Torque-induced (gyroscopic precession)

Torque-induced precession (gyroscopic precession) is the phenomenon in which the axis of a spinning object (e.g. a part of a gyroscope) "wobbles" when a torque is applied to it. The phenomenon is commonly seen in a spinning toy top, but all rotating objects can undergo precession. If the speed of the rotation and the magnitude of the torque are constant the axis will describe a cone, its movement at any instant being at right angles to the direction of the torque. In the case of a toy top, if the axis is not perfectly vertical the torque is applied by the force of gravity tending to tip it over.

The response of a rotating system to an applied torque. When the device swivels, and some roll is added, the wheel tends to pitch.

The device depicted here is gimbal mounted. From inside to outside there are three axes of rotation: the hub of the wheel, the gimbal axis and the vertical pivot.

To distinguish between the two horizontal axes, rotation around the wheel hub will be called 'rolling', and rotation around the gimbal axis will be called 'pitching.' Rotation around the pivot axis is called 'spinning'.

First, imagine that the device is spinning around the pivot axis. Then some rotation around the wheelhub is added. Imagine the gimbal axis to be locked, so that the wheel cannot pitch. The gimbal axis has sensors, that measure whether there is a torque around the gimbal axis.

In the picture, a section of the wheel has been named 'dm1'. When the rolling starts, section dm1 is at the perimeter of the spinning motion. Section dm1 has a lot of velocity and as it is forced closer to the center of rotation, it tends to move in the direction of the top-left arrow in the diagram (shown at 45^o in the direction of rolling). Section dm2 of the wheel starts out at the center of rotation, and thus initially has zero velocity before the wheel is rolled. A force would be required to increase section dm2's velocity to the velocity at the perimeter of the pivot axis' plane. If that force is not provided then section dm2's inertia will make it move in the direction of the top-right arrow. Note that both arrows point in the same direction.

The same reasoning applies for the bottom half of the wheel, but there the arrows point in the opposite direction to that of the top arrows. Combined over the entire wheel, there is a torque around the gimbal axis when some rolling is added to rotation around a vertical axis.

It is important to note that the torque around the gimbal axis arises without any delay; the response is instantaneous.

In the discussion above, the setup was kept unchanging by preventing rotation around the gimbal axis. In the case of a spinning top, when the spinning top is tilting, gravity exerts a torque. Instead of rolling over, the spinning top pitches. The pitching motion reorients the spinning top with respect to the torque that is being exerted. The result is that the torque exerted by gravity elicits gyroscopic precession rather than causing the spinning top to fall to its side.

Precession or gyroscopic considerations have an effect on bicycle performance at high speed. Precession is also the mechanism behind gyrocompasses.

Gyroscopic precession also plays a large role in the flight controls on helicopters. Since the driving force behind helicopters is the rotor disk (which rotates), gyroscopic precession comes into play. If the rotor disk is to be tilted forward (to gain forward velocity), its rotation requires that the downward net force on the blade be applied roughly 90 degrees (depending on blade configuration) before, or when the blade is to one side of the pilot and rotating forward.

To ensure the pilot's inputs are correct, the aircraft has corrective linkages which vary the blade pitch in advance of the blade's position relative to the swashplate. Although the swashplate moves in the intuitively correct direction, the blade pitch links are arranged to transmit the pitch in advance of the blade's position.