Calling Nick Lappos - Blade Stall

[dClbydalpha]

AnFI, the discussion of such concepts is important, but fundamentally the premise that for a given rotor system there is a "coning angle" that is the equivalent to a "stall angle" for a fixed wing does not stand up against the physics of the situation.

I am glad you acknowledge the nature of downwash. Downwash is the important factor that appears to be missing from your conceptual model, and where my musings began. The reason I suggest a uniform downwash, and a linear twist is that it makes the first calculations easier. If you can envisage the form of the integral that incorporates a linear twist and a uniform downwash then you can see how it can be extended to more exotic implementations.

So there are a number of forms of the equation below but it is pretty well recognisable

dL=1/2 ρ c dr a [ θ - u/Ωr - τ(r/R ) ]

c is the chord at that section
dr is the element of radial blade
a is the coefficient of lift of the aerofoil with α
θ is the original pitch of the blade
u/Ωr is the difference of α generated by the downwash with respect to the tangential velocity of the blade
τ(r/R) is the difference of α generated by the twist of the blade

If you choose not to have a uniform downwash, u, then you replace u with a function that represents the value of u at blade element r. Similarly for τ. But even in its simplest form it shows the importance of the induced downwash term when calculating lift.

Your suggestion of providing a blade design that matches lift to centrifugal force is intriguing, but can only really be considered as self-defeating to your hypothesis. I'll explain the steps why in words rather than equations.

Change CL such that it is proportional to the distance along the rotor.
Lift is now changed with proportion to the distance along the rotor, except for the fact that the change in lift has induced a change in the relationship between local downwash and tangential velocity i.e. it has changed the α and therefore the lift, so the lift is slightly off of the expected value.
You compensate this delta by tweaking the rate of change of CL along the blade and so now the lift is as you required.
What you find by doing this is that the "tweak" is only valid for a given rotor speed. You change the rotor speed and you need a different relationship between CL and r. Without adaptive aerodymanics this is impossible.


So what have we discovered?
The concept of relating coning angle to a "stall" condition can only be done for a known rotor system, with a specific relationship between CL and r, and at a particular rotor speed. Something that I hoped I had pointed to in my original posted reply. This is a long way from the concept of a generic, rotor speed independent relationship hypothesised.

This of course is totally academic as it has so far only touched on the rotor in hover. As soon as any cyclic commands are input, then the disc tilts and the axis of the cone along with it. Having done that we will start to translate, creating an asymmetry of lift. The whole concept of "stall" then involves flapping, advancing blade and retreating blade dynamics.

There is a relationship between aerodynamic and inertia forcings, called the Lock number, which is important to rotor design. But that is another topic.

So I'm genuinely sorry AnFI I don't see what this important topic is. I must be missing the scenario you are thinking of as there doesn't appear to me to be any reason to monitor coning angle as a critical flight parameter. To the pilots out there, have any of you flown with a coning angle indicator marked with a critical value?