The Inertial Guidance Platform

Rigidity in space is the property everything else rests on.

1. Mount a heavy rotor in a two-axis gimbal so it is free to point in any direction.
2. Spin it up and note the direction its axis points.
3. Carry the whole assembly around the room, rotating the frame in every direction.
4. Watch the spin axis.

The frame turns; the spin axis does not. The rotor is holding an orientation fixed relative to space itself while its mounting rotates around it, and the gimbals are simply allowing that to happen without transmitting torque.

Now push gently on the spinning rotor and observe: it does not move in the direction you pushed, but at right angles to it. That is precession, and it is the source of every counter-intuitive behaviour in the rest of this blueprint.

Isolate a small platform from every rotation of the vehicle around it.

1. Build three nested gimbal rings, each free about a different axis.
2. Mount the inner platform carrying the gyros and accelerometers.
3. Fit pickoffs to sense any relative rotation, and small torque motors to drive each gimbal.
4. Close a loop that drives the motors to keep the pickoffs reading zero.

The platform now stays fixed in inertial space while the vehicle rotates freely around it, and the gimbal angles read out the vehicle’s attitude directly. The loop is not steering the platform — it is removing friction, driving the gimbals so the platform never has to be pushed.

Three gimbals have a famous flaw. Rotate the vehicle so two gimbal axes line up and the platform loses a degree of freedom entirely — gimbal lock, after which the platform tumbles and the reference is destroyed. Apollo carried a display warning the crew away from those attitudes, and Michael Collins famously suggested they carry a fourth gimbal instead.

This is where the errors come from, and the mechanism is arithmetic rather than mechanical.

1. Leave an accelerometer perfectly still and log its output for ten minutes.
2. Compute the mean — this is bias, and it should be zero and will not be.
3. Integrate the logged signal once to get apparent velocity, and again to get apparent position.
4. Plot both against time.

A stationary sensor reports a steadily growing velocity and a position error that grows with the square of time. A bias of one milli-g — roughly a thousandth of gravity — produces about 176 metres of position error after ten minutes, from a sensor that never moved.

That is the central problem of inertial navigation and it cannot be solved by better integration. Integration is faithful; it is faithfully integrating an error.

An accelerometer cannot tell you which way is up, and this is not a defect you can engineer away.

1. Hold an accelerometer stationary and note it reads 1 g upward.
2. Drop it — in free fall — and note it reads zero.
3. Tilt it slowly and watch the components change.
4. Now consider a sensor reading 1 g and try to determine whether it is sitting still or accelerating upward in space.

There is no measurement that distinguishes them. That is the equivalence principle, and it means the guidance computer must SUBTRACT a modelled gravity vector from every reading — which requires knowing where you are, which is what you were trying to compute.

The loop closes on itself: use current position estimate to look up gravity, subtract it, integrate to update position, repeat. Errors in position produce errors in the gravity model, which produce errors in position.

An inertial system must be told where it is once. Everything after that is arithmetic.

1. With the platform level and stationary, use the accelerometers to find the local vertical — gravity defines it.
2. Now use the gyros to detect Earth’s rotation, about 15 degrees per hour, and find the direction of its axis.
3. From vertical and the rotation axis, compute true north.
4. Time how long the measurement takes to become repeatable.

Gyrocompassing finds north with no magnetic compass and no outside signal, using only the fact that the Earth turns — but the signal is tiny and it takes minutes of averaging to extract it. That is why a launch vehicle sits on the pad with its guidance running long before ignition, and why the countdown includes a point after which alignment cannot be repeated without starting over.

The magnetic compass, by contrast, is instant and points at a wandering magnetic pole that is not north. One is slow and true; the other is fast and approximately right — and which you want depends entirely on whether you are steering a ship or hitting a target 300 km away.