Tidal Forces

June 20, 2012

There's a saying that time and tide wait for no man. In a famous anecdote about man versus nature, Cnut the Great, king of England, Denmark, and other parts of Scandinavia about a millennium ago, set his throne at the sea shore and commanded the tide to halt. The tide, of course, refused his command, and this was supposedly a lesson to his countrymen that kings are not as omnipotent as some would hope. Perhaps sea level change caused by global warming will give a similar lesson to today's leaders.

Not much to look at, but very expensive to hold. Scandium, named after King Canute's Scandinavia, is presently about $150 per gram.[1] (Photo by Heinrich Pniok, via Wikimedia Commons).

Most people think of tides only in relation to bodies of water, but the Moon will exert forces on sensitive equipment. In the vacuum tube days, I read an article in which an amateur radio operator tuned in a frequency reference station on his receiver and plotted the position of his tuning dial versus the position of the Moon. There was a noticeable change.

In those days, tuned circuits were mechanical, using variable capacitors and inductors, so it's likely that he was measuring tidal forces. I think you would need to believe that the vacuum tubes and their cabinet provided a constant thermal environment, and he wasn't really seeing diurnal temperature variations.

How much of a force does the Moon exert on an 80 kilogram human? Plugging the Moon's mass (7.345 x 10²² kg), its distance from the Earth (about 385,000 km), and the gravitational constant G (6.674 x 10^-11 N m² kg⁻²) into Newton's gravitational equation,

F = G m₁ m₂ / r² =
(6.674 x 10^-11)(80)(7.345 x 10²²)/(3.85 x 10⁸)² =
0.00265 newton =
0.27 gram-force

What all this means is that I'll weigh 0.0005 pounds less when the Moon is overhead, and 0.0005 pounds more when the Moon is underfoot. That change won't be detected on my bathroom scale, but there are sensitive pieces of equipment that respond to tidal forces. Pauline Gagnon, a member of the CERN ATLAS team, reports in a recent blog article that the Large Hadron Collider (LHC) must be adjusted to compensate for tidal forces.[2]

Tidal forces were also seen in the predecessor to LHC, the Large Electron Positron collider (LEP). The cause is the differential tidal force seen at one side of the 27 km accelerator versus the other. This causes the circular accelerator to slightly alter shape, so the proton beam would wander if corrections were not applied. the accelerator also deforms from changes in the water level of nearby Lake Geneva.[2]

To illustrate how important tidal forces are, there are 872 papers posted on arXiv with the word "tidal" in their title, 56 of which had been published up to June 10 of this year. Only four of the 872 address the Earth-Moon system. Although the Earth-Moon tidal system is presently not that scientifically interesting, it's become technologically very interesting because of the desirability of extracting energy from the tides.

Amplitude of the tides, in centimeters. The white lines are co-tidal with a one hour time difference. NASA image by R. Ray, Goddard Space Flight Center, via Wikimedia Commons.

Needless to say, there's much energy contained in the movement of the vast quantity of ocean water (see figure, above). The two main methods to extract this energy are tidal stream generators and tidal barrage generators.

A tidal stream generator extracts energy from the movement of water during the ebb and flow of the tides. Placement of turbines underwater will extract this energy, and it's not hard to see that technologies that are used for wind energy harvesting can be applied to tidal energy harvesting. Tidal barrage generators work by trapping high tide water behind a dam for energy extraction by flowing the water through turbines at low tide.

All this energy is enough to get anyone excited, even cosmologists, who are not usually thought to be interested in things close to Earth. Hermann Bondi, who is famous for the development of the now-discredited steady-state theory of the universe, was chairman of a 1981 commission that studied the possibility of a barrage on the Severn estuary.

The committee proposed a 16 km (10 mile) long barrage, which would be a major engineering feat. This barrage would have generated more than 7 gigawatts, which is the equivalent power output of nearly ten nuclear power plants, but it was never built.

References:

1. Daniel J. Cordier, "Scandium," US Geological Survey, Mineral Commodity Summaries, January, 2012).
2. Pauline Gagnon, "Is the moon full? Just ask the LHC operators," Quantum Diaries, June 7, 2012