Abstract

We explain how the rotation of a boomerang generates non-uniform lift causing precession making it return after traveling a long distance.

A Boomerang Acts Like a Wing

That the rotation of a boomerang improves flight stability and eliminates wobbling is easy to understand. To

understand that the rotation also increases the distance a boomerang can travel and makes it return, is less obvious.

To understand the remarkable flight characteristics of a boomerang, it is necessary to understand how the wing of an airplane or bird is capable of generating large lift L with small drag D, with a lift/drag ratio L/D between 10 and 20, as explained in the Knol Why It Is Possible to Fly . With this basis, we now seek to understand the flight of a boomerang, starting with the observation that a boomerang acts like a pair of wings generating lift and drag just like a wing.

A boomerang is flat on one side and slightly curved on the other with cross-section like a non-symmetric wing with rounded leading edge meeting the air oriented as in the following figure, also indictaing how it is thrown by an aboriginal inventor in person:

Shortcut to Action of a Wing

In the following pictures we decribe how the flow of air around a wing generates large lift and small drag by a perturbation of zero lift/drag potential flow arising from a mechanism of instability at separation changing the pressure distribution around the trailing edge. The perturbed flow does not separate at the crest because the boundary layer is turbulent which in a fluid of small viscosity acts like a slip boundary condition. On the other hand, viscous flow with a laminar boundary layer separates at the crest and gives poor lift and large drag.

Sideview of velocity and pressure, and topview of streamwise vorticity of Naca0012 wing at aoa = 14. Observe the turbulent streamwise vorticity emanating from separation instability. Computed solution of the Navier-Stokes equations with slip boundary condition [1]. It is possible that the rims (and holes of some frisbees) of a frisbee trigger transition to turbulence in the boundary layer and thus improves
the flight.

Principle of action of a wing: Potential flow (upper left) with zero lift/drag modified by low-pressure counter-rotating rolls of streamwise vorticity from instability mechanism at separation (upper right), switching the pressure on rear wing (bottom left ) to give both lift and drag (H high, L low pressure). Viscous flow separating at the crest with low lift and large drag (bottom right).

Action of a Boomerang

The following figure is taken from the educational site Hyperphysics and describes how for a

vertically rotating boomerang the horisontal spin interacts with the horisontal torque arising from a larger lift force on the top because of higher speed relative to the air, to generate a vertical torque causing a precession causing a deviation to the left and making the boomerang return:

The explanation of the precession is correct, but as concerns the generation of lift Hyperphysics refers to Nasa confusion, which does not offer any explanation of lift, only confusion. But Why It Is Possible to Fly offers an explanation as shown above, which thus combined with the effect of precession, explains the essence of the flight of a boomerang:

the wing shape generates lift from rotation and forward motion
the spin combined with torque from non-uniform lift causes a drift to the left (if thrown with the curved side to the left).

A closer look shows that the boomerang is thrown slightly tilted clockwise from the vertical, which after the speed has been reduced and the boomerang has turned around makes the return in more horisontal position.

As concerns lift, we understand that the rapid rotation of a boomerang makes the boundary layer turbulent even with moderate forward speed of the boomerang, which makes the it into an efficient wing with L/D > 10 allowing a long distance of travel under moderate initial speed. A boomerang with L/D = 20 will be able to fly 200 meters if it climbes to a height of 10 meters.

What determines if the boundary layer is turbulent (which is good) or laminar (which is bad) is the

Reynolds number = Re = UL/v where U is a relevant speed, L is a relevant length scale and v is

(kinematic) viscosity which for air is about 0.00001. The switch from laminar to turbulent boundary

layer occurs at Re ~ 100.000. This means that for a non-rotating boomerang at normal throwing speeds, the boundary layer is laminar with separation on the crest and poor lift/drag ratio. On the other hand, for a

rapidly rotating boomerang, the boundary can become turbulent which evidently drastically improves the lflight characteristics.

The WFDF WFDF World Record long distance boomerang is 238 meters, that is 476 m with return,

to be compared with discus throw: 74m, hammer throw: 81m, and javelin throw: 98m (without return).

Misconceptions and Confusion

The flight of a boomerang carries the same misconceptions and confusion as the generation of lift and drag of a wing:

Popular Mechanics on LIFT: Air passing over the curved top of a boomerang’s airfoil — at the leading edge of the wing — is forced to go faster than air passing over the relatively flat underside. As described by Bernoulli’s principle, this generates less pressure above the wing, creating upward lift.
Popular Mechanics: Eric Darnell, a soft-spoken 62-year-old Quaker and backyard inventor from South Stafford, has coached three U.S. boomerang teams and explains with a blizzard of information about airfoil shapes, Reynolds numbers, local atmospheric conditions, wind shear and the effects of drag: “One of the things that is near and dear to my heart about boomerangs is that there’s still some magic involved. You can’t completely computerize them. I’ve seen computer-designed boomerangs, and they’re junk… it’s not in textbooks about airfoils.”
Boomerangs.com:The question, what kind of mechanisms convert the drag force into the lift one, still remains under discussion.
Sports Science:The air moves faster over the upper surface than the air moving over the lower surface. This means that a pressure differential exists between the lower and upper surface which translates into lift.
Research Support Technologies: Air stream “sticks” to surface and bends down the near upper surface of the wing not due to Pillow phenomenon but due to Coanda effect.