The electromagnets will be stationary (stator). A set of permanent magnets will be located on each rotor. The alternate phasing of the electromagnets will synchronize the two rotors. A means of assuring counter-rotation at startup must be incorporated if 2-phase is used instead of 3-phase. As on alternative A, the relatively slow speed of the rotor blades is achieved because of the large motor diameter, but it does not take advantage of the 2:1 reduction.

Some predictions for the not to distant future;
~ Rotors will be powered by electric motors.
~ The use of an electric disk-motor will eliminate the need for gears.
~ Dual main-rotors will have a separate motor for each rotor and the inter-phasing of these rotors will be maintained electrically by encoders.

"~ The use of an electric disk-motor will eliminate the need for gears."

No. Electric motors have a maximum torque/mass figure driven by the 1 tesla flux in the mag circuit. Gears are good in that they allow the motor to spin at high RPM to maximise power/mass. Disc motors reduce mass/torque (less mag circuit iron) but would still benefit from high rpm.

Your knowledge of electricity is far above mine, so I get to question you.

Mass/Torque:

An electric motor that is extremely fast and small has an advantage. However, the helicopter rotor is a large disk with insignificant thrust comes from its center. Why could not a reasonably large diameter, linear induction disk motor be an integral part of a special rotor hub, which is shaped like a very large Frisbee? It might have thousands of poles (with 50% or 33% of them activate at one time) and air bearings to maintain the gap. The weight will be kept down by the preceding integration, composite construction and the elimination of the gearbox.

To double the motor's speed on coaxial helicopters, the motor could be located between the rotors, with the 'armature' connected to one rotor and the 'stator' to the other rotor.

Potential Intermeshing failure:

What if triple redundancy was applied to all facets of the drive. In other words, separate batteries, motors, and controls etc. Electrical systems are very reliable, but, if one system went down, the other two would probable still provide slow level flight.

The large electrical force and its large moment arm should be able to maintain rotor inter-phasing, considering that CNC milling machines can inter-phased multiple motors to within a 10th to 100th of a degree.

Just a demented idea.

"Why could not a reasonably large diameter, linear induction disk motor be an integral part of a special rotor hub, which is shaped like a very large Frisbee?"

Why not, but aerospace motors and generators run at 80'000 rpm regardless of shape. Any less and you are just introducing unecessary weight.

"It might have thousands of poles (with 50% or 33% of them activate at one time) and air bearings to maintain the gap."

Why not. Sounds unecessarily complex to me though and doesnt get around the torque/mass limitation. You are just packing more copper into the 1 Tesla mag flux.

"The weight will be kept down by the preceding integration, composite construction and the elimination of the gearbox."

Nope. You still need an iron return circuit, which is the cause of the 1 Tesla limit. Careful design can just about get up to 2 Teslas. Nano carbon fibre promises room temp superconductivity, but you won't be able to buy 'em for quite a while.

"To double the motor's speed on coaxial helicopters, the motor could be located between the rotors, with the 'armature' connected to one rotor and the 'stator' to the other rotor."

Sounds draggy. Why not just use an epicyclic reduction gearset (lowest mass for given torque) and run the motor at 80'000 rpm, or whatever is centrifugally achievable? Why not use a gas turbine...

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"What if triple redundancy was applied to all facets of the drive."

Then, as long as pilot (or more likely operator) has common sense to ground aircraft on single failure, the crew only crash and die during a triple failure. What if a +ve lightning strike over the north sea wipes out all of the redundancy?

"The large electrical force and its large moment arm should be able to maintain rotor inter-phasing..."

Agreed, but so should gears. My concern comes from the fact that the best motor will likely be a brushless DC requiring power electronics, unless you want all the wear and reliability problems of a brush. The power electronics, although reliable, do go wrong and never when you want them too. You are talking about aerospace motors, which will have to run at high rpm, and are going to be expensive. When was the last time you drove a hybrid car? I drive a diesel.