08.b Boek sewtha.pdf

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10 — Offshore wind

61 Figure 10.2. UK territorial waters with depth less than 25 m (yellow) and depth between 25 m and 50 m (purple). Data from DTI Atlas of Renewable Marine Resources. © Crown copyright.

we take the total coastline of Britain (length: 3000 km), and put a strip of turbines 4 km wide all the way round, that strip would have an area of 13 000 km2 . That is the area we must fill with turbines to deliver 16 kWh/d per person. To put it another way, consider the number of turbines required. 16 kWh/d per person would be delivered by 44 000 “3 MW” turbines, which works out to 15 per kilometre of coastline, if they were evenly spaced around 3000 km of coast. Offshore wind is tough to pull off because of the corrosive effects of sea water. At the big Danish wind farm, Horns Reef, all 80 turbines had to be dismantled and repaired after only 18 months’ exposure to the sea air. The Kentish Flats turbines seem to be having similar problems with their gearboxes, one third needing replacement during the first 18 months.

Deep offshore The area with depths between 25 m and 50 m is about 80 000 km2 – the size of Scotland. Assuming again a power per unit area of 3 W/m2 , “deep” offshore wind farms could deliver another 240 GW, or 96 kWh/d per person, if turbines completely filled this area. Again, we must make corridors for shipping. I suggest as before that we assume we can use one third of the area for wind farms; this area would then be about 30% bigger than Wales,

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62

Sustainable Energy – without the hot air

and much of it would be further than 50 km offshore. The outcome: if an area equal to a 9 km-wide strip all round the coast were filled with turbines, deep offshore wind could deliver a power of 32 kWh/d per person. A huge amount of power, yes; but still no match for our huge consumption. And we haven’t spoken about the issue of wind’s intermittency. We’ll come back to that in Chapter 26. I’ll include this potential deep offshore contribution in the production stack, with the proviso, as I said before, that wind experts reckon deep offshore wind is prohibitively expensive.

Some comparisons and costs So, how’s our race between consumption and production coming along? Adding both shallow and deep offshore wind to the production stack, the green stack has a lead. Something I’d like you to notice about this race, though, is this contrast: how easy it is to toss a bigger log on the consumption fire, and how difficult it is to grow the production stack. As I write this paragraph, I’m feeling a little cold, so I step over to my thermostat and turn it up. It’s so simple for me to consume an extra 30 kWh per day. But squeezing an extra 30 kWh per day per person from renewables requires an industrialization of the environment so large it is hard to imagine. To create 48 kWh per day of offshore wind per person in the UK would require 60 million tons of concrete and steel – one ton per person. Annual world steel production is about 1200 million tons, which is 0.2 tons per person in the world. During the second world war, American shipyards built 2751 Liberty ships, each containing 7000 tons of steel – that’s a total of 19 million tons of steel, or 0.1 tons per American. So the building of 60 million tons of wind turbines is not off the scale of achievability; but don’t kid yourself into thinking that it’s easy. Making this many windmills is as big a feat as building the Liberty ships.

For comparison, to make 48 kWh per day of nuclear power per person in the UK would require 8 million tons of steel and 0.14 million tons of concrete. We can also compare the 60 million tons of offshore wind hardware that we’re trying to imagine with the existing fossil-fuel hardware already sitting in and around the North Sea (figure 10.4). In 1997, 200 installations and 7000 km of pipelines in the UK waters of the North Sea contained 8 million tons of steel and concrete. The newly built Langeled gas pipeline from Norway to Britain, which will convey gas with a power of 25 GW (10 kWh/d/p), used another 1 million tons of steel and 1 million tons of concrete (figure 10.5). The UK government announced on 10th December 2007 that it would permit the creation of 33 GW of offshore wind capacity (which would deliver on average 10 GW to the UK, or 4.4 kWh per day per person), a plan branded “pie in the sky” by some in the wind industry. Let’s run with a round figure of 4 kWh per day per person. This is one quarter of my

Deep offshore wind: 32 kWh/d

Shallow offshore wind: 16 kWh/d Hydro: 1.5 kWh/d

Light: 4 kWh/d

Heating, cooling: 37 kWh/d

Jet flights: 30 kWh/d

Biomass: food, biofuel, wood, waste incin’n, landfill gas: 24 kWh/d

PV farm (200 m2/p): 50 kWh/d

PV, 10 m2/p: 5

Car: 40 kWh/d

Solar heating: 13 kWh/d

Wind: 20 kWh/d

Figure 10.3. Offshore wind.

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

10 — Offshore wind

63

shallow 16 kWh per day per person. To obtain this average power requires roughly 10 000 “3 MW” wind turbines like those in figure 10.1. (They have a capacity of “3 MW” but on average they deliver 1 MW. I pop quotes round “3 MW” to indicate that this is a capacity, a peak power.) What would this “33 GW”’ of power cost to erect? Well, the “90 MW” Kentish Flats farm cost £105 million, so “33 GW” would cost about £33 billion. One way to clarify this £33 billion cost of offshore wind delivering 4 kWh/d per person is to share it among the UK population; that comes out to £550 per person. This is a much better deal, incidentally, than microturbines. A roof-mounted microturbine currently costs about £1500 and, even at a very optimistic windspeed of 6 m/s, delivers only 1.6 kWh/d. In reality, in a typical urban location in England, such microturbines deliver 0.2 kWh per day. Another bottleneck constraining the planting of wind turbines is the special ships required. To erect 10 000 wind turbines (“33 GW”) over a period of 10 years would require roughly 50 jack-up barges. These cost £60 million each, so an extra capital investment of £3 billion would be required. Not a show-stopper compared with the £33bn price tag already quoted, but the need for jack-up barges is certainly a detail that requires some forward planning.

Costs to birds Do windmills kill “huge numbers” of birds? Wind farms recently got adverse publicity from Norway, where the wind turbines on Smola, a set of islands off the north-west coast, killed 9 white-tailed eagles in 10 months. I share the concern of BirdLife International for the welfare of rare birds. But I think, as always, it’s important to do the numbers. It’s been estimated that 30 000 birds per year are killed by wind turbines in Denmark, where windmills generate 9% of the electricity. Horror! Ban windmills! We also learn, moreover, that traffic kills one million birds per year in Denmark. Thirty-times-greater horror! Thirty-times-greater incentive to ban cars! And in Britain, 55 million birds per year are killed by cats (figure 10.6). Going on emotions alone, I would like to live in a country with virtually no cars, virtually no windmills, and with plenty of cats and birds (with the cats that prey on birds perhaps being preyed upon by Norwegian whitetailed eagles, to even things up). But what I really hope is that decisions about cars and windmills are made by careful rational thought, not by emotions alone. Maybe we do need the windmills!

