> ... though the pendulum appeared to change direction as it swung, in fact the plane of its swing remained constant ....
Nope. Unless you're at one of the poles, the period of the rotation of the plane is not 24 hours; the plane can hardly be fixed.
Wikipedia says a bit about this:
And there was a nice article in the American Mathematical Monthly some years back, which I found here:
But the basic idea is something like this: Say you're in the Northern Hemisphere. As the Earth rotates, your path essentially pushes you to the right (where "forward" is west). If you have a swinging pendulum with you, then the plane of its swing will rotate just as if you were on a flat surface, walking in a very large circle. The closer you are to the equator, the less you are moving to the right, the larger is this theoretical circle, and the slower the plane turns.
Langewiesche doesn't have time for a discourse on the physics of the pendulum -- which is basically just another kind of gyro. He has just a couple of sentences for his aside, and his readers are not physicists, so he grabs for the example of the Foucault pendulum, because that's a pendulum experiencing gyroscopic forces that every science museum visitor has seen.
I would have been better just to say that the plane changes, showing that the Earth rotates, and leave the explanations for another time.
Just like the glass of water though, if the plane were to stop rolling, the tea would immediately spill. It has nothing to do with "bending gravity", simply the reactive centrifugal force imparted by the turn itself.
If the pilot turns the plane at the correct rate, it's a 1 G maneuver. If he turns a little too fast (like spinning your arm too fast) the downward acceleration relative to the fuselage becomes greater than 1 G. If he turns too slowly, the downward acceleration is less than 1G and the tea might spill.
I use the term downward acceleration because "G Force" is not a term that physicists like to use.
So yes, if you stopped at the top of the roll, the liquid would indeed fall out. The reason it doesn't is that the plane is continuing to roll, and the acceleration of the plane away from its upside down position is greater than the acceleration due to gravity. The liquid is "falling" at 9.8 meters per second, but the plane - and hence the glass - is being pushed at a faster rate.
So if you kept flying upside down the tea would eventually fall, right?
No. Eventually the plane would hit the ground, since it is not only falling but also generating "lift" in a downwards direction.
youtube up the video of him flying the f-86 sabre if you want to be stunned.
or a 707:
This is only true if the rudder is not being used. It is possible to turn a plane without banking it, and to bank a plane without turning it using the rudder. The former maneuver is called a skidding turn, and the latter is called a slip.
Would this be considered an example of a dangerously confusing user interface?
I think people get confused when they see the marking representing the planes wings not moving relative to the console, but they see the blue-and-red thing inside the instrument moving. So they assume that their control inputs are causing the artificial horizon to move, when in reality, they are moving the plane and the artificial horizon is remaining still, just like the real horizon would.
Presumably there is some sort of mental issue with the "size" of the horizon -- when you look out the window, it's really big, so of course you're not moving it. Newer cockpits make the artificial horizon bigger, perhaps to compensate for this effect: http://www.cockpitgps.com/VOR_magnetic_variation/G1000CBEAV-...
I know that as long as I remember "fly the little airplane, not the horizon", it's not a problem. And as the comment below mentions, you also have a turn indicator, which clearly shows "R" when you're turning right and "L" when you're turning left: http://www.unitedinst.com/images/TurnSlip9500Series.gif
However, I don't think it's technically correct to say the passengers "have no way of guessing the airplane's degree of bank."
At some point I suspect gravity would override the masking sense of motion that he talks about.
We have a bubble level in our heads for sensor. Not a gyro.