Inertial-guidance systems use devices such as accelerometers and gyroscopes to measure changes in the position, velocity, and attitude (orientation) of a vehicle. Such measurements form the basis of a technique, sometimes called inertial navigation, whereby the course of a vehicle is planned without recourse to external navigation aids, such as stars or a global positioning system. Inertial-guidance systems are used in missiles, space vehicles and satellites, aircraft, ships, and submarines; they also have applications in land and deep-sea surveying.
The first inertial-guidance system was developed during World War II for the German V-2 missile, first launched in September 1944. The V-2 design used gyroscopes to stabilize the attitude of the missile in flight and a single accelerometer to measure acceleration along the flight axis. The rocket engine extinguished once the required speed had been achieved. Engineers in the United States developed a complete inertial-navigation system based on accelerometers and gyroscopes by 1948. Ten years later, the efficiency of such a system was proved by its success in accurately navigating the nuclear submarine USS Nautilus under the Arctic ice cap.
Measuring acceleration
Devices that measure acceleration—one of the fundamental measurements in inertial guidance—are called accelerometers. A simple accelerometer consists of a mass suspended between two taut springs. By Newton’s Second Law of Motion, an accelerating mass experiences a force (F) that is related to the product of its mass (m) and the rate of acceleration (a) by the equation F ∝ ma.
When an accelerometer is in an accelerating vehicle, the force that accelerates the mass in the accelerometer arises from the compression and extension of the springs that support the mass. By Hooke’s law of elasticity, the amount of extension or compression of the springs is proportional to force, so such an accelerometer can be calibrated to measure acceleration in terms of the displacement of the mass from its rest position.
Another type of accelerometer uses transducers that produce an electrical signal in response to the pressure—and therefore the force—that an accelerating mass exerts on them. The output voltage of such a transducer is generated by the piezoelectric effect. The magnitude of the voltage increases with increasing pressure in a predictable manner so that this type of accelerometer measures acceleration in terms of voltage.
Components of acceleration
An accelerometer is sensitive to acceleration in one dimension—along the axis of the springs of a mass-and-spring accelerometer, for example. For this reason, an inertial-guidance system must have three accelerometers mounted along three perpendicular axes, which are typically North–South, East–West, and vertical. The outputs from the three accelerometers are combined to give acceleration in three dimensions and corrected to eliminate acceleration owing to gravity.
Velocity and displacement
If an object accelerates at a constant rate for a given period of time, its change in velocity can be calculated by multiplying the rate of acceleration by the duration of the acceleration. A mathematical procedure called integration, which performs such a calculation for each instant in a given period of time, calculates velocity changes even when the rate of acceleration varies. Modern inertial-guidance systems have microprocessors that perform this type of integration. A second integration with respect to time converts the plot of velocity against time into a plot of displacement, or distance travelled, along the axis of measurement of the accelerometer.
