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15th February 2003

 

Sustainable electrical power production

It would seem that to burn planet Earth's fossil fuel resources to create electrical power is unsustainable for the increasing population of our species. This is especially so if the developed world fraction of that population continues to use the energy so produced in such processes as ironing although there are many others. If that population fraction wishes to continue in those practices then they should, if it is at all possible, use a primary energy source that is renewable. President George W Bush (USA, July 2001) requires that any technical solution to the ongoing energy crisis should result in reduced production of greenhouse gases. Fortunately, this problem has solutions that should be applicable democratically.

Below is indicated methods to produce electrical power in sustainable and useful quantities using but a little imagination, some new and redundant engineering supplies, a few basic tool skills and management in some of the space above telegraph poles, over reservoirs and in other areas.

The term ‘nuclear power’ defines electrical energy derived from nuclear fission chain-reaction vessels. Since none has successfully stored the waste materials generated by this industry for anything like 1% of a single half-life of Plutonium’s decay, it is not yet possible to place this source of energy production within the renewable category.

 

Introduction

As we, sp. homo sapiens, writhe, spiral and accelerate towards the nothing of extinction, this is a thought that may or may not prove too late. It concerns the sustainable production of electrical power without the need to consume the Earth's fossil fuel reserve.

There has been an enormous increase in greenhouse gas emissions from fossil fuel combustion during the 20^th and 21^st centuries and this is known to be detrimental to our health. Davis (1997) predicts that eight million human deaths will be directly attributable to the effects of the aerosol particles (smokes) and poisonous gases created in the combustion between now and the year 2020. It is notable that the number of deaths that are forecast to be attributable to the effects of smoking cigarettes for this period is about three million; road-traffic-accident deaths will total five million; AIDS-related deaths, ten million; war deaths, two to five thousand million and those attributable to the effects of secondary smoking in public places, one thousand.

About one third of the current inflammation is related to the production of electrical power in magnificently inefficient generating stations: an oft-quoted figure is that a mere 10 to 20% of a typical fossil fuel burning power station’s heat energy is converted into electrical energy and that the remainder is vented (wasted) through the boiler’s chimney into the local atmospheric boundary layer.

For reasons unknown, little effort has been made towards the re-use of this waste heat in Combined Heat and Power (CHP) schemes. For example, at Scandinavian latitudes and on the Isle of Man, CHP has supplied electrical power and water at 60 ± 10º Celsius to many homes since the mid-1960s.

In an earlier report of the International Panel on Climate Change (IPCC, 1995), one of our finest normal-science forums and associated bureaucracies, recommendations were made such as:

By early in the 21^st century AD, more than 1/3 ^rd of the developed world’s electrical power production should be derived from primary energy resources that are renewable.

This was in part to ensure that Earth's known, limited and dwindling fossil fuel reserve would not continue to be converted to carbon dioxide and water vapour as the fuel is burnt to create steam that drives turbines to produce electrical power that is transported across hundreds of kilometres (miles) by wires that were wrought from the ground to homes where it is used to make kilogramme lumps of metal hot such that a few billion clothes could be ironed each day, as hitherto.

Clearly, the rate of combustion of fossil resources has near-doubled since the 1960s and the demand continues to accelerate. The forest fires that rage continuously across the planet are probably not the sole product of increased television exposure. The current energy crisis across the USA is attributable in part to the massive over use of air-conditioners and clothes presses and is associated with the chaotic responses inherent in atmospheric and capitalist systems alike.

The work towards the production of useful and sustainable energy here is based upon the development and deployment of wind wheels. The devices convert some of the energy in the wind into electrical power that is used locally to provide heat and light.

The wind’s turbulent, near surface flow is used by many others as their primary renewable energy supply and Hugh Piggott gives the details of wind-power schemes and other links. The use of re-cycled materials is a high recommendation.

Wind wheel, version 4.2, in development.

