You Are Here by Colin Ellard Page A

a rocket that not only could escape from the earth’s atmosphere but could be guided to a target using some kind of navigational system. Later in life, as a rocket scientist in the New Mexican desert, Goddard designed a navigational systembased on the gyroscope, a device invented 300 years earlier by the French scientist Léon Foucault. 9
    The wedding of Goddard’s solid rocket boosters and Foucault’s gyroscope produced one of the great shapers of twentieth-century world politics: the ballistic missile. The navigational problems of ballistic missiles are not very different from those of nursing gerbils finding their way home in the dark. In both cases, knowing where you are means understanding where you’ve been. In rocket mechanics, such problems are solved using a clever combination of accelerometers and gyroscopes.
    A basic accelerometer can be thought of as nothing more than a mass, a spring, and a ruler. As the mass is accelerated, it exerts a force on the spring that causes the spring to stretch. The ruler measures the extent of the stretch, and this measurement yields the size of the acceleration.
    As shown in Figure 3, gyroscopes are commonly constructed using a series of rotating rings called gimbals. As the object that carries the gyroscope rotates through space, the gimbals rotate. Measuring the size of the rotation can generate information about changes in heading, or direction.

    Figure 3 : The rotating wings of a gyroscope provide directional information
    Both gyroscopes and accelerometers rely on some basic physical laws describing how things that contain mass move. Anything with mass contains inertia, which can be thought of as resistance to movement. Gyroscopes and accelerometers, because they rely on inertia, are said to be the instruments of “inertial navigation.” Together, these machines provide all the information necessary to calculate position, provided that the arithmetic can be worked out.
    Inertial navigation is very difficult to do well over long periods of time. The path of a vehicle carrying accelerometers and gyroscopes can be reconstructed from the entire record of every
change
in heading or velocity, provided one knows exactly
when
these changes took place. But here’s the problem: no inertial guidance system has perfect precision. For that matter, no machine has perfect precision. Every measurement of acceleration or heading change contains an error, and these errors will accumulate as inexorably as the interest on delinquent income tax payments. This kind of inaccuracy, called integration drift, will become more and more serious as time goes by. There are two main ways to counteract this kind of error. One solution is to have a means of measuring velocity that does not depend on the inertial guidance system. Another is to allow the guidance system to come to rest. When the machine carrying the system halts, the velocity falls to zero and so does the value for integration drift. Both these error-correcting mechanisms are used, but the second one is obviously useful only on the surface of the planet, where friction and gravity can bring systems to a halt. It is not very good for rocket navigation, where making things stop can be tricky.
    Though the gyroscopes and accelerometers in our middle ears look markedly different from those found in missiles and rockets, the principles involved are exactly the same, and the vestibular system found in mammals suffers from the same type of integration drift.
    An animal using its vestibular system for navigation is subject to an accumulating error. Every time the animal turns or moves forward, the error for that movement segment is added to the error from all previous movement segments. Although ants also suffer from this cumulative error, the intrinsic error of their estimates of the sizes of turns is smaller than for mammals because the sun compass can yield more accurate estimates of turn size than can the vestibular system.
    Given all this, we