To: The man formerly known as - Yes, it does correspond to the length of an Earth pendulum (radius, actually, not diameter) - but, on its own, that's not much of an explanation - although that's usually all you get in most ATPL textbooks.
If you do a mathematical analysis of the V/R and U/R feedback loops, you come up with a differential equation that defines the feedback term. Since you're using the radius of the Earth, that's one of the constants, and another is the value of gravity. If you know something about control engineering, you can show that the oscillation is a form of Simple Harmonic Motion and that the period can be calculated from the equation:
T = 2 pi x Square root (R/g)
where R is the radius of the Earth (3437.7 nm) and g is 32.2 feet per second per second.
Substitute that lot into the above equation and you'll find it comes to 84.36 minutes.
It so happens that a pendulum is also an example of SHM and has the same defining equation. Some people often explain platform levelling carried out by the V/R feedback loop in term of a pendulum analogy, though I think that, unless it's done well, it generally tends to confuse.
The pendulum analogy explanation goes as follows:- Imagine your INS platform bolted at right angles to a pendulum which runs from your aircraft to the centre of the Earth. Then, as you travel over the Earth, the pendulum bob will stay in the centre of the Earth, so your platform will stay horizontal to the Earth's surface. That's V/R loop levelling. But if you start with the pendulum out of true, it will swing with a pendulum period of:
T = 2 pi x square root (L/g)
But in this case, L is Earth radius, 3437.7 nm - so a pendulum would behave exactly like an electro-mechanical V/R loop.
I actually prefer to tell my students the proper explanation. Personally, I think it's easier.
Don't get the idea that I think you need this level of depth to be an airline pilot. I don't. Nor is this kind of mathematical approach right for every student. But you did ask.
All the best
Paul
[ 01 January 2002: Message edited by: Paul Hickley, Gen Nav Spec, Oxford ]
[ 01 January 2002: Message edited by: Paul Hickley, Gen Nav Spec, Oxford ]
[ 01 January 2002: Message edited by: Paul Hickley, Gen Nav Spec, Oxford ]</p>