 

A further driving force behind this work is the knowledge that there is ample automotive engineering and other pieces of redundant engineering equipment already existent on the planet to accomplish the tasks required. That is, the processes from raw-materials extraction to device-functionality are achieved, mostly, at the outset. The requirement is satisfied with only a little imagination and some basic tool skills to bolt the bits and pieces together atop of masts, towers and generally in the free atmosphere: none of the requirements come close to the trickery of rocket science or M-theory. Naturally, there will be maintenance on the devices and the management and execution of the required tasks is an overhead for the communities involved. The location of any generating station must be open to public debate and the democratic process.

Also, there is very little fear that by using this energy it becomes lost to Gaia (Lovelock, 1988) and will result in nothing but doom. First order calculations show that the amounts of energy borrowed from the renewable resource are miniscule in comparison with the reservoir. And anyway, there is nothing more certain than the doom of the heat death of the universe as predicted by the second law of thermodynamics, and that is some way off, yet.

An extrapolation of the basic idea indicates a path amongst the various devastations predicted for our species by many current commentators be they social, religious, political, economic, climatic, galactic, 'So it goes', chaotic or not.

It is appreciated, however, that it may be far too late already for Homo sapiens. Manabe et al, 2001 and Mann, 2001 show that the current, average, atmospheric surface-layer, dry-bulb temperature leads a very steeply ascending slope on a trace that is over one thousand years in length. And therefore, we may be just whistling in the wind, but what the heck? As our population total becomes more unsustainable with each passing hour, it is a wonder that this was not tried sooner. Maybe it could/should be issued to schools, colleges, universities and others as a last resort challenge? Maybe it was?

This global-resource management failure is due in part to the massive human population pressure and in a larger part, to the Capitalist driver known as 'Profit'. In the period from the late 1960s to the early 2000s, global population numbers were expected to increase by around 50% from 4 to 6 gigapeople (Kildron & Segal, 1981) and this they did. An equivalent linear growth rate would increase by more than 160 thousand people per day or add to humanity the 1975 UK population, ~ 56 megapeople, per year.

Since the late 19th century the space above each telegraph pole here in Holwick and probably elsewhere, has been essentially void. The volume of space concerned is roughly equal to half of that of the pole itself. During some of the time it is noted that some members of some species of bird use some of this space during their flight, rest and sometimes death.

Research at School House shows that a simply modified standard bicycle wheel, 27 inches in diameter and with a 1¼ inch rim, can be made to produce useful electrical power as the local wind speed rises above five metres per second (ms^-1) or eleven miles per hour (mph). The effective power output of the version 3 unit is around 3 Watts at minute average wind speeds near 10ms^-1 (23mph). Future device versions, will improve the design in aspects of performance, simplicity and the number of recycled components used.

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Site and instrumentation

In Holwick, the School was built in the 19^th century AD when the lead-mining industry was a major employer throughout Teesdale and children were numerous: consequently, Holwick’s population grew to its 1905 maximum of approximately two hundred. Currently, the School is equipped with a small array of instruments used to make measurements of some of the local meteorological variables (weather conditions). Wind speed and direction, atmospheric pressure, air temperature, visibility, humidity and precipitation totals are each monitored on a frequent and intermittent basis. Currently, the local press, Durham County Council, and others make their records of local readings available. Historical and notable meteorological events can be traced over many millions of years for the Pennine Hills region of the United Kingdom. The Manley (1952) and UMIST (1960-93) references show the results from a few contemporary experiments made at and around the summits[1] of the northern Pennine Fells.

The School is sited on the 'knee' of a local-terrain point of inflexion. The road climbs from the southeast then levels-out as it passes by. It rises more gently into the west but does not climb above the cliffs of Holwick Scars on its southern flank before it ends near Holwick Lodge. The land around the School falls to the river Tees to the north and east and some of the closest telegraph poles are higher, and some are lower, than middle-Holwick’s chimney pots. Local ground level is near 296m (950 feet) above mean sea level (UK, O/S reference NY904271).

Of the observed variables wind speed is measured with a Digitar™ cup-type anemometer that is mounted at chimney height. This is five metres above local ground level and is approximately the same height as a telegraph pole.

