vertical axis tidal current genrator paper salter and taylor

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  • 8/2/2019 Vertical Axis Tidal Current Genrator Paper Salter and Taylor


    Vertical-axis tidal-current generatorsand the Pentland FirthS H Salter and J R M Taylor

    School of Engineering and Electronics, University of Edinburgh, Edinburgh, UK

    The manuscript was received on 1 March 2006 and was accepted after revision for publication on 13 November 2006.

    DOI: 10.1243/09576509JPE295

    Abstract: This paper extends ideas presented to the World Renewable Energy Conference [ 1, 2].

    One idea involves the impedance of flow channels and its relevance to the maximum tidal-stream resource. Estimates of the inertial and damping terms of the impedance of the PentlandFirth suggest a much higher resource size than studies based purely on the kinetic flux, becauseadding extra turbines will have less effect on flow velocities than in a low impedance channel.This very large resource has pushed the design of the turbine towards the stream velocities,depth, and seabed geology of this site. A second idea is an algorithm to control the pitch ofclose-packed vertical-axis generators to give an evenly distributed head. Finally, there are sug-gestions for a seabed attachment aimed specifically for conditions in the Pentland Firth andintended to allow rapid installation of a self-propelled tidal-stream generator.

    Keywords: vertical-axis turbine, tidal stream, marine-current generator, channel impedance,low-head hydro, variable pitch, Betz momentum theory, Darrieus, troposkien, tri-link, inflatable


    The earliest field work on Darrieus-type underwaterturbines was reported by Fraenkel [3]. It involvedtesting models of fixed pitch vertical-axis rotors andconfirmed the performance in water to be compar-able to results obtained with fixed-pitch verticalaxis wind turbines.

    Pitch variation was an essential feature of the Edin-burgh vertical-axis tidal-current generator which wasfirst described at the 1998 European wave energy

    conference at Patras [4] and is shown in Fig. 1. Thedesign had several layers of short blades with vari-able pitch. The layers were separated by ellipticalsection rings and cross-braced by streamlined wires

    which gave torsional and shear rigidity. Power take-off was above the surface and out at the rim,housed in a floating torus. It used a quad ring-cam,variable-displacement, high-pressure oil pump togive the correct torque to convert from a variableinput speed to the constant speed required by syn-chronous generators. The cam rollers could also

    perform the function of a geometrically tolerantbearing providing axial and radial location. Theblade pitch was controlled only by the choice of atorque limit which allowed blades to adjust theirown pitch-angle above a chosen level of pitchtorque so as to prevent stall. Mooring was by tensionlegs which passed through the centre of pressure ofthe rotor to avoid inducing pitching torque. How-ever, tank tests showed that tension legs wouldsuffer unacceptable snatch loads following any slack-ening, even in quite small waves.


    An important question for all tidal projects is theextent to which the introduction of generatingplant will reduce the flow. This can be thought ofin terms of the impedance of the flow, a concept

    which is familiar to electrical engineers but less soto mechanical, marine, and civil engineers eventhough there are many instances where it can be

    useful. One anthropomorphic way to think of impe-dance is as the determination needed for a currentto overcome obstacles placed in its path. One of the

    Corresponding author: School of Engineering and Electronics,University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JL,

    UK. email: [email protected]


    JPE295 # IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy

  • 8/2/2019 Vertical Axis Tidal Current Genrator Paper Salter and Taylor


  • 8/2/2019 Vertical Axis Tidal Current Genrator Paper Salter and Taylor


    all the others. A useful listing of the components,periods, and relative phases of 18 components forDelaware Bay is given in reference [8].

    Thevenins theorem says that an electrical network

    of any complexity can be reduced to a single voltagesource in series with a single impedance driving theload under study. The drive voltage would be what-ever voltage would be present if the load understudy were absent. Its analogy in water flows is thehead difference that would be developed if a dam

    were built across the channel entry. The impedancein series with that head would be the total series/par-allel combination of the other channels in theabsence of the channel under study.

