A phenomenon that applies to (gasp!) gyroscopes and other entities that exhibit similar characteristics, for example car engines and helicopter rotors.

A gyroscope, when spinning, will tend to resist being tilted off its rotational axis. Gyroscopic precession is the reason for this, as well as the amusing things that you can make gyroscopes do. The principle essentially states that a force applied to a rotating object will take effect 90° around the direction of rotation. That's why it feels so weird when you're in the science museum doing that experiment where you hold a spinning bicycle wheel by its axle and try to tilt it.

The diagram below illustrates how this works. Um, pretend that it's a gyroscope viewed in plan, spinning clockwise.

If we apply a downward force here (ascii art inaccuracies notwithstanding)...
              |
              |
              V
         _.-""""-._
       .'     |    `.
      /       | 90°  \
     |        |       |
     |        |-------|<--- ...it takes effect here.
     |                |
      \              /
       `._        _.'
          `-....-'

Instead of tilting towards 12 o'clock, the gyroscope tilts towards 3 o'clock. This principle can induce interesting behaviour. Take the following situation:

                   
   _       || <--G  _
  |_|      ||      |_|
  |A|------||------|B|
  |_|      ||      |_|
  | |      ||      | |
  | |              | |
__| |______________| |__

G is a wheel on an axle, which is supported between two posts A and B. Say you start the wheel spinning in a clockwise direction, looking from B. If you leave it, it'll keep spinning until it stops. But what if you remove B? Once you do there is nothing to counteract gravity at that end. What happens? Common sense dictates that the unsupported end of the axle - and therefore the wheel - will simply fall to the ground. Actually something more interesting occurs...

              A
              ||
              ||
              ||\
              ||  \  ______
             _||_   /      \
                   |        |
      <--------    |    \   |
  Resulting force   \_____\/
                            \
                        |
                        V
                     Gravity

Since the wheel is spinning clockwise (as we look at it in the diagram above), the force acting to pull the wheel downwards will translate to pull it sideways, to the left. The wheel will start to spin - to precess - around A on the axle and will continue to do so, apparently defying gravity as long as it is spinning at a sufficient rate. As it slows it will gradually descend to ground level as the energy stored in the gyroscope is depleted, reducing the force counteracting gravity. Other things like a gyroscope walking tightrope, hanging on the end of a piece of string or spinning around at a strange angle are all down to gyroscopic precession.

This principle affects many things, such as the reaction of wind generators to crosswinds, the way cars react to turning, and, um, the earth (I'll come back to this). The crankshaft/flywheel arrangement of the engine may be thought of as a gyroscope of sorts, which like all gyroscopes is resistant to changes of attitude. The effect this has on the car depends on which way the engine is mounted - longitudinally or transversally (the crankshaft being in line with, or perpendicular to the car's direction of travel, respectively. Consider a couple of cars, A with a transverse engine and B with a longitudinal engine:

        ______       ______
       | ____ |     | |  | |                   _______
   X  |||____|||   || |  | ||                 /   1   \
       |      |     |  ||  |                 |         |
       |  A   |     |      |                 |2   O   3|
      ||      ||   ||   B  ||                |         |
       |______|     |______|                  \___4___/

                        X          Reference flywheel, as seen from X

X - vantage point, from which the engine of the car is rotating clockwise.

This is simplified, the flywheel representing the engine since it, handily, is a spinning disc. Now, if both cars were travelling along at a fair rate of knots and made a sharp right turn, they would react differently to one another.

Turning car A right would, seen from above, in effect be rotating the engine clockwise, or applying a force towards point 2 of the flywheel. The flywheel is rotating clockwise, so gyroscopic precession will result in the force being exerted on point 1. Since the engine is fixed to the body of the car, the car will - notwithstanding other effects such as weight transfer - lean to the right. Car B, on the other hand, has the engine mounted at a different orientation. Turning car B right, again effectively rotating its engine, will again apply a force towards point 2 of the flywheel. Gyroscopic precession will again result in that force being exerted on point 1, but because the engine orientation is different, will pitch the car forwards. With a left turn, the opposite will occur: car A will lean to the left and car B will pitch backwards.


Gyroscopic precession is also a critical consideration in helicopter rotor system design. Without being too specific about the mechanics (covered elsewhere), in order for a helicopter to make pitching movements its rotor disc - the disc traced by the rotor blades as they turn - must be tilted in the desired direction. For the helicopter to pitch forwards the rotor disc must be pitched forwards. For a backwards pitch the rotor disc must be tilted backwards, and so on.

Fair enough, but because the rotor blades spin about a centre they have some gyroscopic behaviour, so it's not as simple as just applying force to the rotor disc in the desired direction. The controls must act to tilt the rotor disc in a direction which is 90° 'behind' the desired direction; the direction in which the force is applied depends on the direction the rotor blades turn: clockwise or anti-clockwise. The principle is fairly simple but it horrendously complicates the way a helicopter's rotor system must be designed, already a thicket of deeply nested force-counteracting mechanisms, without any of which the helicopter could not fly.

If a helicopter's rotors turn anti-clockwise when viewed from above - as do those of most modern helicopters - if the rotor disc is to be pitched forward, that motion must be preceded by 90°. That is, the control system must act to tilt the rotor disc 90° before the desired pitch direction, which would be 90° clockwise in this case. So if we want the rotor disc to pitch towards the 12 o'clock position we must act to pitch it towards the 3 o'clock position. The result will be a pitch towards 12 o'clock.


As I mentioned earlier, gyroscopic precession also applies to the planet earth, obviously a spinning object too. A combination of the earth's irregular shape (flattened at the poles, bulging slightly at the equator) and the tidal forces of the moon and the sun causes its axis to precess. The action is much like the top of a spinning top tracing a circle as it rotates.

The south pole, comparitively, does not shift much but through a period of roughly 25,800 years the earth's north pole traces a complete circle with a radius of 23.5°. This is why, for example, the north star is currently Polaris but in 3000 B.C. was Thuban, and in 14,000 years will be Vega. The stellar sphere shifts over the 25,800 year period, meaning at different times different stars will be closest to the earth's axis. This is explained further in Precession of the equinoxes.


It is worth noting in closing that gyroscopic precession only applies when a force acts to tilt the axis of a rotating body. Gyroscopic precession has no effect when a force simply changes the position of the axis and not its attitude. With the earlier example of holding a spinning bicycle wheel by its axle, there will be no effect felt if the wheel is moved up, down, forwards, backwards or from side to side without tilting it.


Sources:
  • Cantrell, Paul; "Gyroscopic Precession"; <http://www.copters.com/aero/gyro.html>
  • Siltec Ltd. (author unknown); "Gyroscopic Precession"; <http://physics.nad.ru/Physics/English/gyro_txt.htm>
  • Turner, Glenn; "Gyroscopes"; <http://www.gyroscopes.org/behaviour.asp>

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