The 3-cup anemometer generates a pulse-train output from a reed switch that is closed by the near proximity of a magnet mounted on the rotator shaft. This output is connected electrically to a dedicated data logger for signal processing, unit conversion and display. The primary conversion factor used in the signal processor is that an increase by 4 pulses per second equates to an increase of 1ms^-1 (2mph) in the wind speed. The results are averaged and displayed for successive two-second periods. The maximum gust value is stored in volatile memory and is updated as required. The anemometer cups begin to rotate as the wind speed rises above 2ms^-1 (4mph) and the device is specified to operate to 67ms^-1 (150mph) wind speeds.

The anemometer was installed in 1994 and has operated in conditions that range from Beaufort-scale calm, 0 - 1ms^-1 wind speed, to hurricane force 12, where the hourly average wind speed is in excess of 32ms^-1 (72mph). Many regard Holwick as a ‘windy’ place and, I believe, this is not a reference to the folk that live here. The two greatest gusts of 46ms^-1 (104mph) and 47ms^-1 (107mph) occurred during separate, moderately violent storms (a.k.a. hurricanes or, typhoons) in early January 1995. The local topography including School House itself and the Scars to the south will have forced the immediate airflows somewhat but nevertheless, many trees and branches up to 1.2m (4 feet) in diameter were uprooted or snapped cleanly during the 1995 storms throughout Teesdale and probably, beyond: cf. ‘The Great Storm of 1986’ that was un-forecast by the U.K. Met. Office and ruffled a few more feathers, and felled more trees, across southern UK and northwestern France.

In the twentieth century, most of the highest wind speeds reported in England were measured near the summit of Great Dun Fell (GDF) that is now a U.K. national air-traffic monitoring and associated research station with absolutely no defense purpose whatsoever.

The summit of GDF is some 20km (12miles) to the west-northwest and more than 580m (1900feet) higher in elevation than our hamlet and these upland Fells can experience near-Siberian winter weather (e.g. 1947, 1963, 1978) although their frequency and length of occurrence may be on the decline. At these elevations a dry-bulb thermometer often reads more than 6° C less than one read simultaneously at nearby Carlisle Airport. The maximum wind speed, recorded from the output of the NATS/UK Meteorological Office, Munro™ cup anemometer at the summit station was offscale (>60 ms^-1 ,137 mph) during the second storm of January 1995.

Local records show that the near surface layer between Holwick Scars and the river Tees can experience flows that are completely decoupled from the rest of the local boundary layer. This is manifest when clouds pass into the north yet the breeze is on the north-facing observer's face. The area is sometimes within the returning flow of eddies shed near the edge of the Scars.

In southerly regional winds, the flow down the gentle fell slopes is steered such that the observed 5-metre elevation wind direction is most often from one of two preferred directions - southwest or southeast. Overall, southwesterly wind directions dominate annual wind rose diagrams for this region.

Another localised feature of the north Pennine winds is made apparent in the 'Helm wind' that blows in the Dufton and other fell-side villages of Cumbria/Westmoreland when an easterly component exists in the regional airflow. The gently rising fells plunge swiftly to the valley of the river Eden and the Pennine escarpment is host to the Helm-bar - a rotating sausage of a cloud that concentrates soot and other pollutants within its cloud droplets - until the wind no longer blows easterly. The dynamic of the flow from onset to the end of a Helm as described locally is that the wind direction will have backed into the east to begin and the Helm will blow until the wind direction veers through south again.

Finally, and on a sad note, the wind vane of the Digitar™ anemometry kit is now seemingly immovable and points towards the southwest: and this after barely nine years in operation.

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Wind wheel development

The prototype wind wheel, version 3, uses a standard bicycle dynamo, the Nordlight 2000, manufactured in Switzerland that has a rated output of 6 Volts AC at 3 Watts[2]. The barrel magnet in this dynamo is made to rotate by the transfer of energy from a rotating bicycle wheel. Normally the wheel is rotated as the cyclist travels forwards: in a wind wheel however, the wheel has had the space between consecutive pairs of spokes covered by sticky-backed-plastic tape such that it becomes eighteen-winged. Consequently, as air passes through the wheel it spins. The lowest wind speed at which the wheel is observed to rotate, << 1m/s, is much less than that required to start the anemometer cups.