Figure 10.4. The Magnus platform in the northern UK sector of the North Sea contains 71 000 tons of steel. In the year 2000 this platform delivered 3.8 million tons of oil and gas – a power of 5 GW. The platform cost £1.1 billion. Photos by Terry Cavner.

Figure 10.5. Pipes for Langeled. From Bredero–Shaw [brederoshaw.com].

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

64

Sustainable Energy – without the hot air Figure 10.6. Birds lost in action. Annual bird deaths in Denmark caused by wind turbines and cars, and annual bird deaths in Britain caused by cats. Numbers from Lomborg (2001). Collisions with windows kill a similar number to cats.

30 000

1 000 000

55 000 000

Notes and further reading page no. 60 The Kentish Flats wind farm in the Thames Estuary. . . See www.kentishflats.co.uk. Its 30 Vestas V90 wind turbines have a total peak output of 90 MW, and the predicted average output was 32 MW (assuming a load factor of 36%). The mean wind speed at the hub height is 8.7 m/s. The turbines stand in 5 m-deep water, are spaced 700 m apart, and occupy an area of 10 km2 . The power density of this offshore wind farm was thus predicted to be 3.2 W/m2 . In fact, the average output was 26 MW, so the average load factor in 2006 was 29% [wbd8o]. This works out to a power density of 2.6 W/m2 . The North Hoyle wind farm off Prestatyn, North Wales, had a higher load factor of 36% in 2006. Its thirty 2 MW turbines occupy 8.4 km2 . They thus had an average power density of 2.6 W/m2 . – . . . shallow offshore wind, while roughly twice as costly as onshore wind, is economically feasible, given modest subsidy. Source: Danish wind association windpower.org. – . . . deep offshore wind is at present not economically feasible. Source: British Wind Energy Association briefing document, September 2005, www.bwea.com. Nevertheless, a deep offshore demonstration project in 2007 put two turbines adjacent to the Beatrice oil field, 22 km off the east coast of Scotland (figure 10.8). Each turbine has a “capacity” of 5 MW and sits in a water depth of 45 m.

Hub height: 107 m; diameter 126 m. All the electricity generated will be used by the oil platforms. Isn’t that special! The 10 MW project cost £30 million – this price-tag of £3 per watt (peak) can be

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

65

10 — Offshore wind depth 5 to 30 metres Region

depth 30 to 50 metres

(km2 )

potential resource (kWh/d/p)

(km2 )

potential resource (kWh/d/p)

North West Greater Wash Thames Estuary Other

3 300 7 400 2 100 14 000

6 14 4 28

2 000 950 850 45 000

4 2 2 87

TOTAL

27 000

52

49 000

94

area

area

compared with that of Kentish Flats, £1.2 per watt (£105 million for 90 MW). www.beatricewind.co.uk It’s possible that floating wind turbines may change the economics of deep offshore wind. 60 The area available for offshore wind. The Department of Trade and Industry’s (2002) document “Future Offshore” gives a detailed breakdown of areas that are useful for offshore wind power. Table 10.7 shows the estimated resource in 76 000 km2 of shallow and deep water. The DTI’s estimated power contribution, if these areas were entirely filled with windmills, is 146 kWh/d per person (consisting of 52 kWh/d/p from the shallow and 94 kWh/d/p from the deep). But the DTI’s estimate of the potential offshore wind generation resource is just 4.6 kWh per day per person. It might be interesting to describe how they get down from this potential resource of 146 kWh/d per person to 4.6 kWh/d per person. Why a final figure so much lower than ours? First, they imposed these limits: the water must be within 30 km of the shore and less than 40 m deep; the sea bed must not have gradient greater than 5◦ ; shipping lanes, military zones, pipelines, fishing grounds, and wildlife reserves are excluded.

Second, they assumed that only 5% of potential sites will be developed (as a result of seabed composition or planning constraints); they reduced the capacity by 50% for all sites less than 10 miles from shore, for reasons of public acceptability; they further reduced the capacity of sites with wind speed over 9 m/s by 95% to account for “development barriers presented by the hostile environment;” and other sites with average wind speed 8–9 m/s had their capacities reduced by 5%. 61 . . . if we take the total coastline of Britain (length: 3000 km), and put a strip of turbines 4 km wide all the way round. . . Pedants will say that “the coastline of Britain is not a well-defined length, because the coast is a fractal.” Yes, yes, it’s a fractal. But, dear pedant, please take a map and put a strip of turbines 4 km wide around mainland Britain, and see if it’s not the case that your strip is indeed about 3000 km long. – Horns Reef (Horns Rev). The difficulties with this “160 MW” Danish wind farm off Jutland [www.hornsrev.dk] are described by Halkema (2006).

Table 10.7. Potential offshore wind generation resource in proposed strategic regions, if these regions were entirely filled with wind turbines. From Dept. of Trade and Industry (2002b).

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

66

Sustainable Energy – without the hot air When it is in working order, Horns Reef’s load factor is 0.43 and its average power per unit area is 2.6 W/m2 .

62 Liberty ships – www.liberty-ship.com/html/yards/introduction.html – . . . fossil fuel installations in the North Sea contained 8 million tons of steel and concrete – Rice and Owen (1999). – The UK government announced on 10th December 2007 that it would permit the creation of 33 GW of offshore capacity. . . [25e59w]. – . . . “pie in the sky”. Source: Guardian [2t2vjq]. 63 What would “33 GW” of offshore wind cost? According to the DTI in November 2002, electricity from offshore wind farms costs about £50 per MWh (5p per kWh) (Dept. of Trade and Industry, 2002b, p21). Economic facts vary, however, and in April 2007 the estimated cost of offshore was up to £92 per MWh (Dept. of Trade and Industry, 2007, p7). By April 2008, the price of offshore wind evidently went even higher: Shell pulled out of their commitment to build the London Array. It’s because offshore wind is so expensive that the Government is having to increase the number of ROCs (renewable obligation certificates) per unit of offshore wind energy. The ROC is the unit of subsidy given out to certain forms of renewable electricity generation. The standard value of a ROC is £45, with 1 ROC per MWh; so with a wholesale price of roughly £40/MWh, renewable generators are getting paid £85 per MWh. So 1 ROC per MWh is not enough subsidy to cover the cost of £92 per MWh.

In the same document, estimates for other renewables (medium levelized costs in 2010) are as follows. Onshore wind: £65–89/MWh; co-firing of biomass: £53/MWh; large-scale hydro: £63/MWh; sewage gas: £38/MWh; solar PV: £571/MWh; wave: £196/MWh; tide: £177/MWh. “Dale Vince, chief executive of green energy provider Ecotricity, which is engaged in building onshore wind farms, said that he supported the Government’s [offshore wind] plans, but only if they are not to the detriment of onshore wind. ‘It’s dangerous to overlook the fantastic resource we have in this country. . . By our estimates, it will cost somewhere in the region of £40bn to build the 33 GW of offshore power Hutton is proposing. We could do the same job onshore for £20bn’.” [57984r] – In a typical urban location in England, microturbines deliver 0.2 kWh per day. Source: Third Interim Report, www.warwickwindtrials.org.uk/2.html. Among the best results in the Warwick Wind Trials study is a Windsave WS1000 (a 1-kW machine) in Daventry mounted at a height of 15 m above the ground, generating 0.6 kWh/d on average. But some microturbines deliver only 0.05 kWh per day – Source: Donnachadh McCarthy: “My carbonfree year,” The Independent, December 2007 [6oc3ja].

The Windsave WS1000 wind turbine, sold across England in B&Q’s shops, won an Eco-Bollocks award from Housebuilder’s Bible author Mark Brinkley: “Come on, it’s time to admit that the roof-mounted wind turbine industry is a complete fiasco. Good money is being thrown at an invention that doesn’t work. This is the Sinclair C5 of the Noughties.” [5soql2]. The Met Office and Carbon Trust published a report in July 2008 [6g2jm5], which estimates that, if small-scale

Figure 10.8. Construction of the Beatrice demonstrator deep offshore windfarm. Photos kindly provided by Talisman Energy (UK) Limited.

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10 — Offshore wind

turbines were installed at all houses where economical in the UK, they would generate in total roughly 0.7 kWh/d/p. They advise that roof-mounted turbines in towns are usually worse than useless: “in many urban situations, roof-mounted turbines may not pay back the carbon emitted during their production, installation and operation.” 63 Jack-up barges cost £60 million each. Source: news.bbc.co.uk/1/hi/magazine/7206780.stm. I estimated that we would need roughly 50 of them by assuming that there would be 60 workfriendly days each year, and that erecting a turbine would take 3 days. Further reading: UK wind energy database [www.bwea.com/ukwed/].

67

Figure 10.9. Kentish Flats. Photos © Elsam (elsam.com). Used with permission.

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11

Gadgets

One of the greatest dangers to society is the phone charger. The BBC News has been warning us of this since 2005: “The nuclear power stations will all be switched off in a few years. How can we keep Britain’s lights on? ... unplug your mobile-phone charger when it’s not in use.” Sadly, a year later, Britain hadn’t got the message, and the BBC was forced to report: “Britain tops energy waste league.” And how did this come about? The BBC rams the message home: “65% of UK consumers leave chargers on.”

Vader

Charger

Figure 11.1. Planet destroyers. Spot the difference.

From the way reporters talk about these planet-destroying black objects, it’s clear that they are roughly as evil as Darth Vader. But how evil, exactly? In this chapter we’ll find out the truth about chargers. We’ll also investigate their cousins in the gadget parade: computers, phones, and TVs. Digital set-top boxes. Cable modems. In this chapter we’ll estimate the power used in running them and charging them, but not in manufacturing the toys in the first place – we’ll address that in the later chapter on “stuff.”

The truth about chargers Modern phone chargers, when left plugged in with no phone attached, use about half a watt. In our preferred units, this is a power consumption of about 0.01 kWh per day. For anyone whose consumption stack is over 100 kWh per day, the BBC’s advice, always unplug the phone charger, could potentially reduce their energy consumption by one hundredth of one percent (if only they would do it). Every little helps! I don’t think so. Obsessively switching off the phone-charger is like bailing the Titanic with a teaspoon. Do switch it off, but please be aware how tiny a gesture it is. Let me put it this way: All the energy saved in switching off your charger for one day is used up in one second of car-driving. The energy saved in switching off the charger for one year is equal to the energy in a single hot bath. 68

Figure 11.2. These five chargers – three for mobile phones, one for a pocket PC, and one for a laptop – registered less than one watt on my power meter.

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11 — Gadgets

69

Admittedly, some older chargers use more than half a watt – if it’s warm to the touch, it’s probably using one watt or even three (figure 11.3). A three-watt-guzzling charger uses 0.07 kWh per day. I think that it’s a good idea to switch off such a charger – it will save you three pounds per year. But don’t kid yourself that you’ve “done your bit” by so doing. 3 W is only a tiny fraction of total energy consumption. OK, that’s enough bailing the Titanic with a teaspoon. Let’s find out where the electricity is really being used.

Gadgets that really suck Table 11.4 shows the power consumptions, in watts, of a houseful of gadgets. The first column shows the power consumption when the device is actually being used – for example, when a sound system is actually playing sound. The second column shows the consumption when the device is switched on, but sitting doing nothing. I was particularly shocked to find that a laser-printer sitting idle consumes 17 W – the same as the average consumption of a fridge-freezer! The third column shows the consumption when the gadget is explicitly asked to go to sleep or standby. The fourth shows the consumption when it is completely switched off – but still left plugged in to the mains. I’m showing all these powers in watts – to convert back to our standard units, remember that 40 W is 1 kWh/d. A nice rule of thumb, by the way, is that each watt costs about one pound per year (assuming electricity costs 10p per kWh). The biggest guzzlers are the computer, its screen, and the television, whose consumption is in the hundreds of watts, when on. Entertainment systems such as stereos and DVD players swarm in the computer’s wake, many of them consuming 10 W or so. A DVD player may cost just £20 in the shop, but if you leave it switched on all the time, it’s costing you another £10 per year.

Some stereos and computer peripherals consume several watts even when switched off, thanks to their mains-transformers. To be sure that a gadget is truly off, you need to switch it off at the wall.

Powering the hidden tendrils of the information age According to Jonathan Koomey (2007), the computer-servers in US datacentres and their associated plumbing (air conditioners, backup power systems, and so forth) consumed 0.4 kWh per day per person – just over 1% of US electricity consumption. That’s the consumption figure for 2005, which, by the way, is twice as big as the consumption in 2000, because the number of servers grew from 5.6 million to 10 million.

Figure 11.3. This wasteful cordless phone and its charger use 3 W when left plugged in. That’s 0.07 kWh/d. If electricity costs 10p per kWh then a 3 W trickle costs £3 per year.

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70

Sustainable Energy – without the hot air

Gadget

Power consumption (W) on and active

on but inactive

Computer and peripherals: computer box cathode-ray display LCD display projector laser printer wireless & cable-modem Laptop computer

80 110 34 150 500 9 16

55

Portable CD player Bedside clock-radio Bedside clock-radio Digital radio Radio cassette-player Stereo amplifier Stereo amplifier II Home cinema sound DVD player DVD player II TV Video recorder Digital TV set top box Clock on microwave oven

2 1.1 1.9 9.1 3 6 13 7 7 12 100 13 6 2

Xbox Sony Playstation 3 Nintendo Wii

160 190 18

Answering machine Answering machine II Cordless telephone Mobile phone charger Vacuum cleaner

5 1600

standby

3 2 5

off

Table 11.4. Power consumptions of various gadgets, in watts. 40 W is 1 kWh/d.

2 0 1

17

Laptop: 16 W

9

Computer: 80 W

0.5

1 1.4

LCD 31 W

CRT Printer: 17 W 108 W (on, idle)

3 1.2

7 6 10

1.2 6 0 4 5 10 1 5 2.4 2 2

2 3 1.7 0.5

Projector: 150 W

Digital radio: 8 W

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11 — Gadgets

Other gadgets Deep offshore wind: 32 kWh/d

A vacuum cleaner, if you use it for a couple of hours per week, is equivalent to about 0.2 kWh/d. Mowing the lawn uses about 0.6 kWh. We could go on, but I suspect that computers and entertainment systems are the big suckers on most people’s electrical balance-sheet. This chapter’s summary figure: it’ll depend how many gadgets you have at home and work, but a healthy houseful or officeful of gadgets left on all the time could easily use 5 kWh/d.

Mythconceptions “There is no point in my switching off lights, TVs, and phone chargers during the winter. The ‘wasted’ energy they put out heats my home, so it’s not wasted.” This myth is True for a few people, but only during the winter; but False for most. If your house is being heated by electricity through ordinary bar fires or blower heaters then, yes, it’s much the same as heating the house with any electricity-wasting appliances. But if you are in this situation, you should change the way you heat your house. Electricity is high-grade energy, and heat is low-grade energy. It’s a waste to turn electricity into heat. To be precise, if you make only one unit of heat from a unit of electricity, that’s a waste. Heaters called air-source heat pumps or ground-source heat pumps can do much better, delivering 3 or 4 units of heat for every unit of electricity consumed. They work like back-to-front refrigerators, pumping heat into your house from the outside air (see Chapter 21). For the rest, whose homes are heated by fossil fuels or biofuels, it’s a good idea to avoid using electrical gadgets as a heat source for your home – at least for as long as our increases in electricity-demand are served from fossil fuels. It’s better to burn the fossil fuel at home.

The point is, if you use electricity from an ordinary fossil power station, more than half of the energy from the fossil fuel goes sadly up the cooling tower. Of the energy that gets turned into electricity, about 8% is lost in the transmission system. If you burn the fossil fuel in your home, more of the energy goes directly into making hot air for you.

Notes and further reading page no. 68 The BBC News has been warning us . . . unplug your mobile-phone charger. The BBC News article from 2005 said: “the nuclear power stations will all be switched off in a few years. How can we keep Britain’s lights on? Here’s three ways you can save energy: switch off video recorders when they’re not in use; don’t leave televisions on standby; and unplug your mobile-phone charger when it’s not in use.”

Gadgets: 5 Light: 4 kWh/d

Heating, cooling: 37 kWh/d

Jet flights: 30 kWh/d

Shallow offshore wind: 16 kWh/d Hydro: 1.5 kWh/d

Biomass: food, biofuel, wood, waste incin’n, landfill gas: 24 kWh/d

PV farm (200 m2/p): 50 kWh/d

PV, 10 m2/p: 5

Car: 40 kWh/d

Solar heating: 13 kWh/d

Wind: 20 kWh/d

Figure 11.5. Information systems and other gadgets.

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Sustainable Energy – without the hot air

68 Modern phone chargers, when left plugged in with no phone attached, use about half a watt. The Maplin power meter in figure 11.2 is not accurate enough to measure this sort of power. I am grateful to Sven Weier and Richard McMahon of Cambridge University Engineering Department who measured a standard Nokia charger in an accurate calorimeter; they found that, when not connected to the mobile, it wastes 0.472 W. They made additional interesting measurements: the charger, when connected to a fully-charged mobile phone, wastes 0.845 W; and when the charger is doing what it’s meant to do, charging a partly-charged Nokia mobile, it wastes 4.146 W as heat. Pedants sometimes ask “what about the reactive power of the charger?” This is a technical niggle, not really worth our time. For the record, I measured the reactive power (with a crummy meter) and found it to be about 2 VA per charger. Given that the power loss in the national grid is 8% of the delivered power, I reckon that the power loss associated with the reactive power is at most 0.16 W. When actually making a phone-call, the mobile uses 1 W. Further reading: Kuehr (2003).

Figure 11.6. Advertisement from the “DIY planet repairs” campaign. The text reads “Unplug. If every London household unplugged their mobile-phone chargers when not in use, we could save 31,000 tonnes of CO2 and £7.75m per year.” london.gov.uk/diy/

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

12

Wave

If wave power offers hope to any country, then it must offer hope to the United Kingdom and Ireland – flanked on the one side by the Atlantic Ocean, and on the other by the North Sea. First, let’s clarify where waves come from: sun makes wind and wind makes waves. Most of the sunlight that hits our planet warms the oceans. The warmed water warms the air above it, and produces water vapour. The warmed air rises; as it rises it cools, and the water eventually re-condenses, forming clouds and rain. At its highest point, the air is cooled down further by the freezing blackness of space. The cold air sinks again. This great solarpowered pump drives air round and round in great convection rolls. From our point of view on the surface, these convection rolls produce the winds. Wind is second-hand solar energy. As wind rushes across open water, it generates waves. Waves are thus third-hand solar energy. (The waves that crash on a beach are nothing to do with the tides.) In open water, waves are generated whenever the wind speed is greater than about 0.5 m/s. The wave crests move at about the speed of the wind that creates them, and in the same direction. The wavelength of the waves (the distance between crests) and the period (the time between crests) depend on the speed of the wind.

The longer the wind blows for, and the greater the expanse of water over which the wind blows, the greater the height of the waves stroked up by the wind. Thus since the prevailing winds over the Atlantic go from west to east, the waves arriving on the Atlantic coast of Europe are often especially big. (The waves on the east coast of the British Isles are usually much smaller, so my estimates of potential wave power will focus on the resource in the Atlantic Ocean.) Waves have long memory and will keep going in the same direction for days after the wind stopped blowing, until they bump into something. In seas where the direction of the wind changes frequently, waves born on different days form a superposed jumble, travelling in different directions. If waves travelling in a particular direction encounter objects that absorb energy from the waves – for example, a row of islands with sandy beaches – then the seas beyond the object are calmer. The objects cast a shadow, and there’s less energy in the waves that get by. So, whereas sunlight delivers a power per unit area, waves deliver a power per unit length of coastline. You can’t have your cake and eat it. You can’t collect wave energy two miles off-shore and one mile off-shore. Or rather, you can try, but the two-mile facility will absorb energy that would have gone to the one-mile facility, and it won’t be replaced.

The fetch required for wind to stroke up big waves is thousands of miles. We can find an upper bound on the maximum conceivable power that could be obtained from wave power by estimating the incoming power 73

Figure 12.1. A Pelamis wave energy collector is a sea snake made of four sections. It faces nose-on towards the incoming waves. The waves make the snake flex, and these motions are resisted by hydraulic generators. The peak power from one snake is 750 kW; in the best Atlantic location one snake would deliver 300 kW on average. Photo from Pelamis wave power www.pelamiswave.com.

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

74 per unit length of exposed coastline, and multiplying by the length of coastline. We ignore the question of what mechanism could collect all this power, and start by working out how much power it is. The power of Atlantic waves has been measured: it’s about 40 kW per metre of exposed coastline. That sounds like a lot of power! If everyone owned a metre of coastline and could harness their whole 40 kW, that would be plenty of power to cover modern consumption. However, our population is too big. There is not enough Atlantic-facing coastline for everyone to have their own metre. As the map on p73 shows, Britannia rules about 1000 km of Atlantic coastline (one million metres), which is 1/60 m per person. So the total raw incoming power is 16 kWh per day per person. If we extracted all this power, the Atlantic, at the seaside, would be as flat as a millpond. Practical systems won’t manage to extract all the power, and some of the power will inevitably be lost during conversion from mechanical energy to electricity. Let’s assume that brilliant wave-machines are 50%-efficient at turning the incoming wave power into electricity, and that we are able to pack wavemachines along 500 km of Atlantic-facing coastline. That would mean we could deliver 25% of this theoretical bound. That’s 4 kWh per day per person.

As usual, I’m intentionally making pretty extreme assumptions to boost the green stack – I expect the assumption that we could line half of the Atlantic coastline with wave absorbers will sound bananas to many readers. How do the numbers assumed in this calculation compare with today’s technology? As I write, there are just three wave machines working in deep water: three Pelamis wave energy collectors (figure 12.1) built in Scotland and deployed off Portugal. No actual performance results have been published, but the makers of the Pelamis (“designed with survival as the key objective before power capture efficiency”) predict that a two-kilometrelong wave-farm consisting of 40 of their sea-snakes would deliver 6 kW per metre of wave-farm. Using this number in the previous calculation, the power delivered by 500 kilometres of wave-farm is reduced to 1.2 kWh per day per person. While wave power may be useful for small communities on remote islands, I suspect it can’t play a significant role in the solution to Britain’s sustainable energy problem. What’s the weight of a Pelamis, and how much steel does it contain? One snake with a maximum power of 750 kW weighs 700 tons, including 350 tons of ballast. So it has about 350 tons of steel. That’s a weight-topower ratio of roughly 500 kg per kW (peak).

We can compare this with the steel requirements for offshore wind: an offshore wind-turbine with a maximum power of 3 MW weighs 500 tons, including its foundation. That’s a weight-to-power ratio of about 170 kg per kW, one third of the wave machine’s. The Pelamis is a first prototype; presumably with further investment and development in wave technology, the weight-to-power ratio would fall.

Sustainable Energy – without the hot air Wave: 4 kWh/d Deep offshore wind: 32 kWh/d

Gadgets: 5 Light: 4 kWh/d

Heating, cooling: 37 kWh/d

Jet flights: 30 kWh/d

Shallow offshore wind: 16 kWh/d Hydro: 1.5 kWh/d

Biomass: food, biofuel, wood, waste incin’n, landfill gas: 24 kWh/d

PV farm (200 m2/p): 50 kWh/d

PV, 10 m2/p: 5

Car: 40 kWh/d

Solar heating: 13 kWh/d

Wind: 20 kWh/d

Figure 12.2. Wave.

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

75

12 — Wave

Notes and further reading page no. 73 Waves are generated whenever the wind speed is greater than about 0.5 m/s. The wave crests move at about the speed of the wind that creates them. The simplest theory of wave-production (Faber, 1995, p. 337) suggests that (for small waves) the wave crests move at about half the speed of the wind that creates them. It’s found empirically however that, the longer the wind blows for, the longer the wavelength of the dominant waves present, and the greater their velocity. The characteristic speed of fully-developed seas is almost exactly equal to the wind-speed 20 metres above the sea surface (Mollison, 1986). – The waves on the east coast of the British Isles are usually much smaller. Whereas the wave power at Lewis (Atlantic) is 42 kW/m, the powers at the east-coast sites are: Peterhead: 4 kW/m; Scarborough: 8 kW/m; Cromer: 5 kW/m. Source: Sinden (2005). Sinden says: “The North Sea Region experiences a very low energy wave environment.” 74 Atlantic wave power is 40 kW per metre of exposed coastline. (Chapter F explains how we can estimate this power using a few facts about waves.) This number has a firm basis in the literature on Atlantic wave power (Mollison et al., 1976; Mollison, 1986, 1991).

From Mollison (1986), for example: “the large scale resource of the NE Atlantic, from Iceland to North Portugal, has a net resource of 40–50 MW/km, of which 20–30 MW/km is potentially economically extractable.” At any point in the open ocean, three powers per unit length can be distinguished: the total power passing through that point in all directions (63 kW/m on average at the Isles of Scilly and 67 kW/m off Uist); the net power intercepted by a directional collecting device oriented in the optimal direction (47 kW/m and 45 kW/m respectively); and the power per unit coastline, which takes into account the misalignment between the optimal orientation of a directional collector and the coastline (for example in Portugal the optimal orientation faces northwest and the coastline faces west). – Practical systems won’t manage to extract all the power, and some of the power will inevitably be lost during conversion from mechanical energy to electricity. The UK’s first grid-connected wave machine, the Limpet on Islay, provides a striking example of these losses. When it was designed its conversion efficiency from wave power to grid power was estimated to be 48%, and the average power output was predicted to be 200 kW. However losses in the capture system, flywheels and electrical components mean the actual average output is 21 kW – just 5% of the predicted output (Wavegen, 2002).

Photo by Terry Cavner.

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

13

Food and farming Modern agriculture is the use of land to convert petroleum into food. Albert Bartlett

We’ve already discussed in Chapter 6 how much sustainable power could be produced through greenery; in this chapter we discuss how much power is currently consumed in giving us our daily bread. A moderately active person with a weight of 65 kg consumes food with a chemical energy content of about 2600 “Calories” per day. A “Calorie,” in food circles, is actually 1000 chemist’s calories (1 kcal). 2600 “Calories” per day is about 3 kWh per day. Most of this energy eventually escapes from the body as heat, so one function of a typical person is to act as a space heater with an output of a little over 100 W, a medium-power lightbulb. Put 10 people in a small cold room, and you can switch off the 1 kW convection heater. How much energy do we actually consume in order to get our 3 kWh per day? If we enlarge our viewpoint to include the inevitable upstream costs of food production, then we may find that our energy footprint is substantially bigger. It depends if we are vegan, vegetarian or carnivore. The vegan has the smallest inevitable footprint: 3 kWh per day of energy from the plants he eats.

Figure 13.1. A salad Niçoise.

Minimum: 3 kWh/d

Figure 13.2. Minimum energy requirement of one person.

The energy cost of drinking milk I love milk. If I drinka-pinta-milka-day, what energy does that require? A typical dairy cow produces 16 litres of milk per day. So my one pint per day (half a litre per day) requires that I employ 1/32 of a cow. Oh, hang on – I love cheese too. And to make 1 kg of Irish Cheddar takes about 9 kg of milk. So consuming 50 g of cheese per day requires the production of an extra 450 g of milk. OK: my milk and cheese habit requires that I employ 1/16 of a cow. And how much power does it take to run a cow? Well, if a cow weighing 450 kg has similar energy requirements per kilogram to a human (whose 65 kg burns 3 kWh per day) then the cow must be using about 21 kWh/d. Does this extrapolation from human to cow make you uneasy? Let’s check these numbers: www.dairyaustralia.com.au says that a suckling cow of weight 450 kg needs 85 MJ/d, which is 24 kWh/d. Great, our guess wasn’t far off! So my 1/16 share of a cow has an energy consumption of about 1.5 kWh per day. This figure ignores other energy costs involved in persuading the cow to make milk and the milk to turn to cheese, and of getting the milk and cheese to travel from her to me. We’ll cover some of these costs when we discuss freight and supermarkets in Chapter 15. 76

Milk, cheese: 1.5 kWh/d

Figure 13.3. Milk and cheese.

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

77

13 — Food and farming

Eggs A “layer” (a chicken that lays eggs) eats about 110 g of chicken feed per day. Assuming that chicken feed has a metabolizable energy content of 3.3 kWh per kg, that’s a power consumption of 0.4 kWh per day per chicken. Layers yield on average 290 eggs per year. So eating two eggs a day requires a power of 1 kWh per day. Each egg itself contains 80 kcal, which is about 0.1 kWh. So from an energy point of view, egg production is 20% efficient.

Eggs: 1 kWh/d Figure 13.4. Two eggs per day.

The energy cost of eating meat Let’s say an enthusiastic meat-eater eats about half a pound a day (227 g). (This is the average meat consumption of Americans.) To work out the power required to maintain the meat-eater’s animals as they mature and wait for the chop, we need to know for how long the animals are around, consuming energy. Chicken, pork, or beef? Chicken, sir? Every chicken you eat was clucking around being a chicken for roughly 50 days. So the steady consumption of half a pound a day of chicken requires about 25 pounds of chicken to be alive, preparing to be eaten. And those 25 pounds of chicken consume energy. Pork, madam? Pigs are around for longer – maybe 400 days from birth to bacon – so the steady consumption of half a pound a day of pork requires about 200 pounds of pork to be alive, preparing to be eaten. Cow? Beef production involves the longest lead times. It takes about 1000 days of cow-time to create a steak. So the steady consumption of half a pound a day of beef requires about 500 pounds of beef to be alive, preparing to be eaten. To condense all these ideas down to a single number, let’s assume you eat half a pound (227 g) per day of meat, made up of equal quantities of chicken, pork, and beef. This meat habit requires the perpetual sustenance of 8 pounds of chicken meat, 70 pounds of pork meat, and 170 pounds of cow meat.

That’s a total of 110 kg of meat, or 170 kg of animal (since about two thirds of the animal gets turned into meat). And if the 170 kg of animal has similar power requirements to a human (whose 65 kg burns 3 kWh/d) then the power required to fuel the meat habit is 170 kg ×

3 kWh/d ≃ 8 kWh/d. 65 kg

I’ve again taken the physiological liberty of assuming “animals are like humans;” a more accurate estimate of the energy to make chicken is in this chapter’s endnotes. No matter, I only want a ballpark estimate, and here it is. The power required to make the food for a typical consumer of vegetables, dairy, eggs, and meat is 1.5 + 1.5 + 1 + 8 = 12 kWh per day. (The daily calorific balance of this rough diet is 1.5 kWh from vegetables;

Carnivory: 8 kWh/d

Figure 13.5. Eating meat requires extra power because we have to feed the queue of animals lining up to be eaten by the human.

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

78 0.7 kWh from dairy; 0.2 kWh from eggs; and 0.5 kWh from meat – a total of 2.9 kWh per day.) This number does not include any of the power costs associated with farming, fertilizing, processing, refrigerating, and transporting the food. We’ll estimate some of those costs below, and some in Chapter 15. Do these calculations give an argument in favour of vegetarianism, on the grounds of lower energy consumption? It depends on where the animals feed. Take the steep hills and mountains of Wales, for example. Could the land be used for anything other than grazing? Either these rocky pasturelands are used to sustain sheep, or they are not used to help feed humans. You can think of these natural green slopes as maintenance-free biofuel plantations, and the sheep as automated self-replicating biofuelharvesting machines. The energy losses between sunlight and mutton are substantial, but there is probably no better way of capturing solar power in such places.

(I’m not sure whether this argument for sheep-farming in Wales actually adds up: during the worst weather, Welsh sheep are moved to lower fields where their diet is supplemented with soya feed and other food grown with the help of energy-intensive fertilizers; what’s the true energy cost? I don’t know.) Similar arguments can be made in favour of carnivory for places such as the scrublands of Africa and the grasslands of Australia; and in favour of dairy consumption in India, where millions of cows are fed on by-products of rice and maize farming. On the other hand, where animals are reared in cages and fed grain that humans could have eaten, there’s no question that it would be more energy-efficient to cut out the middlehen or middlesow, and feed the grain directly to humans.

Sustainable Energy – without the hot air

Figure 13.6. Will harvest energy crops for food.

Fertilizer and other energy costs in farming The embodied energy in Europe’s fertilizers is about 2 kWh per day per person. According to a report to DEFRA by the University of Warwick, farming in the UK in 2005 used an energy of 0.9 kWh per day per person for farm vehicles, machinery, heating (especially greenhouses), lighting, ventilation, and refrigeration.

2 kWh/d

9 kWh/d

The energy cost of Tiddles, Fido, and Shadowfax Animal companions! Are you the servant of a dog, a cat, or a horse? There are perhaps 8 million cats in Britain. Let’s assume you look after one of them. The energy cost of Tiddles? If she eats 50 g of meat per day (chicken, pork, and beef), then the last section’s calculation says that the power required to make Tiddles’ food is just shy of 2 kWh per day. A vegetarian cat would require less. Similarly if your dog Fido eats 200 g of meat per day, and carbohydrates

17 kWh/d

Figure 13.7. The power required for animal companions’ food.

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

79

13 — Food and farming amounting to 1 kWh per day, then the power required to make his food is about 9 kWh per day. Shadowfax the horse weighs about 400 kg and consumes 17 kWh per day.

Wave: 4 kWh/d Deep offshore wind: 32 kWh/d

Mythconceptions I heard that the energy footprint of food is so big that “it’s better to drive than to walk.” Whether this is true depends on your diet. It’s certainly possible to find food whose fossil-fuel energy footprint is bigger than the energy delivered to the human. A bag of crisps, for example, has an embodied energy of 1.4 kWh of fossil fuel per kWh of chemical energy eaten. The embodied energy of meat is higher. According to a study from the University of Exeter, the typical diet has an embodied energy of roughly 6 kWh per kWh eaten. To figure out whether driving a car or walking uses less energy, we need to know the transport efficiency of each mode. For the typical car of Chapter 3, the energy cost was 80 kWh per 100 km. Walking uses a net energy of 3.6 kWh per 100 km – 22 times less. So if you live entirely on food whose footprint is greater than 22 kWh per kWh then, yes, the energy cost of getting you from A to B in a fossil-fuel-powered vehicle is less than if you go under your own steam. But if you have a typical diet (6 kWh per kWh) then “it’s better to drive than to walk” is a myth. Walking uses one quarter as much energy.

Food, farming, fertilizer: 15 kWh/d Gadgets: 5 Light: 4 kWh/d

Heating, cooling: 37 kWh/d

Jet flights: 30 kWh/d

Shallow offshore wind: 16 kWh/d Hydro: 1.5 kWh/d

Biomass: food, biofuel, wood, waste incin’n, landfill gas: 24 kWh/d

PV farm (200 m2/p): 50 kWh/d

Notes and further reading page no. 76 A typical dairy cow produces 16 litres of milk per day. There are 2.3 million dairy cows in the UK, each producing around 5900 litres per year. Half of all milk produced by cows is sold as liquid milk. www.ukagriculture.com, www.vegsoc.org/info/cattle.html 77 It takes about 1000 days of cow-time to create a steak. 33 months from conception to slaughterhouse: 9 months’ gestation and 24 months’ rearing. www.shabdenparkfarm.com/farming/cattle.htm – Chicken. A full-grown (20-week old) layer weighs 1.5 or 1.6 kg. Its feed has an energy content of 2850 kcal per kg, which is 3.3 kWh per kg, and its feed consumption rises to 340 g per week when 6 weeks old, and to 500 g per week when aged 20 weeks. Once laying, the typical feed required is 110 g per day. Meat chickens’ feed has an energy content of 3.7 kWh per kg. Energy consumption is 400–450 kcal per day per hen (0.5 kWh/d per hen), with 2 kg being a typical body weight. A meat chicken weighing 2.95 kg consumes a total of 5.32 kg of feed [5h69fm]. So the embodied energy of a meat chicken is about 6.7 kWh per kg of animal, or 10 kWh per kg of eaten meat.

PV, 10 m2/p: 5

Car: 40 kWh/d

Solar heating: 13 kWh/d

Wind: 20 kWh/d

Figure 13.8. Food and farming.

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

80

Sustainable Energy – without the hot air If I’d used this number instead of my rough guess, the energy contribution of the chicken would have been bumped up a little. But given that the mixed-meat diet’s energy footprint is dominated by the beef, it really doesn’t matter that I underestimated the chickens. Sources: Subcommittee on Poultry Nutrition, National Research Council (1994), www.nap.edu/ openbook.php?isbn=0309048923, MacDonald (2008), and www.statistics. gov.uk/statbase/datasets2.asp.

77 let’s assume you eat half a pound (227 g) a day of meat, made up of equal quantities of chicken, pork, and beef. This is close to the average meat consumption in America, which is 251 g per day – made up of 108 g chicken, 81 g beef, and 62 g pork (MacDonald, 2008). 78 The embodied energy in Europe’s fertilizers is about 2 kWh per day per person. In 1998–9, Western Europe used 17.6 Mt per year of fertilizers: 10 Mt of nitrates, 3.5 Mt of phosphate and 4.1 Mt potash. These fertilizers have energy footprints of 21.7, 4.9, and 3.8 kWh per kg respectively. Sharing this energy out between 375 million people, we find a total footprint of 1.8 kWh per day per person. Sources: Gellings and Parmenter (2004), International Fertilizer Industry Association [5pwojp]. – Farming in the UK in 2005 used an energy of 0.9 kWh per day per person. Source: Warwick HRI (2007). 79 A bag of crisps has an embodied energy of 1.4 kWh of fossil fuel per kWh of chemical energy eaten. I estimated this energy from the carbon footprint of a bag of crisps: 75 g CO2 for a standard 35 g bag [5bj8k3]. Of this footprint, 44% is associated with farming, 30% with processing, 15% packaging, and 11% transport and disposal. The chemical energy delivered to the consumer is 770 kJ. So this food has a carbon footprint of 350 g per kWh.

Assuming that most of this carbon footprint is from fossil fuels at 250 g CO2 per kWh, the energy footprint of the crisps is 1.4 kWh of fossil fuel per kWh of chemical energy eaten. – The typical diet has an embodied energy of roughly 6 kWh per kWh eaten. Coley (2001) estimates the embodied energy in a typical diet is 5.75 times the derived energy. Walking has a CO2 footprint of 42 g/km; cycling, 30 g/km. For comparison, driving an average car emits 183 g/km. – Walking uses 3.6 kWh per 100 km. A walking human uses a total of 6.6 kWh per 100 km [3s576h]; we subtract off the resting energy to get the energy footprint of walking (Coley, 2001). Further reading: Weber and Matthews (2008).

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

14

Tide

The moon and earth are in a whirling, pirouetting dance around the sun. Together they tour the sun once every year, at the same time whirling around each other once every 28 days. The moon also turns around once every 28 days so that she always shows the same face to her dancing partner, the earth. The prima donna earth doesn’t return the compliment; she pirouettes once every day. This dance is held together by the force of gravity: every bit of the earth, moon, and sun is pulled towards every other bit of earth, moon, and sun. The sum of all these forces is almost exactly what’s required to keep the whirling dance on course. But there are very slight imbalances between the gravitational forces and the forces required to maintain the dance. It is these imbalances that give rise to the tides. The imbalances associated with the whirling of the moon and earth around each other are about three times as big as the imbalances associated with the earth’s slower dance around the sun, so the size of the tides varies with the phase of the moon, as the moon and sun pass in and out of alignment. At full moon and new moon (when the moon and sun are in line with each other) the imbalances reinforce each other, and the resulting big tides are called spring tides.

(Spring tides are not “tides that occur at spring-time;” spring tides happen every two weeks like clockwork.) At the intervening half moons, the imbalances partly cancel and the tides are smaller; these smaller tides are called neap tides. Spring tides have roughly twice the amplitude of neap tides: the spring high tides are twice as high above mean sea level as neap high tides, the spring low tides are twice as low as neap low tides, and the tidal currents are twice as big at springs as at neaps. Why are there two high tides and two low tides per day? Well, if the earth were a perfect sphere, a smooth billiard ball covered by oceans, the tidal effect of the earth-moon whirling would be to deform the water slightly towards and away from the moon, making the water slightly rugby-ball shaped (figure 14.1). Someone living on the equator of this billiard-ball earth, spinning round once per day within the water cocoon, would notice the water level going up and down twice per day: up once as he passed under the nose of the rugby-ball, and up a second time as he passed under its tail. This cartoon explanation is some way from reality. In reality, the earth is not smooth, and it is not uniformly covered by water (as you may have noticed). Two humps of water cannot whoosh round the earth once per day because the continents get in the way.

The true behaviour of the tides is thus more complicated. In a large body of water such as the Atlantic Ocean, tidal crests and troughs form but, unable to whoosh round the earth, they do the next best thing: they whoosh around the perimeter of the Ocean. In the North Atlantic there are two crests and two troughs, all circling the Atlantic in an anticlockwise direction once a 81

away from the moon

N

towards the moon

Figure 14.1. An ocean covering a billiard-ball earth. We’re looking down on the North pole, and the moon is 60 cm off the page to the right. The earth spins once per day inside a rugby-ball-shaped shell of water. The oceans are stretched towards and away from the moon because the gravitational forces supplied by the moon don’t perfectly match the required centripetal force to keep the earth and moon whirling around their common centre of gravity. Someone standing on the equator (rotating as indicated by the arrow) will experience two high waters and two low waters per day.

Copyright David JC MacKay 2009. This electronic copy is provided, free, for personal use only. See www.withouthotair.com.

day. Here in Britain we don’t directly see these Atlantic crests and troughs – we are set back from the Atlantic proper, separated from it by a few hundred miles of paddling pool called the continental shelf. Each time one of the crests whooshes by in the Atlantic proper, it sends a crest up our paddling pool. Similarly each Atlantic trough sends a trough up the paddling pool. Consecutive crests and troughs are separated by six hours. Or to be more precise, by six and a quarter hours, since the time between moon-rises is about 25, not 24 hours. The speed at which the crests and troughs travel varies with the depth of the paddling pool. The shallower the paddling pool gets, the slower the crests and troughs travel and the larger they get. Out in the ocean, the tides are just a foot or two in height. Arriving in European estuaries, the tidal range is often as big as four metres. In the northern hemisphere, the Coriolis force (a force, associated with the rotation of the earth, that acts only on moving objects) makes all tidal crests and troughs tend to hug the right-hand bank as they go. For example, the tides in the English channel are bigger on the French side. Similarly, the crests and troughs entering the North Sea around the Orkneys hug the British side, travelling down to the Thames Estuary then turning left at the Netherlands to pay their respects to Denmark.

Tidal energy is sometimes called lunar energy, since it’s mainly thanks to the moon that the water sloshes around so. Much of the tidal energy, however, is really coming from the rotational energy of the spinning earth. The earth is very gradually slowing down. So, how can we put tidal energy to use, and how much power could we extract?

Rough estimates of tidal power When you think of tidal power, you might think of an artificial pool next to the sea, with a water-wheel that is turned as the pool fills or empties (figures 14.2 and 14.3). Chapter G shows how to estimate the power available from such tide-pools. Assuming a range of 4 m, a typical range in many European estuaries, the maximum power of an artificial tide-pool that’s filled rapidly at high tide and emptied rapidly at low tide, generating power from both flow directions, is about 3 W/m2 . This is the same as the power per unit area of an offshore wind farm. And we already know how big offshore wind farms need to be to make a difference. They need to be country-sized. So similarly, to make tide-pools capable of producing power comparable to Britain’s total consumption, we’d need the total area of the tide-pools to be similar to the area of Britain. Amazingly, Britain is already supplied with a natural tide-pool of just the required dimensions. This tide-pool is known as the North Sea (figure 14.5). If we simply insert generators in appropriate spots, significant power can be extracted. The generators might look like underwater wind-

Sustainable Energy – without the hot air

Figure 14.2. Woodbridge tide-pool and tide-mill. Photos kindly provided by Ted Evans. tidepool

sea high water

low water

range

82

Figure 14.3. An artificial tide-pool. The pool was filled at high tide, and now it’s low tide. We let the water out through the electricity generator to turn the water’s potential energy into electricity. tidal range

power density

2m 4m 6m 8m

1 W/m2 3 W/m2 7 W/m2 13 W/m2

Table 14.4. Power density (power per unit area) of tide-pools, assuming generation from both the rising and the falling tide.

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14 — Tide

Atlantic Ocean

North Sea

mills. Because the density of water is roughly 1000 times that of air, the power of water flow is 1000 times greater than the power of wind at the same speed. We’ll come back to tide farms in a moment, but first let’s discuss how much raw tidal energy rolls around Britain every day.

Figure 14.5. The British Isles are in a fortunate position: the North Sea forms a natural tide-pool, in and out of which great sloshes of water pour twice a day.

Raw incoming tidal power The tides around Britain are genuine tidal waves – unlike tsunamis, which are called “tidal waves,” but are nothing to do with tides. Follow a high tide as it rolls in from the Atlantic. The time of high tide becomes progressively later as we move east up the English channel from the Isles of Scilly to Portsmouth and on to Dover. The crest of the tidal wave progresses up the channel at about 70 km/h. (The crest of the wave moves much faster than the water itself, just as ordinary waves on the sea move faster than the water.) Similarly, a high tide moves clockwise round Scotland, rolling down the North Sea from Wick to Berwick and on to Hull at a speed of about 100 km/h. These two high tides converge on the Thames Estuary. By coincidence, the Scottish crest arrives about 12 hours later than the crest that came via Dover, so it arrives in near-synchrony with the next high tide via Dover, and London receives the normal two high tides per day. The power we can extract from tides can never be more than the total power of these tidal waves from the Atlantic. The total power crossing the lines in figure 14.6 has been measured; on average it amounts to 100 kWh per day per person.