boomerangs?

[rnichilo]

I have always wondered how a boomerang manages to reach a certain distance and then start back towards its thrower...

 

I never really thought about the mechanics of it much, mostly because im not to great with physics, so does anyone here have an explanation on how boomerangs "work"?

 

-Does it return, because you throw it fast and its spinning fast but as it slows down, it still keeps spinning, causing it to...uhh never mind.

[Johnny5]

I have always wondered how a boomerang manages to reach a certain distance and then start back towards its thrower...

 

I never really thought about the mechanics of it much' date=' mostly because im not to great with physics, so does anyone here have an explanation on how boomerangs "work"?

 

-Does it return, because you throw it fast and its spinning fast but as it slows down, it still keeps spinning, causing it to...uhh never mind. [/quote']

 

 

I've never thought about this myself, but as with any question of this nature, one needs to use the laws of physics to answer it.

 

I could try to google for the answer, but then again i could try to figure it out on my own.

 

Lets see.

 

You throw a boomerang in some direction, with some initial velocity v.

 

Now the boomerang itself is spinning very fast, and this matters.

 

What happens, is quite the result of an interaction with the boomerang, and the surrounding air.

 

Now, a boomerang is shaped like a V kind of.

 

So its center of mass does not lie within the object itself.

 

The boomerang approximately travels in a circle, and this is what you want to understand. Why does it do that, instead of just keep going away, in a straight line.

 

Now, the velocity v is a vector, and it is from the origin of some reference frame to the center of mass of the boomerang.

 

The boomerang itself is spinning, and the axis of revolution passes through the center of mass. So you can think of a reference frame moving with the boomerang, with the center of mass permanently at rest at the origin of this frame.

 

So if you treat the motion of the origin of that frame as the place whose position in the thrower's frame as being the point in question, then that place moves roughly in a circle.

 

So let m denote the mass of the boomerang.

 

There is a centripetal acceleration of

 

mv^2/R

 

Where R is the radius of the boomerang's orbit, in the thrower's frame.

 

Now, if there were no air at all, then there would be no centripetal acceleration.

 

 

So we can answer the question the following way...

 

The air exerts a force F on the boomerang, and this force arises because the boomerang is spinning in the rest frame of the air.

 

The boomerang also exerts a force F, on the surrounding air.

 

Using classical physics

 

F = mv^2/R

 

To go any further into the problem, would require the use of aerodynamics. And there are quite a few assumptions in there about air resistance.

 

Such as force is proportional to v.

 

Certain assumptions which hold in one situation, wont in another.

 

You could work air pressure into the solution of the problem too.

 

Now a frisbee doesn't come back to you.

 

So I think the answer lies in the V shape of the boomerang, and the fact that it's spinning, and some formula with air pressure involved in it.

 

At least thats a start anyways.

 

Now I will google to see what others say.

 

Here is a cool site: Physics of a boomerang

 

Here is Bernoulli's answer

 

Here is something i found:

 

Definition: A statement of the conservation of energy in a form useful for solving problems involving fluids. For a non-viscous, incompressible fluid in steady flow, the sum of pressure, potential and kinetic energies per unit volume is constant at any point.

p + qv2/2 + qgy = constant

 

where p is the pressure, q is the density, v the velocity and y the height in a gravitational field of strength g, all measured at the same point. This quantity is then constant throughout the fluid.

 

Bernoulli's principle is used for, but not essential to, lift by airplanes.source

 

To really say you have answered the question, your approach has to predict circular motion. In fact, really it should predict the actual motion.

 

You have to model everything, decide what are the important variables, and ultimately predict a roughly circular path. It's not an easy problem.

 

Regards

 

PS: I can't resist trying to answer it.

 

Here is another link to something which says that the boomerang precesses.

 

I am trying to find a mathematical derivation which predicts circular motion.

 

Here is an exact quote from the source above:

 

When a boomerang is tossed in the correct manner, the wings rotate through the air and react to the aerodynamic and gyroscopic forces. These forces cause the boomerang to circle around and lay down as it returns, until it descends in a horizontal hover. During the flight of the boomerang, the following principles come into play: Bernoulli's relation, gyroscopic stability, gyroscopic precession, and Newton's laws of motion. We shall examine how these forces cause a boomerang to return to the thrower.

 

 

Here is another site which discusses lift.

 

Here is someone who is getting to the heart of it

 

A boomerang does funny things because it is in fact a gyroscope. Aerodynamic forces generate a twisting moment which cause the "gyroscope" to precess and to move on a circular path. (Taken from the link above)

 

All the math needed, for a first approximation to understanding the motion of a boomerang, and thus the answer to your question, is at the site there.

 

Read from "What is a couple?" to equation 8.

 

Start out with this:

 

t = I a

 

The LHS is the greek letter tau, and stands for "torque" or "turning force."

 

On the RHS the letter I stands for moment of inertia, and the letter alpha stands for angular acceleration.

 

I am trying to find a site which gives a clear presentation.

[reverse]

I have always wondered how a boomerang manages to reach a certain distance and then start back towards its thrower...

 

I never really thought about the mechanics of it much' date=' mostly because im not to great with physics, so does anyone here have an explanation on how boomerangs "work"?

 

-Does it return, because you throw it fast and its spinning fast but as it slows down, it still keeps spinning, causing it to...uhh never mind. [/quote']

 

circular motion is circular motion.

 

two forces.

 

in this case lift comes into play as well.

 

I wonder how a stoneage people stumbled across this "quirk" in the first place.

 

here is a perfect diagram of the flight.

 

http://www.rangs.co.uk/howaboomworks.htm

 

 

this is another crazy hunting tool that must have been a fluke.

 

http://www.hollowtop.com/atlatlbob.htm

 

[Johnny5]

circular motion is circular motion.

 

two forces.

 

in this case lift comes into play as well.

 

I wonder how a stoneage people stumbled across this "quirk" in the first place.

 

here is a perfect diagram of the flight.

 

http://www.rangs.co.uk/howaboomworks.htm

 

 

Nice picture of the path, not exactly a circle, not an ellipse, but a closed orbit nonetheless.

[reverse]

You know, I just had a thought.( don’t look so surprised )

 

We think of stone age peoples as less technologically advanced than say iron age peoples.

 

But… what we see in these unique hunting tools is the employment of structural properties similar to the current use of Kevlar and other modern day cutting edge technologies.

 

Perhaps it is foolish to look at technological advancement in terms of metal.

[towjyt]

Here is a web site that explaines it quite well

 

http://science.howstuffworks.com/boomerang.htm

[Glider]

I made a boomerang that works extremely well. I've nearly killed myself with it many times (it's quite large too).

 

Thje way I did it was to make each of the 'wings' an aerofoil profile. Holding the flat side in the palm of your hand, the top blade (pointing forward) has the leading edge facing forward and the blade in your hand has the leading edge facing back. When thrown (hard) it gains altitude and circles around really well.

 

On traditional boomerangs, I believe they are not quite so complex as to have actual aerofoil profiles, but they still have a flat side and a curved side and this acts in the same way (obviously).