Currently, the observed electrical output from the wind wheel is a 5 to 25V peak to peak amplitude, near-sinusoid waveform with frequencies around 800 ± 300Hz at 20 ± 10ms^-1 (23 to 67mph) wind speeds. Some part of the distortion in the output waveform can be traced to wheel buckle. Electromagnetic saturation becomes apparent in the signal waveform as the wind speed rises above 25ms^-1 (57mph). At such speeds the wind imparts enough spin to the wheel to produce a 1khz, 25V peak-to-peak, square-wave output from the dynamo.

Frequencies like this are generated by cyclists speeding in a straight line at a speed given by:

(27 * pi * 1000)/(gear ratio, 27:1) ~ 3142 inches per second.

This converts to 79ms^-1 or 178mph. From this we note that the wheel’s rim speed is around three times that of the wind speed and that we are approaching the engineering limits of a standard bicycle.

As the dynamo's output A.C. voltage varies widely in both amplitude and frequency with wind speed, it is best to convert this output to a more convenient form for future use. This is achieved with a conditioning circuit built of a fuse, capacitors and diodes to charge an array of 12V lead-acid batteries.

The dynamo output is brought to the fuse: if the load were to exceed 18 Watts then, theoretically, the fuse would blow - in practice, approximately twice this load appears sustainable for up to an hour or two during storms.
 
The battery charging circuitry is a based upon diode pumps: these lift the root mean square value of the dynamo’s output to approximately 13V to charge the battery array. Currently, five lead/acid batteries are in parallel use.

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'Blue-skies' extrapolation and proposal

 Wind wheel 4.2 that drove a Nissan Micra™ alternator, briefly.

If a single wind wheel per cubic metre were to be installed at 5m above local ground level then a total power extraction of 1 terawatt from an area roughly half that of the United Kingdom throughout a good fraction of a year is sustainable. This extraction is ‘sustainable’ in that a one-terawatt extraction represents approximately 1 part in 400 thousand of the atmospheric reservoir (see calculation below). We are aware of the atmosphere’s chaotic behaviour resulting from the passage of a tornado, thermonuclear detonations and a butterfly’s wing flap.

Alternatively, logarithmic cones could be built in desolate, mid-latitude zones. These constructions rely on observations that show the hourly average wind speed’s vertical profile over a given surface has a logarithmic form:

U(z) = u^* ln(z/z₀)

Where: U is the wind speed in ms^-1 and z is the height above the surface in metres; u^* is known as the friction velocity and relates the mean and turbulent flow velocities to the underlying surface and atmospheric stability; the parameter z₀ is known as the roughness length and is highly surface-dependent: grasses are rougher than sand and sand is rougher than ice. Physically, z₀ is the height above a surface at which there is no mean airflow: it is an observation that wormholes have but slight draughts.

For introductory studies on mean and turbulent flows see for example, Stull, 1988 and Yelland et al, 1992.

Electrical power generating stations based upon wind wheel objects arranged in logarithmic pyramids are proposed.

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Renewable sources of electrical power production

These sources include geothermal, tide, wind and wave energy, hydro-electricity, bio-diesel, insolation converters, light-element (low-Z) fusion reactors and heavy-element (high-Z), fission/fast-breeder reactors and the hydrogen economy[3].

Techniques that control the nuclear fusion of hydrogen isotope nuclei (e.g. Tokamak reactors and focused laser implosions) have been claimed 'To be production ready in about 30 years time.' by various commentators every five years or so since 1957 when Harold Macmillan the U.K., Tory, Prime Minister said that, ‘Coal will soon be a penny a ton.’ Is this a 'Holy Grail' for the western world?

The idea that humanity or even cyborgity can instigate a management plan that will run without hitch for a minimum period of 100,000 years - about the time taken for a few grammes (1 tsp) of Plutonium (²³⁸₉₄Pu) to decay b-radioactively to below LD50 levels - remains untenable, and should continue to rule-out high-Z, fission reactors, for the foreseeable future.

Renewable resources powered generation schemes that contributed ~5% to the U.K. total demand in 2000; nuclear fission supplied ~20%; coal, oil & gas supplied the rest, ~75%.

