Inertial Navigation Systems — Page 235, Lesson 277

Right, let's get into the heart of inertial navigation. We've got a gyro-stabilized platform that holds accelerometers steady in space, but here's the problem: the aircraft isn't flying in space. It's flying on a rotating Earth, and we treat that Earth as round. So if the platform stays fixed in space, the accelerometers would tilt relative to the ground as the Earth turns beneath them. That's no good, because we want the accelerometers to sense acceleration in the horizontal direction only, relative to the Earth. So we have to compensate for two things: the Earth rotating, and the Earth being round. Let me introduce the term "apparent wander." This is the drift of the platform that we have to correct for, caused by Earth rotation and by the aircraft moving over the Earth. There are two distinct compensations here. First, the earth rate compensation. This is a function of latitude, because what we're compensating for is the horizontal component of the Earth's rotation rate as felt by the gyros. At the equator, that horizontal component is zero degrees per hour. As you travel north or south from the equator, it increases, reaching a maximum of plus or minus 15.04 degrees per hour at the poles. That 15.04 is the Earth's rotation rate projected onto the horizontal plane at the pole. Second, we have transport rate compensation. This one is developed using the velocity signal. The electronics that carry this signal contain a term proportional to the Earth's radius. So the transport rate signal that torques the gyro is, in reality, the velocity of the aircraft divided by the Earth's radius. Both the earth rate and the transport rate compensations are applied by torquing the gyro—physically commanding the gyro to precess to cancel that apparent wander. Now, there are more compensations generated within the system. We have to handle Coriolis and centrifugal effects. The centrifugal accelerations arise because the platform rotates to maintain the local Earth vertical. The Coriolis accelerations arise because the aircraft follows a curved path in space when flying normal Earth-referenced flights. And there are additional compensations necessary because the Earth is not a perfect sphere. So the whole system works like this: the platform is torqued to stay level with the local vertical, the accelerometers sense horizontal acceleration, and the integrators turn that acceleration into velocity and position. The compensations we just talked about are what keep the platform honest as the Earth rotates and the aircraft moves over its curved surface.