Inertial Navigation Systems — Page 235, Lesson 277

Let's pick up with the heart of the inertial navigation system — the part where we stop treating the platform as if it's floating in space and start making it behave as if it's sitting on a rotating, round Earth. I want you to remember the gyro-stabilized platform we talked about earlier. Left completely alone, that platform stays fixed in space. But the aircraft isn't operating in space — it's operating on an Earth that is rotating, and an Earth we assume to be round. So if we want the accelerometers to stay level with respect to the Earth's surface, and to sense only the horizontal acceleration of the aircraft, we have to compensate for two things: the Earth rotating, and the Earth being round. That brings us to the first big idea: apparent wander. Corrections must be made to the gyroscopically stabilized platform to allow for apparent wander caused by Earth rotation and by the aircraft moving over the Earth. There are two distinct compensations here, and I want you to keep them separate in your mind. The first is earth rate compensation. This one is a function of latitude. Why latitude? Because what we're compensating for is the horizontal component of the Earth's rotation rate that the gyros actually feel — and that horizontal component varies with latitude. At the equator, that value is zero degrees per hour. As you travel further north or south, it increases until it reaches a maximum of plus or minus 15.04 degrees per hour at the poles. So the amount of torquing we apply to the gyro depends entirely on where you are in latitude. The second is transport rate compensation. This one is developed using the velocity signal. The electronics through which that velocity signal is sent contain a term proportional to the Earth's radius. So in reality, the transport rate signal that torques the gyro is the velocity of the aircraft divided by the Earth's radius. That's the formula to hold onto: transport rate equals velocity divided by Earth's radius. Now, here's the key point: both the earth rate compensation and the transport rate compensation are applied by torquing the gyro. We physically twist the gyro to make the platform behave as if it's level with the Earth, even though the Earth is rotating underneath it and the aircraft is moving over a curved surface. But those two aren't the only compensations generated within the system. There are a number of them. We also have to compensate for Coriolis and centrifugal effects. And there are other compensations necessary because the Earth is not a perfect sphere. Let me unpack those two accelerations, because they're easy to confuse. First, centrifugal accelerations — these are caused by the platform rotating to maintain the local Earth vertical. Second, Coriolis accelerations — these are caused by the aircraft following a curved path in space when flying normal Earth-referenced flights. So one comes from the platform's own rotation, the other from the aircraft's curved path through space. Let me show you how this all fits together. — this is Figure 18.2, the accelerometer and integrators. And — Figure 18.3, the accelerometer itself. These show you the physical hardware that senses the acceleration and feeds those velocity signals we just talked about. So the whole picture is this: the accelerometers sense horizontal acceleration, the velocity signal comes out of them, that velocity gets divided by the Earth's radius to produce the transport rate, the latitude determines the earth rate, and both of those torque the gyro to keep the platform level. On top of that, the system compensates for Coriolis, centrifugal, and the non-spherical shape of the Earth. That's the complete set of corrections that make an inertial platform work on a real, rotating, round planet.