Phase lag (rotorcraft)
Encyclopedia
Logically, it would seem that for a helicopter
Helicopter
A helicopter is a type of rotorcraft in which lift and thrust are supplied by one or more engine-driven rotors. This allows the helicopter to take off and land vertically, to hover, and to fly forwards, backwards, and laterally...

 to roll to the left (see flight dynamics
Flight dynamics
Flight dynamics is the science of air vehicle orientation and control in three dimensions. The three critical flight dynamics parameters are the angles of rotation in three dimensions about the vehicle's center of mass, known as pitch, roll and yaw .Aerospace engineers develop control systems for...

), lift would be required on the right and a downward force would be required on the left. That is, after all, how an airplane rolls to the left: aileron
Aileron
Ailerons are hinged flight control surfaces attached to the trailing edge of the wing of a fixed-wing aircraft. The ailerons are used to control the aircraft in roll, which results in a change in heading due to the tilting of the lift vector...

s on the trailing edge of the wings simultaneously increase lift on the right and reduce it on the left. Such is not the case with the helicopter, however, but determining that took some trial and error. When Igor Sikorsky
Igor Sikorsky
Igor Sikorsky , born Igor Ivanovich Sikorsky was a Russian American pioneer of aviation in both helicopters and fixed-wing aircraft...

 built the first helicopter, he first set up the controls much as for an airplane, as described previously: if he wanted the craft to drift left, the swashplate was tilted left so the blades would be at maximum pitch (and therefore greatest lift) on the right and minimum pitch (minimum lift) on the left. Much to his surprise, however, the helicopter moved backwards in this configuration. When applied forward input with the control stick, the craft moved left. This was because of phase lag: an input to a rotating mass (such as a gyroscope
Gyroscope
A gyroscope is a device for measuring or maintaining orientation, based on the principles of angular momentum. In essence, a mechanical gyroscope is a spinning wheel or disk whose axle is free to take any orientation...

or the rotor of a helicopter, is felt 90° along the plane of rotation after the point of input. More formally, "a system in resonance receives a periodic excitation force sympathetic with the natural frequency of the system. The flapping frequency of a centrally hinged system is equal to the speed of rotation. Therefore, maximum response occurs 90 degrees after maximum periodic excitation." (Navy Helicopter Flight Training Instruction 2004)

To rig the helicopter for controllable flight, Sikorsky moved the point at which the rotors were attached to the rotating swashplate by 90°. With this new rigging, when he moved the cyclic left, the rotors were at minimum pitch off the nose, and maximum pitch off the tail, and he rolled left. Modern helicopters are rigged the same way.This 'rigging' is known as the advance angle and is the difference in the angle from the rotor hub to the blade pitch control arm and the angle from the rotor hub to the axis around which the blade pitch is changed.
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