and how do you apply Bernoulli's theorem to it?
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:
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.
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.
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.
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.
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:
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.
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.
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 web site 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.
Do you have that last bit on ctrl+v now Jeff? :P
I should or at least keep a copy of it as a text document.
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