Understanding the Physics of Boomerangs: Applying Bernoulli's Theorem

[vin300]

and how do you apply Bernoulli's theorem to it?

 

[mgb_phys]

http://plus.maths.org/issue7/features/boomerangs/index.html

 

[rcgldr]

http://plus.maths.org/issue7/features/boomerangs/index.html

Not all boomerangs fly in a smooth circle, they have to be designed and thrown just right. Some boomerangs have sufficient outwards roll response to result in a figure 8 pattern. Regarding the web site:

1. What is (near enough) the shape of the flight path of a boomerang?
A. out and back on a straight line;
B. circular;
C. around the four sides of a square.

Circular is rare. The radius and altitude usually change during flight, and as mentioned sometimes the result is a figure 8 pattern. A hint of the transition into the figure 8 pattern where an outward roll has gone beyond horizontal is evident in a few clips of the videos there.

4. A helicopter rotor has four blades each in the shape of:
A. a feather;
B. an airplane wing;
C. a circular tube.

Unlike wings, most helicopter rotors use symmetrical air foils, to eliminate the pitch down reaction torque of a cambered airfoil. The pitch down torque puts a strain on the rotor head connections, and can cause the rotor blades to flex in the downward direction at the tips.

6. The lift force of a spinning boomerang is directed mostly:
A. downwards;
B. towards the centre of its circular flight path;
C. there is no lift force.

By definition, the lift force is the force perpendicular to the path of the boomerang. In the case of a boomerang, the lift force is nearly perpendicular to the plane formed by the rotating boomerang. So the lift force is upwards and/or inwards.

7. As a spinning boomerang moves forward the uppermost blade moves:
A. at the same speed as the centre of the boomerang;
B. faster than the centre of the boomerang because it is spinning and moving forwards at the same time;
C. downwards.

Boomerangs can be thrown underhanded and fly just fine, so it's not the uppermost blade, but the forward moving blade that moves fastest with respect to the air.

8. The top of the boomerang generates more lift than the bottom because:
A. it is bigger;
B. it is moving faster;
C. it is heavier.

Faster is relative to some frame of reference. This effect is better stated as the amount of mass of air affected by an air foil passing through a volume of air is greater above an airfoil than below, for most air foils, but not all. Here is an exception:

9. The difference in lift between the top and the bottom of the boomerang:
A. doesn't matter;
B. forms a couple which causes gyroscopic precession;
C. causes the boomerang to bend.

There is no difference in "lift" between top and bottom of an airfoil. An airfoil just senses a difference in pressure, lower above, higher below, regardless of the deviation from ambient pressure. The gyroscopic precession occurs because a torque along the pitch axis results in a reaction along the roll axis. In the case of a boomerang, a pitch down torque results in an inwards roll.

10. Lift on a boomerang causes circular motion and gyroscopic precession:
A. which is too complicated for me to understand;
B. which balance perfectly - truly a wonderful miracle of nature;
C. which the Aborigines could have told you 10,000 years ago.

A. which is too complicated for anyone to understand;

Navier Stokes equations can't be exactly determined for all but the simplest of reactions between solids and fluids or gases. All anyone can do is get a close approximation and then use wind tunnels or actual flight testing to confirm aircraft design.

The basic concepts can be defined, but a "balanced" boomerang that truly holds a constant radius while is slows down would require a good balance between pitch to roll coupling, throw direction, hrow speed, and the rate of initial rotation of the boomerang from the throw.

Bernoulli

In most (real world) cases, the interaction between a solid moving through a fluid or gas violates Bernoulli principle. Bernoulli principle applies to the reaction of that fluid or gas away from the immediate vicinity of the interaction with a solid. So Bernoulli is violated when the boomerang interacts with the air, but the surrounding air's response to the change in speed or pressure of the air near the boomerang do comply with Bernoulli. This website about propellers explains this:

But at the exit, the velocity is greater than free stream because the propeller does work on the airflow. We can apply Bernoulli'sequation to the air in front of the propeller and to the air behind the propeller. But we cannot apply Bernoulli's equation across the propeller disk because the work performed by the engine (by the propeller) violates an assumption used to derive the equation.

http://www.grc.nasa.gov/WWW/K-12/airplane/propanl.html

 

[xxChrisxx]

Do you have that last bit on ctrl+v now Jeff? :P

 

[rcgldr]

Do you have that last bit on ctrl+v now Jeff?

I should or at least keep a copy of it as a text document.