How to Behave if you are Rotating

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This chapter is meant to make you understand the "instincts" of a rotating object, such as a diabolo, a frisbee, a boomerang, a ballet danser making a pirouette or an autogyro rotor. The autogyro rotor is somewhat special, because it has a limited freedom of choosing its own rotating axis.

Let's start with the diabolo. You can correct the orientation of diabolo if you know the first law of rotating things:
Thou shalt react a quarter of a cycle later.

An example. If you look at the picture, you can see me holding a diabolo. Suppose I move my right hand forward (towards you) and my left hand backward (away from you). If the diabolo is not spinning, it will turn left (yawing movement). However, if the diabolo is spinning, it will turn either forward or backward (banking movement). If the direction of rotation is such that the right-hand side is moving up, it will rotate forward.
In other words: If I give it a turn about a vertical axis, it will respond by turning about a horizontal axis.

This phenomenon is also visible in autogyro rotors: clearly the advancing blade will get the most lift and will therefore be pushed up. As a reaction it will be the front blade (a quarter of a cycle later) that moves up.

Let's look at a frisbee. If you throw it without giving it a spin, it will increase its angle of attack until it whirls out of the air. This will happen just within a few meters.
Now throw it again, but give it a spin while you are throwing it. Now it can fly easily over a hundred meters. It will turn slightly away from the thowing-hand if you have launched it horizontally. This brings us to the second law of rotating things:
The faster you spin, the less you should bother to react to external torques that are not acting about the rotating axis.
In other words:
The faster you rotate, the more stable you are.

In an autogyro rotor, rotational speed is needed to keep the blade flapping at a normal level. If, for whatever reasons, the rotor turns at a low speed, the blades can hit the stops too hard due to excessive blade flapping. This is one of the reasons why the rotor must be secured when the autogyro is parked outside.

You might be more familiar with a boomerang. Let's use the aforementioned laws to describe the path of a boomerang.
Using the second law it will show a slow change of course.
Using the first law, we come to a complicated orbit. You launch a boomerang like this: Take the boomerang in your right hand, by the lower blade. Hold the boomerang such that it will generate lift towards the left. Throw it away with a good spin.
The upper blade will now generate the most lift, causing the front blade to be pushed to the left (first law). The boomerang turns left and will keep on turning left until it gets back to you or runs into something. As a secondary effect, the front blade is so wide that it will catch wind, causing the lower blade to be pushed a little to the left as well, so that the boomerang "flattens out": it will fly in a more horizontal way when it gets back to you.
With some boomerangs (I've seen one that did it in my life) you can see another phenomenon: it catches up more rotational speed just after you've let it go. This is something familiar. It's called autorotation.
You can now understand why the hinges in rotors are so important. Before Juan de la Cierva built his autogiros, he built models first. These models flew relatively well, but when he built the first real-size autogiros, these aircraft rolled over to the size when taking off. In fact, the rotors still behaved like boomerangs. It was only when he realised that his models could fly because of the flexibility of their blades, when Juan de Cierva decided to use flapping hinges.


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