Originally Posted by
SplineDrive
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.
We are actually in agreement on the bulk of what is being discussed from a theoretical standpoint, however the idea that one can actually leverage existing (high) modulus materials used on the X2 and S97 and continue to scale up to achieve a physically manufacturable stated 1:1 cross sectional area increase to yield the required 16x stiffness to maintain strain and loads is the issue at hand. A real physical implementation will always require variations (typically the larger the less efficient the structure due to manufacturing constraints, and achieving scaled stiffness will almost invariably require more material and weight) which make for significant diminishing returns.
Even with bleeding edge UHM materials the weights still increase to a point where hub attachment and inboard structure gets to be the root (no pun intended) of the challenge for a high speed flying vehicle, not to mention the potential ILS issues that are readily apparent with very thick laminates making use of such a high percentage of stiff materials attempting to keep weight down.