The 2000 UK demand for electrical power was of the order of 1 terawatt (1 x 10¹² Watts), 24, 7 52. This equates to 8700 terawatt hours = 8.7 petawatt hr. At 4.2 pence per kilowatt-hour (Powergen’s unit of preference in the UK) this ‘costed’ £42 thousand million ($26 billion) to the customers.

In some perverse and absurd perspective, this is about the cost of one United States Air Force, B1 ‘Stealth’ Bomber. However, the payload, pilot, touch-up paint and a fill of fuel are not included in the list of purchases and the actual price is determined by creative accountancy.

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LD50, Lethal dose 50: The amounts of a toxic substance that will cause the deaths of 50% of an exposed human population within a specified time, usually a few hours.

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The electrical power generation game

There will be prizes and there is but one rule: Don’t panic.

Individuals or collections are to devise, plan and build a supply of electrical power from generators that convert energy from a renewable source.

It is essential to employ re-cycled products in the generator construction.

The length of time that the supply, at minimum, keeps lit a 12V, 21W ‘Halogen’ light bulb is to be maximised but, please, minimise the light-pollution as astronomy becomes more difficult nightly.

Projects that keep a bulb lit for 1-10 revolutions; 1-10 minutes; 1-10 hours; 1-10 days; the months of February and October; 1-10 years; 1-10 centuries; 1-10 millennia etc. succeed.

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Greenhouse gases

Water vapour and carbon dioxide dominate the atmospheric transmission of infrared radiation (i.e. heat) but methane, sulphates and other atmospheric trace constituents may be shown to be important differentially.

For more detailed studies of planetary atmospheres look here.

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Fossil fuels

These include coal, oil, natural gas, wood, peat, methane, bio-diesel, water, hydrogen &c.

For more detailed studies of fossil fuel resources look here.

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Nuclear power? Nein danker!

Burn fossil fuels to make electricity?

To make clothing flat?

And some think that Spike Milligan is mad?

It will all burn.

Momentarily.

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Western world

This collection of states is also known as the prosperous North as opposed to the poor South. The state list includes the members of the European Union, the USA, Japan and others.

Some numbers and some of their names

0 = zero = nothing = nought = e^iπ + 1.

1/10 = one divided by ten = one tenth = 0.1 = 10% = 10^-1 = ten raised to the power minus one.

10^-100 = the end of the first inflationary period in the expansion of the universe measured in seconds.

10^-35 = 1 planck*.

9.10908 x 10^-31 = the mass in kilogrammes of an electron at rest.

1.67 x 10^-27 = the mass in kilogrammes of a nucleon at rest.

10^-18 = atto = 1a.

10^-15 = femto = 1 zillionth = 1f.

10^-12 = pico = 1 trillionth = 1p.

10^-9 = nano = 1 billionth = 1n.

10^-6 = micro = 1 millionth = 1m (mu).

10^-3 = milli = 1 thousandth = 1m.

1 = one.

1.414213562… = √2 = the positive square root of two.

2.718281828… = e = the natural number[4].

3. 1415926535897932… = π (pi) = the ratio of the circumference to the diameter of a plane circle[5].

10³  = kilo = 1 thousand = 1k.

10⁶  = mega = 1 million = 1M.

2.997925 x 10⁸ = c = the speed of light (m/s) in vacuo.

10⁹  = giga = 1 milliard UK = 1 billion elsewhere = 1G.

10¹² = tera = 1 billion UK = 1 trillion elsewhere = 1T.

10¹⁵ = peta = 1 billiard* = 1 zillion elsewhere = 1P.

10¹⁸ = exa = 1 trillion UK = 1E.

10²¹ = 1 trilliard*.

6.02255 x 10²³ = Avagadro’s number, N_A, per mole of substance. The volume that a mole of diatomic gas occupies is ~22.4 litres at standard temperature and pressure, STP[6].

10²⁴ = 1 zillion UK.

10²⁷ = 1 zilliard*.

10^10000000000 = ten raised to the power (ten raised to the power ten) = 1 googol = the thermodynamic heat death time constant of the observable universe measured in seconds.

