Today's helicopters require the rotor to product the lift and the forward propulsion.
It would appear that the inclusion of a propulsive device, such as a propeller, will reduce the thrust that is demanded from the rotor, for a given forward velocity. This lower thrust from the rotor will mean a reduction of the high pitch angle on the retreating blades. In turn, this will result in a retreating tip that is further from stall and a retreating root that is producing less negative lift.
All of the above should result in a slightly fast forward speed for a given power. Perhaps, the Lynx speed record could be considered as an example of this.
In addition, since less of the 'given power' is being consumed by the main rotor it means that less power is consumed by the tail rotor or the drag of the rudder to counter the rotor's torque. This was previously look at by Sikorsky when they placed a swingable tail rotor on an existing craft.
Makes one think that a union of the helicopter and the gyrocopter may be in the future.
Makes one think that
a union of a symmetrical twin rotor helicopter and the gyrocopter may be in the future.