Jeff Condit
Thu, 23 Dec 2004 19:11:20 -0800
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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