomerang, although the Boomerang itself is similar in both cases. They were both apparently invented by Aborigines in Australia many centuries ago. A few remote tribes in Africa and Asia also throw a device which is extremely similar to the Boomerang.

One version of the Boomerang is entirely functional, as it is (or was) used to help get animals for food. It is generally designed to be somewhat heavier than the other version, to cause a greater impact on an animal, primarily due to the rapidly spinning and somewhat sharp end of the Boomerang shape. It is thrown intended as a "one way" boomerang, which is intended to strike a prey animal, even 300 or even 500 feet away from the thrower. The other version is entirely for entertainment and competition, and this is the one that most modern people know about. It is thrown such that it is supposed to fly in an approximate circular path, with the intention that the thrower might even catch the Boomerang after the throw. The circular path is commonly around 100 feet in diameter.

During my College education in Advanced Physics, I did a lot of calculations and Designed and Built my own Boomerang. It was quite successful but I found that actually getting it to come back to where I had thrown it from was apparently beyond my skill level, although a few times it came back close enough that I ran a few steps and was able to catch it before it hit the ground!

My Boomerang generally started off flying slightly upward for a while, as my initial Vertical force Vector began somewhat greater than the weight of my Boomerang was. As I would watch it circle, after around about half of its "circle" it had achieved its highest altitude (of maybe 15 feet) and I noticed that it then slowly lost altitude, due to Aerodynamic Drag slowing the spin rate of the Boomerang and therefore contributing less Vertical upward Force Vector to counteract that constant downward weight Vector.

A Boomerang is a device which entirely flies due to an Aerodynamic process called Bernoulli Lift. The Bernoulli mathematical formulas (actually based on Newton's Equations of Motion of a hundred years earlier) can be used to do the Engineering to Design and Build a Boomerang and also to know how to hold it and throw it.

I only ever built the "circling" versions of boomerangs, so my experimental knowledge does not include the performance of the (heavier) "straight path" versions. A Boomerang is carved out of a piece of hardwood about two feet long, such that it has a rather wide Vee shape. The cross-sectional shape of each half of the Boomerang is asymmetric, that of an airfoil. It is held somewhat like a throwing hatchet is held, but slightly tilted over (to the right side for all Boomerangs I have ever seen). When a boomerang is thrown, it is held nearly vertically. As it is thrown, a wrist snap makes it spin. It spins, like the throwing hatchet spins. I suspect that right-handed people must make most boomerangs, as the side that has the more "bulged" side (airfoil-like) seems to always (personal observation) be to the left side (as it is held). I do not know if boomerangs are made which are "left-handed" (opposite). But the ones I have thrown have all created a Bernoulli Lift which acted to circle toward the left.

This (nearly) horizontal force vector constantly acts to curve the path of the boomerang. If it is thrown well, it follows an entire horizontal circle (to the left) and returns to landing near the thrower. For Bernoulli Lift critics, there is no possible other explanation for why a boomerang makes that constant turn to the left, except that it is due to a Bernoulli Lift.

If the specific contour shape of the boomerang airfoil is carefully measured, and the rate of spin and weight of the boomerang are measured, it is not that hard to use the Bernoulli equation to calculate the radius of curvature that a specific boomerang should fly in. In other words, using the Bernoulli equation, it is actually possible to Engineer a boomerang to circle at specific diameter flight circle! That's another clear proof of both the Bernoulli equation and Bernoulli Lift, and the boomerang has been around for many centuries!

I have noticed that many "experts" provide explanations of how and why a Boomerang flies as it does which are at least partially wrong! Some even claim that a Precession effect of a spinning gyroscope is partially responsible, but those "experts" have clearly never done the math of the Euler Equations as they would see that such an explanation is not mathematically valid.

The boomerang is not actually held exactly vertical when throwing, but (a right-handed Boomerang) is held slightly tilted to the right. The rotational spin (due to a snap of the wrist) therefore creates the Bernoulli force Vector that is slightly upward of being straight horizontal to the left. This small upward vertical component of the force Vector overcomes the vertical weight Vector of the boomerang, which keeps it from crashing down. (That is why the comment above regarding needing to know the weight of the final Boomerang is needed during the Engineering of its Design and carving. The actual flight path is neither completely a level horizontal circle nor is it even all actually circular. Eventually, as aerodynamic drag slows down the boomerang's spin, the Bernoulli force Vector also reduces. This results in a somewhat egg-shaped flight path, where the radius of the curvature gradually increases, such that the Boomerang is generally flying in a nearly constant curved direction as it completes its flight. This becomes obvious as you practice throwing a Boomerang, and need to walk to retrieve it!

Once the vertical component of the spin-induced Bernoulli Lift Vector drops to less than the weight of the boomerang, it falls and crashes. Again, practice determines the tilt angle to hold the Boomerang to delay this landing for as long as possible, and it also encourages learning to develop a consistent wrist snap action to initiate the Boomerang spin rate to be as fast as possible.

In these paragraphs is everything there is to say about the Physics of Boomerangs, and it is entirely due to Bernoulli Lift! The needed math for Engineering and Design is entirely the Bernoulli Equation and the Euler Differential Equation set.

A Boomerang thrower learns how much he needs to tilt the Boomerang to the right is dependent on his ability to snap his wrist!

This presentation was first placed on the Internet in January 2015.

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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago