Originally Posted by
SansAnhedral
Spline claims that:
Exactly how do you propose you achieve stiffness for the same strain within a linearly scaled aero envelope without increasing structure and in turn weight?
An increase in size by a factor of 2 would require a
quadratic increase in stiffness (EI), as your material modulus is invariant in our example case. Greater stiffness with the same materials requires more material, and results in larger weight and therefore larger loads. This is a snowball effect. Mach scaling a rotor radius 200% is a cubic function for mass, square function for loads.
A blanket statement like:
in light of the immense structural changes required by scaling up is dubious. I've seen it time and time again on trade studies of rigid rotors - from coax to tiltrotor.
In any case, the added mass has a cascading effect on mast moments and rotor hub structure also increasing the sizing in the non-blade rotating system as well.
If rigid rotors in general scaled as easily as you suggest here, then existing conventional medium and heavy helicopters would already implement that rotor system as it offers significantly better control power and a far less complex and costly rotor head assembly. Sikorsky also would not have candidly admitted that
X2 technology does not scale beyond the medium class in 2011
Edit: The link is now dead, I wonder why?
Alt reference
Sans, when you double the rotor radius and hold solidity, blade number, and airfoil family constant, you get a fourth order increase in cross section stiffness as part of that scaling. Mass per unit length is a second order scaling which leads to natural frequencies being inversely linear with the radius doubling, which is good, because so does the rotor rpm to hold tip speed constant. That also means that fan plots tend to look similar for each type of rotor, somewhat regardless of diameter. Of course, specific design details like abrasion strip thickness and other details don't scale linearly with rotor radius, so there is some variation in resulting fan plot, but the principle holds. This is true for articulated and rigid rotors.
My previous comments on strains is also true for articlated and rigid rotors and it's why I've been able to use the same materials for all of my rotor designs despite an order of magnitude range in their diameters.
The reason we don't see more rigid rotors is as you alluded... they do weigh more. The flapping hinge, despite the mechanical complexity, is a wonderful elegant invention. A rigid rotor produces high vibration, huge moments, and not always in helpful directions. They're twitchy, high gain beasts. Do they have their applications? I believe yes, but certainly not for every helicopter design.