    A measure of the impedance between two pointsin a channel could be calculated from measurementsof the head difference at the points and the mean of

    their current velocities. The acoustic Doppler currentprofiler method [9] is excellent for measuring vel-ocity and direction through the entire water column.Satellite measurements can give accurate measure-ments of changes of the mean level of large oceansbut this requires many transits, and advice from D.TPugh (2006; personal communication) is that they

    would not give enough coverage over the PentlandFirth for the required resolution. His suggestion is tomeasure changes of head through the tidal cycleusing bottom-mounted pressure transducers at anumber of points along a channel over a period of a

    few months, together with simultaneous velocitymeasurements at the same points. Recently devel-oped instruments combine both pressure and acous-tic Doppler velocity measurements [10].

    Before deciding on a programme of field measure-ments it is worth trying to make an approximate esti-mate. The simplest analysis would reduce a complexnetwork of channels to three impedances. The first isthe impedance, which sets the flow induced by theastronomical forcing function from the Atlantic.This would be in parallel with the impedance of theparallel paths through and north of the Orkneys

    which can allow water to bypass the Pentland Firth.It is known from reference [11] that there are quitelarge phase differences between tidal levels at thenearest observing stations at Kinlochbervie and

    Wick, so at least some of these impedances musthave complex terms analogous to inductance andcapacitance. Finally, there is the impedance of thePentland Firth itself. The celerity of a long shallow

    water wave over a 70 m bed would be 26 m/s so itwould take ,15 min to travel along the full length.This seems very short compared with the 12.42 hM2 tidal period and so it might be thought that thereactive terms ought not to be dominant.

    The Proudman Laboratory has developed numeri-cal tidal prediction software known as POL andkindly supplied their time-series prediction of water

    level and velocity components for points at eachend of the Pentland Firth (R. Protor, 2006, personalcommunication). The slope of the water surfacecould be calculated from the difference in head pre-

    dictions. The eastward (conventionally known as U)component of velocity was almost the same at eachend. The phase relationship of head to velocity wasof particular interest. There are two ways to get anestimate. The easiest and crudest, suitable for engin-eers in a hurry, is to look at the times of zero cross-ings and assume that the records are well-behavedsine waves. A square wave is generated using alogic statement that gives a value one if the head ispositive and the velocity is negative or if the head isnegative and the velocity positive. The markspaceratio of the square wave will give a measure ofphase. For the main length of the Pentland Firth

    between 588440N 38180 W and 588420N 3890 W thezero crossing method gives a lag between head andvelocity of 638.

    A more respectable phase calculation, suitable formathematicians, uses Fourier transforms. Thesecarry all the information about each separate com-ponent of the spectrum. For each frequency thetransform produces a real and imaginary numberindicating the amplitude and phase of that com-ponent relative to a notional cosine wave of thesame frequency with 08 referred to the beginning ofthe record.

    The ratio of the imaginary to the real amplitude ateach frequency gives the tangent of the phase anglebetween the signal and the notional cosine wave.Repeating this for both head and velocity recordsgives the inertial and resistive parts of the channelimpedance between the observation points. Thetechnique can give spillage over into adjacent fre-quencies, and so it can be useful to integrate over ashort section of the frequency spectrum. Betweenthe map coordinates given above, the phase lagbetween the head and the velocity of the strong M2frequency as measured by this technique was 468.This is shown in the Lissajous plot of slope againstthe Ucomponent of velocity in Fig. 2.

    Based on the electrical analogy, this implies that,despite the short channel-propagation time, flow-rates are defined by the inertia of the water in thePentland Firth just as much by bed friction or theentry orifice. The installation of quite large numbersof turbines in several close-packed banks will changethe phase of the velocity but not initially to the sameextent as its magnitude, so there is a second reason toexpect a higher resource than would be indicatedpurely from the present kinetic flux.

    By dividing the differences between each sample

    in the Proudman velocity data by the time intervalbetween them the acceleration of the flow can be cal-culated. The difference in head between two

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    positions along the channel gives us the force thatwould have to be exerted by some very large, imagin-ary piston to produce the flow. Mass can be calculated

    when force and acceleration are known. For theProudman Pentland data this mass, 2.7 1013 kg, isabout double what would have been calculated fromlength, depth, and width. The reason for the increase

    is that any reduction in width or depth will need ahigher local acceleration which will add to therequirement for the driving force and also the localkinetic energy.

    Inertia behaves in a linear fashion with flow accel-eration being proportional to driving slope. However,the flowrates in both short orifice-controlled andlong friction-controlled channels will depend onthe square root of the driving head difference. This

    would selectively reduce the higher velocities, dis-torting the wave form and producing odd-order har-monics which could be detected by Fourier analysisof the velocity signal, giving spikes above the fre-quencies of the major components. Figure 3 showsthe spectrum of an acoustic Doppler velocitymeasurement collected by A. Owen (2006, personalcommunication) at Burra Sound opposite an invertedversion of the Proudman Pentland velocity signal.

    The peak measured velocity at Burra was 3 m/s, while for the modelled Pentland Firth data it wasonly 2.2 m/s but the spectra have been normalizedto have equal areas. The frequency axis has beenset so that the strong 12.42 h M2 period is at unity.Clearly there are strong odd-order harmonics in thereal measurement but none in the numerical one.

    This rudimentary analysis tells us only what is hap-pening between the observing points but more aboutthe impedances looking west into the Atlantic Ocean

    and east into the North Sea should be known. Thesewill add to the channel impedance and so reduce theeffects of high turbine numbers even further. It is safe

    to expect that the increase of the northerly leakageimpedance due to turbine installations in the Burraand Eynhallow Sounds, where the first painful full-scale lessons will be learned, will improve the econ-omics of the Pentland Firth and vice versa.

    A useful numerical experiment would be to build adam across the west entry to the Pentland Firth andrecord the new tidal head and the change in velo-cities in the bypass channel round the north of theOrkneys and in the channels between the islands.This work would indicate the best positions for thedeployment of a pattern of combined pressuresensors and acoustic Doppler velocity sensors,

    which would finally allow us to estimate accuratelythe Pentland Firth resource. Although numericalmodels are very powerful, it is unfortunate that sofew real velocity measurements from the PentlandFirth are available in the public domain.


    Although the horizontal-axis configuration is nowuniversal for wind turbines, the vertical-axis con-

    figuration with rim-drive, faired rings betweenblade banks and cross-bracing [2] shown in Fig. 1may have some advantages for tidal streams and

    Fig. 2 A Lissajous plot of slope against easterly

    velocity at the ends of the Pentland Firth

    Fig. 3 A comparison of the Fourier transforms of real

    observations of current velocities showing odd

    harmonic components (suggesting truncation

    of the higher velocities) with a spectrum of

    numerical data plotted negatively. The

    frequency scaling is adjusted to put the

    12.42 h M2 component at unity

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    marine currents, especially in high impedance chan-nels. The arguments are as follows.

    1. The rectangular flow window of the vertical-axis

    rotor, particularly one where the rotor depth ofindividual machines can be tailored withadditional layers of blades, can fill a large fractionof a channel cross-section. An evenly distributedpressure across close-packed contra-rotatingrotors will give lower wake turbulence. It willreduce the leakage between rotors and so mayallow improvements in the performance coeffi-cient above the Betz limit for a rotor in an openfield.

    2. The vertical axis allows a large diameter rotor, which would be stable in pitch and roll andwhich could be used in either deep-or shallow-

    water and allow power ratings of tens ofmegawatts.

    3. By keeping velocity high, the full diameter rim-drive reduces power-conversion forces.

    4. For a given foil velocity, a larger diameter willhave a longer rotation period and so will sufferfewer fatigue cycles and will make lower torquedemands on the pitch-drive system needed foraccelerating the inertia of the blades and theadded inertia of the water around them.

    5. Rotors can generate from flows from any direc-tion, even in turbulent flows, which vary round

    the rotor circumference and through the depthof the channel. Banks of separate short blades

    would allow operation with the right pitchangle in deep water with a large velocity-shear.

