I am not a physicist, but ISTM that since force applied to a rotating mass manifests itself 90º later in the direction of rotation, then for all practical purposes it’s ‘exactly’ 90º. Note that a ‘rigid’ rotor system isn’t actually ‘rigid’. The blades are long and thin in any rotor system, so they are subject to coning. (i.e., as lift is generated and is applied against the mass of the helicopter being pulled by gravity, they flex upward.) Since the rotor diameter is lessened as the tips rise, the blade is subject to Coriolis effect and they speed up. Then you have the flapping and feathering going on. Hold your arm out with your palm flat, and twist your hand as if you’re ‘flying’ it out a car window to represent the cyclic pitch changes. Then make small circles with your entire arm to represent the cyclic speeding up and slowing down due to Coriolis, and the flapping being used to compensate for dissymmetry of lift. There’s a lot going on with those blades!
In all rotor systems, pitch changes are handled by the ‘pitch hinge’. Pitch changes are controlled by the cyclic stick, which moves the stationary star. The blades are attached to the rotating star, which, through linkages, changes the pitch of the blades as they rotate. As expected, the stationary star is linked so that pitch changes are input 90º before they are ‘needed’, and the input manifests itself in the correct place.
In a fully-articulated rotor system, each blade has a lead-lag hinge that allows it to speed up and slow down for the Coriolis effect, and a flapping hinge to allow it to flap up and down.
In a semi-rigid, or teetering, rotor system, the flapping hinge is the central pivot of the rotor system, and is called the ‘teeter hinge’. Like a teeter-totter, the blades flap as a unit, with each one rising the same amount as the other descends.
In a rigid rotor system, you only have the feathering hinge, and the flapping and lead-lag are handled by the flexibility of the blades.
Anyway, with all of that flapping and speeding up and slowing down going on, I don’t know if control inputs manifest themselves exactly 90º in the direction of rotation; but I think if all of the movements are averaged (or cancelled out), they do.
I’m not sure what you mean by ‘stem’. Are you talking about the different types of rotor systems?
Generally, any machine is designed to accomplish a specific mission better than it accomplishes other missions. I’ve never flown a rigid-rotor helicopter. Those are on machines that are larger and more expensive than I could rent. I would assume that rigid rotor systems work better for the missions those helicopters are designed for.
Two of the most popular piston-engine helicopters are the Robinson R22 (and its larger brother, the R44) and the Hughes 269/Schwiezer 300/Sikorsky S300. The former has a semi-rigid rotor system, and the latter has a fully-articulated rotor system. The Robinsons were designed specifically to be inexpensive. (‘Inexpensive’ being quite relative when talking about helicopters.) A semi-rigid rotor system has fewer parts than a fully-articulated system, so it’s easier and less expensive to build and maintain. The Hughes 269 was designed as an Army trainer. Why does it have a fully-articulated rotor system? I don’t know. I could guess that the Army’s larger helicopters (Sikorsky S-58, for example) had fully-articulated systems, and it was seen as advantageous to provide training in a helicopter with the same system; but that guess would be based on virtually nothing. (See how my last guess turned out, upthread.
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I think part of the answer comes down to tradition. Sikorskies tend to have fully-articulated rotor systems, and Bells have semi-rigid rotor systems. Aircraft designers are a conservative bunch, so they built what they knew. Note though, that newer offerings from those companies have helicopters with rigid rotor systems (e.g. Sikorsky UH-60 and Bell 412) for military and industrial use. They must perform their missions better than the other two systems. Also note that materials have come a long way in 70 years, and rigid rotor systems were unavailable when helicopters began to mature.