1 googol^10000000000 = 1 googol raised to the power (ten raised to the power ten) = 1 googolplex.

-1 = that which when added to what you have leaves you with nothing.

i = √-1 = the positive square root of minus one, a.k.a. the imaginary number.

The infinite = ∞ [Symbolically this is a figure eight, 8, upon its side. See Bill Gates if it is not displayed correctly.]

If an individual were to count 10¹² pins then they would have counted a terapin.

The thousandth part of a pede is a millipede.

* possibly

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Redundant engineering

This is the collection of human-made and discarded items of sound engineering value e.g. bicycles, car alternators, batteries and cabling. Some pieces are to be found almost anywhere in the western world and some better places to search include scrap-yards, rubbish dumps and local re-cycling units (if any).

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The energy in the Earth’s atmosphere

The total kinetic energy of the air molecules in each cubic metre of the atmosphere is the sum of each molecule’s ½mV², where m is the molecular mass (average ~ 3 x 10^-26kg) and V is the speed (m/s) at which the molecules travel between collisions. At near-surface atmospheric temperatures and pressures, a mole of gas occupies approximately 22.4 litres of space; the diatomic gases 0₂ and N₂ travel at average speeds near to 400m/s. Hence, in each near-surface cubic metre (~44 mol) of air there is approximately ½ x 3 x 10^-26 x 160 000 x 3 x 10²⁵ > 72 kilojoules of kinetic energy.

However, there are 6 degrees of freedom for the momentum associated with this energy and hence, the fraction in any ‘forward’ direction will be 1/6^th of the total, ~ 12 kilojoules. At a wind speed of 2 mph (U = 1 ms^-1, Beaufort force 1) therefore, there is more than kilowatts of power available in each cubic metre along the wind. This energy is available only if the extraction process causes all of the molecules to come to a complete halt. This, of course, does not happen in any practical engineering design. Indeed, it could not happen in any practical device: if the molecules were brought to a halt then there would be a rapid build up of stationary objects that would prevent any further energy extraction.

In comparison, the kinetic energy per cubic metre associated with bulk atmospheric flow is ½MU² (M is the mass of a cubic metre of atmosphere) is small. Near to the surface M~1.2 kg at S.T.P. and the energy varies as U². That is, at 1 ms^-1 wind speed there is approximately 1 watt per m³ or 1 part in 72 thousand of the molecular reservoir manifest.

A 10%-efficient wind wheel that generates 10 Watts of useful power will borrow about 100 W of power from the atmosphere at U=10ms^-1. This approximates to 1 part in 720 (0.1%) of the atmospheric reservoir and is considered a small perturbation.

Edward Lorenz (1986) described the chaotic response of the atmosphere due to energy perturbations. The result of that work was popularized in the study of non-linear dynamics or ‘Chaos’ theory. A pertinent conclusion from that work ‘chaos exists and operates at all scales’ implies that any of the storms that may brew, or climates that may flip, in Gaia’s chaotic response to the instantiation of a pyramid of wind wheels will have happened anyway. Probably.

The description of the atmospheric response to the flap of a butterfly’s wing shows that the ‘Environmental Impact’ of a logarithmic pyramid on the Earth’s atmosphere, and hence Gaia, is essentially both 0 and 1 where the zero (=0) impact is on the global scale whilst the total impact (=1) occurs at local scales around the ‘size’ of the pyramid. The total impact causes no worry since the effects become ‘lost in event noise’ within a few tens of seconds/hundreds of metres or so.

Lorenz showed that any set of linear differential equations used to model a ‘process’ (including the Earth’s atmosphere) responds chaotically at all scales. This response is illustrated well by the questions and answers relating to the Butterfly effect:

Q) Does the flap of a Butterfly’s wing lead to hurricanes on the other side of the globe?

A) Some of the time.

Q) If the Butterfly did not flap its wings then would this also lead to hurricanes on the other side of the world?

A) Some of the time.

It follows that when an amount of energy is input to, or extracted from, a system, S, at time T, the predictability, p, of the new system at time t > T approaches zero as the ‘prediction time’ or forecast period, increases.

