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Large Scottish Pumped Storage Hydroelectric Reservoir and Dam (@ Coire Glas)

  1. Feb 20, 2012 #1
    I am presenting here my vision for a large pumped storage hydroelectric 2-square kilometres surface-area reservoir and 300+ metre tall dam which I have designed for the Coire Glas site, Scotland.

    (View site using Google Earth where the convenient label is "Loch a' Choire Ghlais" - or, http://tinyurl.com/coireglas)

    I was inspired to conceive and to publish my vision by learning of the Scottish and Southern Energy (SSE) proposal to build a smaller hydroelectric pumped-storage scheme at Coire Glas which has been presented to the Scottish government for public consultation.

    I have not long been aware of the SSE plan for the Coire Glas scheme, not being a follower of such matters routinely, but I was prompted by an earlier tangentially-related news story (about energy storage technology for renewable energy generators such as wind farms) to write to Members of the Scottish Parliament on the merits and urgency of new pumped storage hydroelectric power for Scotland on 14th February and a reply from Ian Anderson, the parliamentary manager for Dave Thomson MSP received the next day, the 15th February informed me about the SSE plan and Ian added "initially scoped at 600MW but, to quote SSE, could be bigger!"

    I replied to Ian "So the schemes proposed by the SSE are welcome and ought to be green-lighted and fast-tracked, but I am really proposing that Scots start thinking long term about an order of magnitude and more greater investment in pumped storage hydroelectric capacity than those SSE plans."

    So I had in mind "bigger would be better" but it was not until the next day on the 16th February when a news story informed me that the SSE plans had been submitted to the Scottish government for public consultation that I thought "this needs consideration now".

    So starting late on the night of the 17th, early 18th February and all through the weekend, I got busy, outlining my alternative vision for a far bigger dam and reservoir at the same location.

    So this is my vision as inspired by the SSE plan. If my vision is flawed then the fault is mine alone. If my vision is brilliant, then the brilliance too is mine. :biggrin:


    The black contour line at 550 metres elevation shows the outline of the SSE proposed reservoir of about 1 square kilometre surface-area and the grey thick line shows the position of the proposed SSE dam which would stand 92 metres tall and would be the tallest dam in Scotland and indeed Britain to date though it seems our dams are several times smaller than the tallest dams elsewhere in the world these days.

    Part of the red contour line at 775 metres elevation, where the red line surrounds a blue shaded area, blue representing water, shows the outline of my larger reservoir of about 2 square kilometres surface-area and the thicker brown line shows the position of my proposed dam which would stand 317 metres tall which would be one of the tallest man-made dams in the world.

    Excavated Reservoir Bed

    The green ellipse of major diameter of 1.5 kilometres and minor diameter of 1 kilometre represents an excavated reservoir bed, as flat and as horizontal as practical, at an elevation of 463 metres.

    Since an excavated reservoir bed is not, that I can see, part of the SSE plan, at any size, I will provide some more information about my vision for that now.

    The basic idea of excavating a flat or flattish reservoir bed is to increase the volume of the water stored in the reservoir because more water means more energy can be stored.

    Depending on the geology and strength of the rock of Coire Glas the walls of the reservoir bed perimeter could be as steep as vertical from the reservoir bed up to the natural elevation of the existing rock surface which would mean, presumably, blasting out rock to create a cliff which at places could be as much as about 290 metres tall.

    Near the dam, the reservoir bed perimeter wall would be only 40 metres or less tall. The further from the dam, the higher the wall will be and the more rock needs to be excavated.

    A vertical reservoir bed perimeter wall would be ideal to maximise reservoir volume wherever the geology provides a strong stone which can maintain a vertical wall face without collapse, a stone such as granite perhaps).

    Where the geology only provides a weaker stone then a sloping perimeter wall at a suitable angle of repose for reliable stability would be constructed.

    So the reservoir perimeter wall could be as sloped as shallow as 45 degrees from the natural elevation at the perimeter of the eclipse sloping down to the reservoir bed at 463 metres elevation in the case of the weakest and most prone to collapse kinds of stone.

    Exactly how strong the stone is at each location I guess we'll only find out absolutely for sure if and when engineers start blasting it and testing the revealed rock wall face for strength.

    The shape of the perimeter of the excavated reservoir bed is not absolutely critical. So long as it ends up as a stable wall or slope, however it is shaped by the blasting, it will be fine. There is no need to have stone masons chip the perimeter smooth and flat! The ellipse is simply the easiest approximate mathematical shape to describe and to draw. If the end result is not a perfect ellipse, don't worry, it will be fine!

    OK, well I guess that's the vision part over. The rest is fairly straight-forward engineering I hope. Oh, and there is always getting the permission and the funding to build it of course which is never easy for anything this big.

    OK, well if anyone has any questions or points to make about my vision or can say why they think the SSE plan is better than mine, or if you don't see why we need any pumped storage hydroelectric scheme at Coire Glas, whatever your point of view, if you have something to add in reply, please do.
  2. jcsd
  3. Feb 20, 2012 #2
    This image does not seem to be displaying in my Google Chrome browser, possibly some incompatibility with the image host? Anyway, for those experiencing this issue, here is the same image again hosted on my own site.

    http://scot.cyberhost.me/forum/media/peterdowcoireglasproposal.jpg [Broken]
    Image also hosted on postimage
    Last edited by a moderator: May 5, 2017
  4. Feb 21, 2012 #3
    Cross section of the Dow-dam reservoir

    http://scot.cyberhost.me/forum/media/damcrosssectionmajordiameter.jpg [Broken]

    Cross section along the major diameter of the elliptical excavation of the reservoir bed

    Also hosted on PostImage.org
    Last edited by a moderator: May 5, 2017
  5. Feb 23, 2012 #4
    Enhanced satellite photograph

    http://scot.cyberhost.me/forum/media/enhancedsatellite.jpg [Broken]

    Image also hosted on PostImage.Org

    Cross section of the Dow-dam
    The Dow-dam would be more than 3 times higher than the proposed SSE-dam. In this diagram, a horizontal line one third of the way up the Dow-dam indicates the relative height of the SSE dam although it is not aligned with this cross-section.

    http://scot.cyberhost.me/forum/media/dowdam.jpg [Broken]

    Image also hosted on PostImage.Org

    Maps showing the line of cross-section viewed from each side

    http://scot.cyberhost.me/forum/media/damwatersidemap700.jpg [Broken]

    Image also hosted on PostImage.Org

    http://scot.cyberhost.me/forum/media/damdrysidemap700.jpg [Broken]

    Image also hosted on PostImage.Org
    Last edited by a moderator: May 5, 2017
  6. Feb 23, 2012 #5

    jim hardy

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    i had trouble with Adobe and couldn't see the SSE links..

    from where will this take water to pump back into reservoir?
  7. Feb 23, 2012 #6
    Well let me see if I can help you Jim.

    Let me guess. You clicked my link to the SSE website and got the SSE Coire Glas Hydro Scheme page OK?

    So you got to this page - http://www.sse.com/CoireGlas/

    Then on the SSE Coire Glas page maybe you clicked "Find out more about the Coire Glas hydro scheme"

    Which should have taken you to the SSE Coire Glas Project Information page - http://www.sse.com/CoireGlas/ProjectInformation [Broken]

    Then on that page there is a list of Adobe PDF download links and it was with those you had a problem?

    Here's the "Figure two scheme overview" link.

    http://www.sse.com/uploadedFiles/Z_Microsites/Coire_Glas_Hydro_Scheme/Controls/Lists/Resources/FigureTwoSchemeOverview.pdf [Broken]

    Now if you just click it, your browser may or may not have a Adobe add on which can display PDF files. If your browser doesn't have the add-on installed you might have problems with an ordinary click.

    The better way maybe for you is to download the PDF file first then see if you can view it.

    To download a file from a link, for example with Internet Explorer browser, Right-click the link and select "Save Target As..".

    I think all computers and browsers can download files from links if you know how.

    So download the PDF file to your PC and then you can view it assuming you have Adobe Reader installed. If you don't have Adobe Reader installed, no worries, because it is free and you should get it because it is very useful to have working on your PC for situations like this so you can download Adobe Reader from the Adobe website. http://www.adobe.com/

    The water is sourced from a Scottish lake, only we call them "lochs", and this one is called "Loch Lochy" which is shown on the far right of this map I posted above.

    http://scot.cyberhost.me/forum/media/damwatersidemap700.jpg [Broken]
    Last edited by a moderator: May 5, 2017
  8. Feb 23, 2012 #7

    jim hardy

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    2018 Award

    Thanks ! You were exactly right.

    The computer froze trying to load them, then complained i didnt have latest version of Adobe so i let it download and install,, but the pages still come up black.

    Downloading and opening the first file worked though. Now i can peruse them at liesure.

    Good luck with it - i'd love to have the skiff rental concession on the lake !!!

    old jim
  9. Mar 9, 2012 #8
    Loch Lochy and vicinity water flow control works

    Here is an annotated satellite photograph of the land south from Coire Glas showing Loch Lochy, Loch Arkaig, the isthmus between the lochs, Mucomir where Loch Lochy empties into the River Spean before it flows on as the River Lochy, the Caledonian Canal and Fort William where the river flows into a sea loch.

    http://scot.cyberhost.me/forum/media/lochywater768.jpg [Broken]

    http://postimage.org/image/3o3vfni9z/]http://s15.postimage.org/3o3vfni9z/lochywater768.jpg [Broken]
    Click to see larger image

    New waterway

    Loch Lochy is separated from a neighbouring loch, Loch Arkaig, by a 2 km wide isthmus, which I have identified on this map as "the Achnacarry Bunarkaig isthmus", after the local place names.

    It ought to be quite straight forward to build a canal or culvert, to connect those two lochs. The idea is that the new waterway would be wide and deep enough, enough of a cross section area under water, perhaps hundreds of square metres, so as to allow free flow from one loch to the other, so as to equalise the surface elevations of the two lochs, so as to increase the effective surface area of Loch Lochy so as to decrease the depth changes to Loch Lochy when water flows in from the Coire Glas reservoir when it discharges water when supplying power.

    Now, Loch Arkaig has a natural surface elevation of 43 metres and this would be lowered to that of Loch Lochy. The surface area of Loch Arkaig is given by wikipedia as 16 km^2 also, (though it looks to me somewhat smaller than Loch Lochy). In addition, partially draining Loch Arkaig to bring its level down to that of Loch Lochy will also reduce its surface area.

    If say, the additional surface area of Loch Arkaig is about 10 km^2 added to Loch Lochy's 16 km^2 this would give an effective surface area of 26 km^2 and reduce the potential depth variation to

    Potential depth variation of Loch Lochy + Loch Arkaig = 400 000 000 m^3 / 26 000 000 m^2 = 15.3 metres.

    Without equalising the loch levels, the depth changes to Loch Lochy that would require to be managed may be potentially more like 25 metres than 15 metres. So the new waterway is an important part of the new water flow control works that Coire Glas/Dow requires to be constructed.

    Additional Loch Lochy water level control measures

    When the Coire Glas reservoir is full, then the water level of Loch Lochy should be prevented, by new water works - drains, dams, flood barriers etc. - from rising due to rainfall and natural flow into the loch above a safe level which allows for the reservoir to empty into the loch without overflowing and flooding.

    The safe "upper-reservoir-full" loch level will likely turn out to be around about 15 metres below the maximum loch level.

    The next diagram showing the new loch drain and the reservoir pump inlets indicates how this might be achieved.

    http://scot.cyberhost.me/forum/media/lochyflow768.jpg [Broken]

    http://postimage.org/image/mpjk6a15d/]http://s8.postimage.org/mpjk6a15d/lochyflow.jpg [Broken]
    Click to see larger image

    The drain from Loch Lochy to the sea which goes underground from the 14 m elevation level in the loch would need capacity for the usual outflow from Loch Lochy which currently goes through the Mucomir hydroelectric station.

    I have estimated the flow through Mucomir from its maximum power of 2MegaWatts and its head of 7m as somewhere near 0.2 Mega-cubic-metres-per-hour and compared that value using a spreadsheet I have written to predict the capacity of water flow through different sizes of drains using the empirical Manning formula and this is also useful for determining the appropriate size of the new water channel between the lochs.

    Ease my quantity :biggrin:

    To construct Coire Glas/Dow/600GW.Hrs/12GW may cost of the order of around £20 billion, but that would be my order of magnitude educated guess more than a professional cost estimate.

    In other words, I'm only really confident at this early "vision" stage that the cost would be closer to £20 billion than it would be to £2 billion or to £200 billion but I'm not claiming to be able to quote an accurate cost estimate at this stage.

    I have not itemised my costs - how much for land, how much for labour, how much for trucks, how much for diggers, how much for cement, how much to install the generators etc. and the SSE have not published itemised costs for theirs either so I can't calculate my costs in a proportion to the SSE's costs.

    Although my version offers 600 GigaWatt-Hours energy and 12 GigaWatts power (or 20 times the capacity and performance) some of the items in my version would cost more than "in proportion", in other words more than 20 times the SSE's cost.

    For example, the cost of my dam will be more like 27 times the cost of the SSE's dam. (3.44 times higher and thicker and 2.27 times longer).

    For example, the cost of excavating 400 million tonnes of rock from the reservoir bed to increase the capacity of the reservoir to hold water (and energy) in my version won't be in proportion to the SSE costs for excavating their reservoir bed because, as far as I know, they don't plan to excavate their reservoir bed at all.

    On the other hand, my land costs are about the same as the SSE's - much less than in proportion. I may well need to use more land to dispose of the additional excavated rock spoil but perhaps when that additional land has been landscaped over it could be resold?

    So it depends how much the land is as a proportion of the SSE's costs. If land is a small part of their costs, if 20 similar sites to build on are just as cheap and easy to buy then my costs will be much more than proportional, since saving land won't save much money.

    If land is scare and valuable and the cost to purchase suitable land with a good chance to get permission to build on it is a significant proportion of the SSE's or anyone's costs to build 20 of their size of hydro dam schemes then my costs may be better than proportional. Sometimes securing suitable land for development can be very problematic, very expensive. Sometimes people won't sell their land. Sometimes the authorities won't agree that the land can be used in this way.

    The SSE say that suitable sites for such pumped storage schemes are rare indeed, so land costs may be very significant and my scheme good value for money.

    If indeed the cost of my scheme is somewhere around £20 billion it is likely to cost far more than the SSE or any electrical power supply company looking to their annual profits for the next few years could possibly afford.

    Something like £20 billion I expect could only be found as a national public infrastructure project, spending government money, like the building of a large bridge or motorway would be.

    A £20 billion government project would require Treasury approval, at least while Scotland is ruled as part of the UK.

    I have suggested funding my much larger hydro dam scheme by re-allocating of some of the Bank of England's "Quantitative Easing" funds which amount to some £300 billion of new money printed with not much to show for it.

    Attached Files:

    Last edited by a moderator: May 5, 2017
  10. Mar 10, 2012 #9
  11. Mar 12, 2012 #10


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    Are these storage and hourly capacity rates reasonable?
    You're creating a resource that could run for 50 hours. So it is much more than a daily load smoothing facility. Why such a margin?
    Separately, where do the 12+ gigawatts come from that are needed to refill the reservoir? Is there a large nuclear complex in the area or is the expectation that surplus wind power will be stored here?
  12. Mar 12, 2012 #11
    The big wind is coming. The time for pumped-storage hydro is now.

    Thank you for your replies Bob S and etudiant.

    I would like to, by way of introduction to my replies, post the following background perspective explaining my interest in new large pumped-storage hydroelectricity schemes in Scotland.

    I possibly hesitated to post this first because I am relatively new here in Physics Forums and I have been subject to some pretty harsh moderation with my first few posts being deleted or locked or something, can't remember exactly, but anyway remembering the need here to be so ultra-clearly "on topic" I wanted to get the physics and engineering clearly out in front in this topic particularly before digressing into the why?s and what for?s of all this.

    This is a statement of the obvious as far as Scottish electrical power-generation engineers and scientists are concerned I expect but I am making this statement anyway, not for the benefit of our scientists or engineers but to inform the political debate about the potential of the Scottish economy "after the North Sea oil runs out" because political debate involves mostly non-scientists and non-engineers who need to have such things explained to them.

    The Scottish economy has a profitable living to make in future in the business of electrical energy import/export from/to English electrical power suppliers and perhaps even to countries further away one day.

    The tried and tested engineering technology we Scots can use in future to make money is pumped-storage hydroelectricity.


    In Scotland, the Cruachan Dam pumped-storage hydroelectric power station was first operational in 1966 and was built there to take advantage of Scotland's appropriate geography and available capital.

    So Scotland has the appropriate geography for pumped-storage hydroelectric power and we have the capital particularly if we invest some of the taxes on North Sea oil before it all runs out and it is all spent.

    Investment in wind-power energy generation is proceeding apace, in Scotland, in England, on and offshore, and that's very "green" and quite clever, though wind power is not as dependable as tidal power, but unless and until sufficient capacity to store energy becomes available to supply needs when the wind isn't blowing then conventional, and perhaps increasingly expensive, coal, gas or oil burning or nuclear energy power will still be needed to keep the lights on when the wind doesn't blow.

    Scottish opportunity
    Here is the opportunity for the Scottish economy in a future where wind-power generation is increasingly rampant: if we Scots build a large capacity of new pumped-storage hydroelectric power stations, not only can we supply all our own Scottish energy needs from "green" renewable energy schemes, but we could provide energy storage capacity for customers outside Scotland, particularly in England, who live in a land not so well endowed with appropriate geography for hydroelectric power.

    In future, a Scotland with investment in a massive pumped-storage hydroelectric capacity could buy cheap English wind-power while the wind is blowing then sell the same energy back to English power suppliers, at a profit, when the wind isn't blowing and the English will pay more for energy.

    So everyone wins, the energy is all green, the electricity supply is always available when it is needed and that is how the Scottish energy economy does very well after the North Sea oil runs out. :cool:

    So problem solved but not job done as yet. We Scots do actually need to get busy investing and building pumped-storage hydroelectric power generation and supply capacity in Scotland now.​

    As you can see Bob from the above, Scotland had a pumped storage hydro dam system operating in 1966 at Cruachan.

    As you can see from the above, the idea is to "load balance" for the variation in wind power availability, which varies over longer periods than one day.

    Right second guess, or the 2nd option of your first guess. Anyway, it will be a surplus wind energy store, though it could also be for other variable renewable sources, perhaps wave power, perhaps tidal as well but probably mostly wind because Scotland and elsewhere in Britain is expected to install a lot of new wind power capacity in future years.

    Oh, and you don't need to pump up the reservoir at 12 GW in fact you possibly will rarely ever pump up at full power. I suppose it depends on how much wind power capacity is installed and what the scheme's power transmission connection to the grid can handle at the time.

    Whatever and whenever surplus wind power is available you can use that power up to the maximum rated power of the pumps which will be round about 12 GW.

    Well I say "will be". That's my plan. The SSE plan is much the same but 20 times smaller.
    Last edited: Mar 12, 2012
  13. Mar 12, 2012 #12


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    If the economic purpose is to load level the 'cheap English wind power', it would be useful to evaluate how expensive local storage would be in comparison, especially as this scheme would need a lot of ancillary power transmission and management, which is not cheap either.
    Separately, 50 hours is skimpy for a wind load leveling facility. I seem to remember the UK this winter suffering from intense cold with essentially no wind for a 2 week period.
  14. Mar 13, 2012 #13
    Not only that. Clearly, local Scottish needs would have first call on such a facility.

    Here is a diagram of peak generation and demand in Britain one year. (The figures I believe are MegaWatts.)

    http://www.nationalgrid.com/uk/sys_09/chap4/images/fig4-1.gif [Broken]

    This exercise was to provide a design to maximise the potential of the Coire Glas site and to me, at least, it is clear that the 20 times more performance in power and energy is all useful or will be when wind generators are carrying a majority of the base load in Scotland.

    If I could have designed a pumped-storage hydro scheme for the Coire Glas site that offered twice the energy store, say 1200 GW.Hours, I would have if it was efficient to do so. It isn't at that site.

    There is not room on Coire Glas for a much bigger reservoir without using substantially more land and requiring other dams and neither could the lower lochs absorb much more volume without big dams around the lochs.

    I doubt that I would design in twice the power or 24 GW even with twice the size of energy store.

    12 GW is plenty for a first site and covers the 10 GW Scottish generation capacity with a little room for expansion.

    If I had two sites in Scotland the size of Coire Glas I may even have split the 12 GWs up into 6GW at each site, each site with about 600GW.Hours & 6GW.

    Siemens is installing I believe another 2.2 GW transmission line underwater from Scotland to England so I think it possible that indeed Scotland may in future need more than 12 GW of power from energy stores but 12 GW is enough for now.

    I have pretty much "maxed out" the Coire Glas site with that design. Possibly other sites could offer more. If the government stepped forward offering the £20 billion or so to build something like this, the first exercise would be to scope out other sites to see if there was anywhere better, that offered more bang for the buck.

    So sure a bigger capacity of energy store would be most useful. This is always the way with energy stores.
    Last edited by a moderator: May 5, 2017
  15. Mar 15, 2012 #14
    Geology of the Coire Glas site
    I have been able to extract this information from the British Geological Survey (BGS) Geology of Britain viewer, from the 1:50 000 scale map.

    http://scot.cyberhost.me/forum/media/coireglashydrogeology800.jpg [Broken]

    Click to see larger image

    According to this map, the bedrock at the site which would be used to build the dam on top of and to extract rock from to create the tunnels for the underground complex seems to be a rock geologists call "psammite" which I understand to mean here "a metamorphic rock whose protolith was a sandstone".

    What neither the map nor the "psammite" name is telling us is how fractured the psammite rock there is and therefore how strong and also how impermeable or otherwise to water this rock is likely to prove to be, both of which would be interesting for any engineers building a pumped-storage hydro dam scheme there to know.

    What does look fairly obvious to me is that the superficial deposit of what the map calls "hummocky (moundy) glacial deposits - diamicton, sand and gravel" would not be strong enough, nor impermeable enough to build any dam on top of and at least along the line of the dam, this glacial deposit ought to be removed to get down to the bedrock within which to establish the foundations of the dam, although I would think that this glacial deposit might be made into aggregate to make the concrete for the dam by the sounds of it.

    Attached Files:

    Last edited by a moderator: May 5, 2017
  16. Mar 16, 2012 #15
    http://www.datasea.info/avatar1.jpgExactly how strong the stone is at each location I guess we'll only find out absolutely for sure if and when engineers start blasting it and testing the revealed rock wall face for strength.
  17. Mar 16, 2012 #16
    Dam foundations and height of the dam above the bedrock
    The top of the Dow-Dam has an elevation of 780 metres by design.

    http://scot.gcehosting.com/forum/media/glacialdeposit.jpg [Broken]

    Image also hosted here

    The lowest elevation of the current ground surface of Coire Glas along the line of the proposed dam is 463 metres and subtracting 463 from 780 is how the initial value of 317 metres for the nominal height of the dam above the existing surface used in previous diagrams was arrived at.

    However, the glacial deposit of as yet unknown thickness is to be removed before building the foundations of the dam within and upon the bedrock.

    Although the lowest surface elevation along the line of the dam of the bedrock too is unknown a formula relating the Height of the Dam Above the Bedrock (HDAB) to the Glacial Deposit Depth (GDD) can be easily stated.

    HDAB = 317 + GDD


    If the GDD turns out to be 13 metres then the dam will be 330 metres tall.
    If the GDD turns out to be 83 metres then the dam will be 400 metres tall.

    http://scot.gcehosting.com/forum/media/damfoundation.jpg [Broken]

    Image also hosted here

    I propose that the height of the Dow-Dam be as tall above the bedrock as it needs to be to keep the top of the dam at an elevation of 780 metres no matter how deep the removed glacial deposit layer turns out to be.

    My approach may well differ from the SSE's approach. The SSE have said that their dam will be "92 metres" high and they may stick to that without having any goal for the elevation of the top of their dam.

    As the diagram indicates, I propose to secure the Dow-Dam to the bedrock by massive piles inserted and secured into shafts which would be drilled into the bedrock.

    Attached Files:

    Last edited by a moderator: May 5, 2017
  18. Mar 19, 2012 #17

    Video which illustrates the principle of using wind turbines and pumped storage hydro dam schemes together.
  19. Mar 22, 2012 #18
    "Dow" equation for the power and energy output of a wind farm.

    "Dow" equation for the power and energy output of a wind farm.

    "The power and energy of a wind farm is proportional to (the square root of the wind farm area) times the rotor diameter".

    In his book which was mentioned to me on another forum and so I had a look, David MacKay wrote that the power / energy of a wind farm was independent of rotor size which didn't seem right to me considering the trend to increasing wind turbine size.

    Now I think the commercial wind-turbine manufacturing companies know better and very possibly someone else has derived this equation independently of me and long ago - in which case by all means step in and tell me whose equation this is.

    Or if you've not see this wind farm power/energy equation before, then see if you can figure out my derivation!
    Last edited: Mar 22, 2012
  20. Mar 24, 2012 #19
    No takers for the derivation challenge huh? OK then.


    Assume various simplifications like all turbine rotors are the same size and height, flat ground and a rotationally symmetrical wind turbine formation so that it doesn't matter what direction the wind is coming from.

    Consider that an efficient wind farm will have taken a significant proportion of the theoretically usable power (at most the Betz Limit, 59.3%, apparently, but anyway assume a certain percent) of all the wind flowing at rotor height out by the time the wind passes the last turbine.

    So assume the wind farm is efficient or at least that the power extracted is proportional to the energy of all the wind flowing through the wind farm at rotor height.

    This defines a horizontal layer of wind which passes through the wind farm of depth the same as the rotor diameter. The width of this layer which flows through the wind farm is simply the width of the wind farm which is proportional to the square root of the wind farm area.

    Wind farm turbine formations

    Therefore the width or diameter of a rotationally symmetrical wind farm is a critically important factor and arranging the formation of wind turbines to maximise the diameter of the wind farm is important.

    Consider two different rotationally symmetrical wind turbine formations, I have called the "Ring formation" and the "Compact formation".

    Let n be the number of wind turbines in the wind farm
    Let s be the spacing between the wind turbines

    Ring formation


    Larger image also hosted here

    The circumference of the ring formation is simply n times s.

    Circumference = n x s

    The diameter of the ring formation is simply n times s divided by PI.

    Diameter = n x s / PI

    Compact formation


    Larger image also hosted here

    The area of the compact formation, for large n, is n times s squared. This is slightly too big an area for small n.

    Area = n x s^2 (for large n)

    The diameter of the compact formation, for large n, is 2 times s times the square root of n divided by PI. This is slightly too big a diameter for small n.

    Diameter = 2 x s x SQRT(n/PI)

    This is easily corrected for small n greater than 3 by adding a "compact area trim constant" (CATC) (which is a negative value so really it is a subtraction) to the s-multiplier factor.

    The CATC is 4 divided by PI minus 2 times the square root of 4 divided by PI.

    CATC = 4/PI - 2 x SQRT(4/PI) = - 0.9835

    This CATC correction was selected to ensure that the compact formation diameter equation for n=4 evaluates to the same value as does the ring formation equation for n = 4, that being the largest n for which the ring and compact formations are indistinguishable.

    The CATC works out to be minus 0.9835 which gives

    Diameter = s x ( 2 x SQRT(n/PI) - 0.9835) (for n > 3)

    Ratio of diameters


    Larger image also hosted here

    It is of interest to compare the two formations of wind farm for the same n and s.

    The diameter of the ring formation is larger by the ratio of diameter formulas in which the spacing s drops out.

    Ring formation diameter : Compact formation diameter

    n/PI : 2 x SQRT (n/PI) - 0.9835

    This ratio can be evaluated for any n > 3 and here are some ratios with the compact value of the ratio normalised to 100% so that the ring value of the ratio will give the ring formation diameter as a percentage of the equivalent compact formation diameter.

    Here are some examples,

    n = 4, 100 : 100
    n = 10, 123 : 100
    n = 18, 151 : 100
    n = 40, 207 : 100
    n =100, 309 : 100
    n =180, 405 : 100
    n =300, 514 : 100
    n =500, 656 : 100

    As we can see that for big wind farms, with more turbines, the ratio of diameters increases.

