You're tracking the heading indicator perfectly on this, the longest leg of your long cross-country solo flight, and the Midwestern terrain is fairly featureless-but still, you should have seen that checkpoint two or three minutes ago. That's got to be the correct river below; there isn't another for more than 100 miles. But none of the bends seem to match your chart, and the bridge you're looking for is nowhere to be found.
You scan the cockpit. The wind correction angle for this leg gave you a cardinal heading, and you've nailed it. Airspeed's where it should be, the wings look level, altitude's perfect. Then you look at the GPS, which you've been ignoring to practice pilotage like your instructor asked-and it says that you're 60 degrees off course.
How could that be? You've kept your heading centered in the heading indicator. You glance at the wet compass which shows...a 60-degree error. When did you last check the heading indicator against the wet compass? Even the best heading indicator can develop significant error if you neglect to reset it for too long.
Otherwise familiar objects are inclined to behave seemingly otherworldly when the axis about which they're rotating is itself inclined by an outside force-that strange phenomenon known as gyroscopic precession. Whether it was that wobbling top you might have marveled at as a kid, a bicycle turning in the direction toward which its rider leans, or as one of the four "left-turning tendencies" you heard about in ground school, pilots have for decades wondered just why it is that when a spinning body is tilted over, instead of obliging in the expected direction, its spin axis leans over in a direction exactly a quarter-revolution beyond where it was pushed. Although this might seem like the Coriolis effect (force in one direction, motion in a perpendicular direction) it is not; this applies to objects undergoing linear motion in a rotating reference frame, while precession involves rotating objects (and their non-rotating observers) in a linear reference frame.
Every rotating object has two qualities. The first is rigidity in space, or resistance to motion (which can seem just as mysterious as precession). This is the principle of the gyroscope, allowing our heading indicators to point true and our attitude indicators (and us) to stay sunny-side up, even in instrument meteorological conditions. The second actually precedes the first, and that is the property of moment of inertia. Possessed by all objects of a given shape and size (rotating or not), it is like a rotational analog to mass, and its magnitude also depends on the axis about which a particular body rotates. A gyroscope's wheel has it; so does a propeller. (For a propeller whose diameter equals that of a wheel of equal weight, it would be about one-half as great.)
In physics, if you take moment of inertia and multiply it by its rotation rate or angular velocity, you get something called angular momentum (a kind of spinning force, and what quantifies the attribute of rigidity in space). This is a vector, having both magnitude and direction (along its axis of rotation and in the direction in which one's thumb points, if the fingers of the right hand were curled to match its rotation according to the "right hand rule").
Our toy top seemingly defies gravity, but not for long. As its angular momentum is torqued downward by gravity, instead of falling over and rolling away, it "falls sideways" and precesses in a circle (in a direction opposite to its spin), and its rotational axis wobbles in an ever-widening cone around an invisible pivot point instead of remaining in a fixed direction. As friction slows it down, this coning goes faster (actually in inverse proportion to the reduction in its rotation rate) until, finally, gravity wins.
Here is an experiment: We'll conjure up a wheel, like the one in Figure 1 (see p. 30), spinning vertically and suspended in space. As you can see, it is spinning with the top going "into the page," as though it would roll away from you if suddenly set down. If this were a trim wheel, we'd say it was spinning about the lateral or pitch axis, and we were rolling in nose-down trim. But let's imagine that this disk represents a spinning propeller. The indicated direction of spin corresponds to that of a normal U.S.-manufactured engine and propeller, if the nose of the airplane is on the left. This is how it might look if we were standing at the airplane's 10 o'clock position, in front of the airplane and to the pilot's left.
Now we will apply a force (in aviation parlance, about the airplane's pitch axis) to the top of the disk, from the right (or "behind the propeller"), as in Figure 1. Now here comes the theoretical part. Let's suppose that we can pick two small pieces of this disk labeled A, and on the other side, B. While A is moving downward, B is going upward. Remembering Newton's First Law, they are going to want to travel in their original direction.
