Only read further if you're interested in global energy.
By the way, I think I was wrong. I had a lapse of imagination.... The
primary energy behind tides would indeed be the rotation of the earth.
Off the cuff, easily thirty times the energy involved in the moon's
revolution....
If such were true one would have to ask, would wind power not also slow
the earth's rotation? I have never heard of any argument for either on
even the smallest measures (from scientist's anyway), but I am no expert
on either system.
Nor I, to be sure; but I find the exercise interesting and educational.
Tidal forces are already resisted. The earth's rotation, if I'm correct,
is already slowing. The rotational energy is being converted into heat,
albeit a tiny amount of heat compared to other sources; however, because
there is no mechanism *increasing* rotation -- to my knowledge -- the
effect accumulates, albeit *very* slowly. Tidal power generation would
probably not increase the friction; it would merely relocate the heat
generation. That is, there would be more heat dissipated in the generating
mechanisms, in the power distribution grid, and at the points of use, and
less heat into the ocean (and shoreline). All of which, it seems to me,
would be so tiny in comparison to heat coming from the sun, that the
difference would be entirely negligible.
I don't know all the ways various slowdown amounts would affect various
things, but clearly at some point it would affect the weather and climate.
Based on sensitive dependence on initial conditions, I would guess the
bounding conditions of weather would likely be affected before a climatic
shift was pronounced. However, when it comes to the amount of energy
there's no need to guess; a simple calculation can be done as follows:
The radius of the Earth is: Re = 6.3781349x106 m
The mass of the Earth is: Me = 5.9736x1024 kg
The nominal period of rotation of the Earth about its axis is: t0 =
(24)(60)(60) = 86400 s
One second longer per day would be: t1 = t0+1 = 86401 s
The nominal angular frequency is: Ï0 = 2Ï/t0 = 7.2722052166x10-05 rad/s
The reduced angular frequency would be: Ï1 = 2Ï/t1 = 7.2721210486x10-05
rad/s
The moment of inertia is approximately: I = (2/5) Me Re2 =
9.720386433952x1037 kg m2
The nominal rotational kinetic energy about its axis is: K0 = (1/2) I Ï02 =
2.5703116621572x1029 J
The reduced rotational kinetic energy is: K1 = (1/2) I Ï12 =
2.5702521652829x1029 J
The energy change is: ÎK = K0 - K1 = 5.94968743x1024 J
NOTE: This estimate is substantially high because is assumes a uniform
density for the Earth, but the real Earth is much denser at the core,
leading to a lower moment of inertia.
One estimate I saw shows that throughout history natural tidal friction
loses about 1023 J per century. However, most of the tidal surges are in
places which are broad, and the water is free to flow in and out over the
entire period with relatively low flow rates and very little elevation
change across the system. Damming up the natural system prevents this flow
until the peak tide where there is an elevational difference if many meters
across the dam. This in effect locks the bulges in the oceans such that the
Earths rotation moves them from being inline with the extraterrestrial
gravitational pulls, causing the gravitational torque which slows down the
Earth's rotation. It is similar tidal losses in the solid material of the
moon that has caused tidal locking wherein the same face is always toward
us, as is characteristic of many moons in the solar system. When the water
is release against the head to generate power, the flow rate is now
substantially increased, resulting in higher flow losses. While it is true
that the vast majority of the energy will end up as heat, that doesn't alter
the fact that 1) the rotational speed is diminished, and 2) the Earth has to
dissipate this excess by increased radiation, contributing to global
warming.
As of 1999 the DOE estimate of global energy use was 4.02x1020 J but
increasing rapidly with emerging 3rd world infrastructures. I don't have a
more recent number, but worldwide efferts to curb this energy rise may have
had some effect. Thus at the current usage we may be slowing down a second
per year every decade or so. You can do your own studies if you like. What
I don't like is that this is never talked about.
The studies I have read on planetary atmosphere kinematics indicate wind
patterns are a product of both tidal effects on the atmosphere and daily
heating cooling cycles. As a result, harnessing wind would probably have a
lesser effect on the rotational kinetic energy.
In large desserts the ground normally reflects a certain aomunt of radiant
energy back into space while absorbing some as heat. If large solar atrrays
in the dessert could the same anount as the normal soil, then to overall
heating of the Earth would be unchanged. The difference would be that
energy would be transferred from the dessert to other clode-by wetter areas
where people live, thus the dessert would be a bit cooler while the
surrounding areas would be a bit warmer. This could cause weather shifts
and slight local climatic changes, but the global effects would be
minimized. Of course, this approach would never be taken because solar
power is expensive, and so is driven by economics which mandate maximum
power conversion per $ invested, resulting in dark colored panes that do not
reflect much of their incident radiation on purpose.
It has been stated that the Earth regulates its own temperature via
increasing cloud cover as global temperatures rise. This is a negative
feedback system. However, geologic evidence indicates the duration of ice
ages is long, which in turn suggests the Earth has at least two stable
states, not just one. (Stable in the shorter term; since the ice ages come
and go in the long term.) Thus if the Earth gets covered with clouds and
subsequently cools down, it does not necessarily lose its cloud cover for a
very very long time even though it gets cold. I think we need to be
focussing on harnessing the renewable energy flowing around the planet and
redirecting it in constructive ways that do not alter the global energy
budget. We should not be beaming in copious amounts more from satellites,
or messing with planetary kinematics, regardless of who's $ is talking. And
we should not be boosting the conversion of convenient stored energy well
beyond sustainable levels except (perhaps) to promulgate an exit from an ice
age.
Jeff Condit
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