    6. In the event of an electrical fault on land, gener-ation can be stopped instantly with no actuatorpower by releasing all the foils to head into thelocal flow direction.

    7. In the highest spring tides and unforeseensurges, pitch angles can be reduced to shedpower and avoid upstream flooding.

    8. The rings that support blades at both endsreduce bending moments by a factor of four rela-tive to cantilevered blades, and thus ease the taskof the bearings needed for variable-pitch.

    9. The bottom ring can reduce tip vortices and giveflow augmentation equivalent to longer blades.

    10. The rings can house pitch actuators and thebottom ring can contain airbags, which can beinflated to lift the entire structure clear of the

    water for inspection or for the removal ofbiofouling.

    11. Generation plant can be easily accessible in thedry and can even be inspected during operation.

    12. Blades can have a constant cross-section, giving

    cheap tooling and perhaps extrusion.13. With internal fuel tanks, Diesel power and

    fast pitch-variation, rotors can become agile,

    self-propelled vessels like tugs equipped withVoith-Schneider propellers [12].

    The most common objection to the vertical-axis con-figuration with fixed-pitch has been that the vel-

    ocities of blades moving upstream are higher thanthose of blades moving downstream. This leads touneven power production across the flow window

    with a risk of stall for part of the rotation and insuffi-cient lift for another part. However, with a sophisti-cated pitch-control this problem can be entirelyovercome. It could be argued that the velocitycompromises are less than those arising from thedifference between hub and tip velocities in ahorizontal-axis machine.

    Wind turbine designers like high tip-speed ratios(five or more) because the requirement for torque

    in the blade roots, shaft, and gearing is inverselyproportional to it. Torque, especially in gears, isexpensive. The limits to high tip-speed ratios areset by increased noise and, above some criticalspeed, by a sharp rise in the damage from impacts

    with rain drops. The torque argument would alsoapply to rotors working in water. However, thedroplet erosion effect is replaced by the muchmore serious effect of cavitation. Even by we choos-ing foil sections with low pressure-coefficients givenby large radii of curvature at the nose, tip-speedratios will be 2.5 or less in the highest currentvelocities.


    The Betz theory [13] for optimal performance of wind turbines in an open flow field requires thatthe momentum of the flow through a rotor shouldbe reduced by two thirds of the upstream value byits passage through the rotor. Strictly this shouldapply to all points across the swept disc. However,as there is a strong reduction in blade velocitytowards the hub of horizontal-axis machines, a com-promise has to be reached with respect to higherchords and increased pitch angles near the hub.The same momentum requirements will apply tovertical-axis wind turbines except that the compro-mise is in the change of relative velocity across the

    window.With vertical-axis marine-current turbines which

    operate at the surface, the situation is slightly differ-ent because water cannot flow over the machine. Ifthey are part of a close-packed array, water will notbe able to flow easily round the sides. If they

    occupy a fairly large fraction of the water depththen it will not be easy for the water to flow beneath.This means that the performance coefficient of large

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    marine current systems should be able to exceed theBetz limit. However, as this will not be the case forthe very first installations it is useful to consider theBetz design criterion.

    Starting with the assumption that the momentumobjective has been achieved and that the water vel-ocity through the entire rotor window is two thirdsof the distant upstream value, the water must experi-ence a force that will reduce its momentum to one-third of the original value while it is passing throughthe rotor. The volume of water must be conserved

    while it is within the swept volume of the rotor.According to the Bernoulli equation there will be anabrupt loss of head going through both the upstreamand downstream arcs of the rotor followed by a slowrecovery along the wake.

    For this analysis, the stream tubes used by Strick-

    land [14] are replaced for the troposkien blades ofthe Darrieus egg-beater wind turbines with verticalstream slits. These are drawn in Fig. 4, where the slitboundaries are defined by points at equal anglesround the circumference of the rotor. This impliesthat the time taken for a blade axis to pass througha slit is constant (An analysis using slits of equal

    width is also possible). It is assumed that thereduction in flow velocity starts some appreciabledistance upstream, that the velocity through therotor is two thirds of the upstream velocity, andthat the reduction to one third is complete at some

    long distance downstream.