Even though this does not occur discontinuously, nor as markedly as we're depicting here, imagine that a short time later the wheel is tilted over 45 degrees, as in Figure 2. (This is what would happen if our wheel was not spinning, and it wasn't attached to anything.) Notice that A and B still have those vectors attached, and they haven't changed their minds about which way they want to keep going.
Following through until that wheel pirouettes around a full 90 degrees, what do we see? In Figure 3, the vectors for A and B are now pointing perpendicular to the plane of rotation! So, now we will allow reality to reenter the picture and let nature take its course; A and B (and all their neighbors) will go where they wanted to all along, taking the wheel with it, and of course the wheel behaves as though it had been "flipped," not forward into the horizontal plane, but about the local vertical-again, 90 degrees "later" along its original direction of rotation from where the force was applied. In actuality, points A and B would now be on the left and right sides, and not on the bottom and top, because this transition doesn't really have these pretended intermediate stages. Of course, the yaw wouldn't be so dramatically extreme, nor as precise as the exactly 90 degrees' worth shown here.
In reality, the initial and final stages would look something like the "start" and "end" states shown in Figures 4 and 5. Do you notice any similarity between how this disk got yawed to the left, and a particular one of those left-turning tendencies for which we compensate by applying right rud-der-say, when raising the tail off the ground for takeoff in a tailwheel airplane? This resemblance was not accidental.
The reason is simple. It's just Newton's first law, the Law of Inertia: Every object at rest tends to continue in its state of rest, and any object in motion tends to maintain uniform motion in a straight line...unless it is compelled to change that state by forces impressed upon it. It is just this phenomenon, in a controlled fashion, that makes your turn coordinator work. The TC has a spinning gyroscope with its axis tilted up about 30 degrees from the aircraft's longitudinal axis, allowing it to indicate both roll and yaw. (The gyros are realigned by springs, allowing the gimbals to deflect and indicate turn rate. Once a turn is completed, the springs return the gyro to its original orientation.) For a given amount of force, the rate of precession of any gyro is determined by the weight, shape, and speed of its rotor: the same factors that determine its rigidity in space. There is a precise relationship between the rigidity of a gyro and the rate at which a given force will cause it to precess. Of course, those mechanical gyroscopes in aircraft must compensate for their small size by very high rotation rates.
On a considerably grander and more sedate scale, gyroscopic precession affects the Earth itself: Extending the planet's rotational axis out into inertial space (through which the sun and planets move, not what we see when we look up) also traces out a conical figure, but this cycle is completed only once every 25,800 years or so. (From your youth to old age, that's all of about 1 degree.) This is why Polaris won't always be and hasn't always been the "North Star" (currently three-quarters of a degree from where the North Pole really points). It's caused by the gravitational forces of the sun and moon on the Earth's "equatorial bulge," along with the tilt of the Earth's axis.
Along with precession of the Earth's rotational axis comes the rotation of the line of intersection of its equatorial plane with that of its revolution about the sun, as the vernal equinox traverses the constellations of the Zodiac-the so-called "precession of the equinoxes." Because of cyclic variations in the plane of the moon's orbit about the Earth (about 18.6 years), there is also a tiny sinusoidal wobble superimposed upon this circular precession, which is known as nutation.
But enough about the cosmos. Back here on Earth at least, you can consider yourself slightly illuminated. You've seen why we need to periodically check our heading indicators for precession, and you should be a little less intimidated by what used to be inexplicable.
Jeff Pardo is an aviation writer in Maryland with a commercial pilot certificate for airplanes, and instrument, helicopter, and glider ratings. He has logged about 1,100 hours in 12 years of flying. An AirLifeLine mission pilot, Pardo also has flown for the Civil Air Patrol.
Want to know more?
The following resources offer additional information on topics discussed in this article:
- Read an analysis of the gyroscopic instruments from the June 1995 AOPA Pilot.
- Review how the gyroscopic instruments work in concert with the rest of the flight instruments in the February 2002 AOPA Flight Training.
Links to these resources are available on AOPA Online.
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