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Ironing

To make one’s clothing and/or other fabrics and materials flat with an Iron.

In order to make the steam-on-demand required by the modern ironer, the metal ‘heat reservoir’ of the iron has its temperature raised to the degree:

T_iron ~ T_damp + 300 K.

Where, T_damp is the temperature of the clothing just before the iron lands.

Globally averaged, T_damp ~ 300 ± 20 K.

It takes approximately five minutes to iron a single pair of denim jeans.

And, no! That does not count the time it takes to get out and put away afterwards the required equipment.

The iron converts about one thousand joules of electrical energy to heat energy per second in order to perform this miracle of modern existence.

Therefore, more than 300 kilojoules of energy is converted from electrical to heat energy in the iron.

By similar reasoning, 1 terawatt is enough energy to iron more than 3 million pairs of denim jeans, in each second.

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Cylindrical volume

The volume of a cylinder is given by:

V_cyl. = ? x R x R x H.

Where, R is the radius of the circular base of the cylinder and H is its height. Pi (?) is taken as approximately equal to 3.1415926…

A bog-standard U.K. telegraph pole approximates to a cylinder of radius 0.3 and height 5 metres (1 foot radius, 20 feet high).

Hence V_{telegraph pole} is around 1½ m³ or 62 cubic feet.

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References

1992 Gardiner, B.A. et al. Boundary-layer turbulence with trees. Forestry Commission, NRS, Roslyn, Scotland, U.K.

1987 Gleick, J. “Chaos – Making a new science”, Penguin, New York, U.S.A.

1984 Hill, M.K.  Instruments, physics and words. Holtech Associates, U.K.

1993 Hill, M.L. Art and primitives. Second Childhood, U.K.

1995 IPCC Second Assessment Report: Climate change.

1981 Kildron, M. & Segal, R. The state of the world atlas. Pluto press & Pan Books ltd., London, SW10 9PG, U.K.

1984 Kuhn, T. The nature of scientific revolutions.

1984 Latham, J. et al. Physics. UMIST, Manchester, M60 1QD, U.K.

1986 Lorenz, C. Deterministic non-periodic flow. Journal of the Atmospheric Sciences, 20, p130

1988 Lovelock, J. The ages of Gaia. W.W. Norton, publishers.

2001 Manabe, S. et al. Exploring natural and anthropogenic variation of climate. Quart.J.R.Met.Soc. 127, pp 1-25.

1952 Manley, G. Climate and the British Scene. Collins Press, St. James's Place, London, U.K.

2001 Mann, M.E. Climate during the past millennium. Weather, 56, pp 91-102.

1992 Mill, C.S. Physics and electronics. UMIST, Manchester, M60 1QD.

1997 O'Dowd, C.D. et al. Some chemistry of atmospheric aerosols. CMAS, Sunderland, SR3 7RJ, U.K.

2001 Phillips, V.T.J., Blyth, A.M., Brown P.R.A., Choularton, T.W., Latham, J. The glaciation of a cumulus cloud over New Mexico. Quarterly Journal of the Royal Meteorological Society, 127, pp 1513-1534

1986 Smith, M.H. et al. Aerosol physics. UMIST, Manchester, M60 1QD, U.K.

1991 Stromberg, I.M. et al. Boundary layer studies around Great Dun Fell, Cumbria. UMIST, Manchester, M60 1QD, U.K.

1988 Stull, R.B. An introduction to boundary layer meteorology. Kluwer Academic Publishers, 3300 AA Dordrecht, the Netherlands.

1992 Taylor, P.K. et al. Atmospheric turbulence above the sea. IOS, Southampton, UK

1998 U.K. Government figures: Conservative 1979 – 1997, Labour 1997 - present.

1998 U.N. regional population estimates.

1994 Yelland, M.J. et al. Measurements of atmospheric turbulence at sea. http://ams.allenpress.com/amsonline/?request=get-abstract&issn=1520-0426&volume=011&issue=04&page=1093

The British Broadcasting Corporation, http://www.bbc.co.uk/

Cable Network News, A Time Warner enterprise. http://cnn.com/

 

Progress 2001, 2002.