On the flapping and lead-lag blade oscillations (in German)

C. Beaty

Gold Supporter
The Australian Aborigines figured out rotor physics several thousand years ago when they developed the boomerang. It flies a curved path as a result of aerodynamic forces causing gyroscopic precession but does it flap and lead/lag while in flight?

A helicopter/gyro rotor neither flaps or lead/lags when viewed from the real axis of rotation, the tip plane axis. Viewed off axis, we can imagine all sorts of motion taking place; for example, the valve stem of a rotating bicycle wheel moves nearer and farther away from the viewer if not viewed along the real axis of rotation so we could say it is flapping but that’s only an illusion.

JC’s plank on a rope should have brought clarity to lead/lag/flap confusion but maybe not.

Jean Claude

Junior Member
As always, coming from Chuck, this is an excellent example.
Seen from an observer on the ground, the accelerations of the valve stem are a very complicated mathematical exercise,
Sans titre.png

While for the physicist, it is nothing complicated: Only the centrifugal acceleration


My physics professor said that "centrifugal" is, at best, misleading; there is only 'centripetal' (positive and negative signs) force.


Supreme Allied Gyro CFI
Your professor was expressing a perfectly reasonable preference for inertial reference frames and the avoidance of "false" apparent forces. An astronaut candidate getting a 9-g centrifuge ride will have difficulty imagining the force as "false".

I used to use the cycloid path of a bike valve stem as an example when teaching pre-calculus students how to write parametric equations (it produces a nice pair with a sine on one axis and a cosine on the other). If you start a demo with a bicycle held stationary at the front of the classroom, with the valve stems on both wheels at the bottom of their travel, and then ask which way the stems will move when you start to push the bike forward, most will predict that it goes backwards at first, and they are surprised to see the real shape.


Active member
Very interesting paper Javier, it seems to support the view held by naca investigators, that it is sufficient to calculate the Fourier sieries for flapping up to second order. How did you come across a German report, do you speak the language? Actually the author makes things even more complicated by using fairly complicated dependent clauses, well them Germans, you know....;-)