    Since the Dow equation for the power and energy of a wind farm is proportional to the diameter of the wind farm then it predicts that the power and energy of the ring formation wind farms will be increased compared to the compact formation wind farms by the same ratio.

    In other words, the Dow equation predicts, for example, that a 100 turbine wind farm in the ring formation generates 3 times more power and energy than they would in the compact formation, assuming the spacing is the same in each case.

    Practical application when designing a wind farm

    My recommendation would be to prefer to deploy wind turbines in a wind farm in the ring formation in preference to the compact formation all other things being equal.

    The compact formation can be improved up to the performance of a ring formation by increasing the turbine spacing so that the circumference is as big as the ring but then if a greater turbine spacing is permitted then the ring formation may be allowed to get proportionally bigger as well keeping its advantage, assuming more area for a larger wind farm is available.

    The ring formation may be best if there is a large obstacle which can be encircled by the ring, such as a town or lake where it would not be possible or cost effective to build turbines in the middle of it and so a compact formation with larger spacing may not be possible there.

    Where it is not possible to install a complete ring formation then a partial ring formation shaped as an arc of a circle would do well also.

    Attached Files:

    Last edited: Mar 24, 2012
  21. Mar 29, 2012 #20
    Reservoir bed drain

    Reservoir bed drain

    The high pressure of water which is deeper than 100 metres has the potential to induce seismic activity or earthquakes in susceptible rock in which a new reservoir has been constructed.

    Coire Glas/SSE/92 m

    Hopefully, reservoir induced seismicity was an issue considered by the SSE when selecting Coire Glas for their hydro dam project.

    I am speculating that this issue may be why the SSE have limited their dam to a height and their reservoir to a depth of 92 metres?

    I would note however that the pressure in the head race tunnels which supply water from the reservoir to the turbines would be proportional to their depth below the surface of the reservoir and this could be as much as 500 metres deep, so there would seem to be some potential for water to penetrate the bed rock from the high pressure water tunnels and induce seismic activity even in the SSE case.

    This is an issue which ought to have been addressed in the many previous pumped-storage hydro scheme projects, most of which seem to have a difference in head of more than 100 metres.

    Given that "understanding ... is very limited" according to Wikipedia, though, I do wonder if the reservoir induced seismicity issue has not always been properly addressed in all previous dam and reservoir construction schemes where the great depth of water and susceptible geology ought to make it a relevant concern?

    Coire Glas/Dow/317+m

    I am proposing measures to counter the reservoir induced seismicity effect in the case that the geology of Coire Glas is susceptible to it and in the general case.

    I propose the construction of a large reservoir surface drain to cover the whole reservoir bed and the reservoir sides too to try to stop the penetration of water under high pressure into fractures in the bedrock and so thereby stop this high pressure water from widening and extending bedrock fractures.

    To illustrate my "reservoir bed drain" concept, I have drawn a diagram comparing the usual no drain on the left, with my proposed reservoir bed drain on the right.


    Image also hosted here.

    So my idea is that the top layer of the drain is as impermeable as practical, using perhaps a layer of reinforced asphalt concrete.

    In engineering practice I believe that impermeable reservoir bed layers have used clay or clay with asphalt or even rubberised asphalt mixed with sand.

    My basic idea is to construct an impermeable layer and to use whatever material is best for that.

    Then working downwards, the permeable drain layers are increasingly bigger loose particles, with sand at the 2nd top then beneath that grit, then gravel, then small stones and finally below all those a layer of large stones.

    The higher layers support the top impermeable layer which is under high pressure from the reservoir water and the lower permeable layers provide many small channels for any (hopefully tiny amounts of) water which forces its way through the supposedly impermeable top layer to drain down the slope of the reservoir bed out under the dam.

    The bottom layer is another impermeable layer to try to make doubly sure that the relatively low pressure water that gets into the drain will find its way out under the dam by following the course of the drain.

    These kinds of layers of different sized loose particles have previously been used to make simple narrow drains and impermeable layers have been added to reservoir beds before now but whether professional dam engineers have ever covered the entire reservoir bed and sides with one large drain I don't know. If not, this could be named the "Dow drain" solution to reservoir induced seismicity!

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