Inertial Navigation Systems — Page 226, Lesson 270

Let’s start with the heart of the whole system, because everything else hangs off this one idea. The fundamental element of the Inertial Navigation System is the Inertial Sensor System, or ISS. That ISS is made up of a stable platform, and on that platform we mount high-quality gyros and accelerometers, plus a computer. So the platform keeps the sensors oriented in space, the gyros keep it stable, and the accelerometers measure acceleration. Now, what does that computer actually do? Its whole job is integration. It takes the accelerometer outputs and integrates them with respect to time to give you velocity. Then it integrates that velocity with respect to time to give you distance travelled. That’s the core mathematical trick of inertial navigation — you measure acceleration, and by integrating twice you get speed and then distance. From that, the system can derive a whole set of navigation data: pitch and roll attitude, true heading, true track, drift, present position in latitude and longitude, ground speed, and wind. So all of that comes out of the basic acceleration measurements. But to turn the ISS into a full Inertial Navigation System, or INS, we add a further computer. This second computer lets you inject and store waypoints, and then it computes track angle error, distance to go, and time to go to reach each waypoint. And that information can be fed to the autopilot, the flight director, or used for normal manual flying. Now, historically, the modern INS was the first self-contained single source of all navigation data. It’s since been joined by the similar IRS — the inertial reference system — which uses laser gyros, and we’ll discuss that later. But the point is, current engineering has produced INS units whose performance, size, and weight far exceed the older navigation systems. Let’s move to the basic principles, because they rest on Newton’s laws of motion. First law: a body continues in a state of rest, or uniform motion in a straight line, unless acted upon by an external force. Second law: the acceleration — that’s the rate of change of velocity — is directly proportional to the force acting on the body, and inversely proportional to its mass. Third law: to every action there is an equal and opposite reaction. But here’s the twist. Einstein, in 1905, destroyed the premise of absolute motion. His theory said nothing is truly at rest. When we say something is at rest, we really mean it’s moving at the same velocity as some other object — its coordinate system and the observer. So rest is relative, not absolute. And the accelerometer, the primary measuring device in an INS, demonstrates this beautifully. It makes no distinction between being at rest and moving at any other fixed velocity. But it does distinguish between truly fixed velocities and those we might regard as fixed but are really fixed speeds along curved paths. That distinction matters, because a curved path involves a change in direction, which is a change in velocity, and the accelerometer senses that. Now let’s look at the accelerometers and integrators themselves. Two accelerometers are mounted at the heart of the inertial system. These devices sense any change in the aircraft’s velocity — either acceleration or deceleration — very accurately. One accelerometer measures acceleration in the north-south direction, and the second measures it in the east-west direction. So you have two axes of measurement. The accelerometer itself is basically a pendulous device. When the aircraft accelerates, the pendulum, due to inertia, swings off its null position. A signal pick-off device tells how far the pendulum is off null. That signal goes to an amplifier, and current from the amplifier is used to drive the pendulum back toward null. That’s the feedback loop that lets the system measure the acceleration precisely. So the whole chain is: acceleration sensed by the pendulum, pick-off measures the deflection, amplifier drives it back, and the computer integrates that acceleration twice to give you velocity and then distance. That’s the foundation of inertial navigation.