    1. The width of each slit and the ideal flow velocityare known: therefore the mass flow through it isalso known. It may help to think of the water asa long train moving through the rotor window.

    2. The tangential velocity of the blades will havebeen chosen with cavitation in mind. For eachslit, the direction and magnitude of the resultantvelocity that would be seen by an observer ridingon a blade are known.

    3. In each slit the component of force acting on the water in the upstream direction should producethe desired two thirds reduction in momentumfor that mass flow. With close-packed rotors inhigh impedance channels, we can choose theforce that will give the same chosen head acrossthe rotor diameter. This is plotted in Fig. 5(a).

    4. This force must be a component of the hydrodyn-amic forces on the blades moving through the slitand, if the blades are not stalled, it will be nearly

    perpendicular to the direction of the resultant vel-ocity on the blades. More accurately, it will beinclined from that direction towards the trailing

    edge of the foil by a small angle whose tangentis the ratio of lift to drag. Away from stall thisangle will be very small, ,18.

    5. If the angle between this resultant force and the

    upstream direction is known, the magnitude ofthe hydrodynamic force that would have theright upstream component from blades in thatslit can be calculated.

    6. The cross-stream component of the force can becalculated, which will allow the calculation ofthe change of direction of the flow through an iso-lated machine or the change of head betweenrotors in a close-packed array of contra-rotatingturbines where the direction changes areprevented.

    7. There will not always be blades in a slit, but thefraction of time that any blade axis will be in a

    given slit can be calculated. Therefore, the bladeforces can be calculated by dividing the slit forceby the fraction of occupancy.

    8. By knowing the blade chord and the resultantvelocity on a blade in any slit the Reynoldsnumber for that slit can be calculated and theappropriate lift and drag coefficients looked up.For known lift and drag, a given choice of bladechord and knowledge of the magnitude of theresultant water velocity at any slit, we cancalculate the angle of incidence that a blade ina slit should have to the resultant local velocity.

    For isolated turbines the additional angleneeded to allow for flow divergence can beadded. The variation of pitch angle through arotation cycle for one design case of a close-packed machine is shown in Fig. 5(b). To avoidexcessive angular acceleration of the bladeinertia, this includes a compromise that losesabout 1 per cent of the blades power. Note thatthe position of maximum pitch angle comesslightly later than the angle to the upstreamdirection.

    9. The useful component of the force driving the tur-bine and the drag on the foil rings and cross-wirescan be calculated. Knowing the useful force andthe blade speed we can calculate the efficiency,the output power, and the torque which wouldhave to be provided by the power conversionmechanism. The contribution to the power ofone blade through a full rotation is shown inFig. 5(c).

    For Fig. 5, the lift and drag coefficients of a NACA0018 foil were taken from Hanley Innovations Multi-Element software [15]. A 140 m diameter rotor wouldhave 20 blades per bank with 2.3 m chord and 11 m

    span and a tip-speed ratio of 2.5. The open-streamvelocity of 3 m/s would generate 11.3 MW per bank.Reynolds number would be 7.6 million.

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    Fig. 4 The geometry of a vertical-axis rotor rotating anti-clockwise seen from above with flow

    from the top of the page. For a tip-speed ratio of two the chord dimension for this

    number of blades has been exaggerated by a factor of two for clarity. The directions of

    the apparent flow at each blade are fixed by the down-stream velocity and the

    tangential velocity of the rotor. Blade and current velocity vectors (shown with arrows)

    and their resultant (shown bold) are in the true proportion. Momentum forces on the

    blades needed for the velocity reduction will be proportional to the width of each slit

    and are shown with a T-bar. The corresponding hydrodynamic lift forces are drawn

    with small circle ends. The blade pitch-angles needed to give the correct lift forces are

    drawn accurately for this chord and tip-speed

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    These steps have been implemented as a Mathcadworksheet, which allows easy variation of all designvariables with instant calculations of the optimumpitch angles, forces, torques, cavitation pressure, effi-ciency, and power. It gives structural weights for anychoice of working stress and total cost based on

    generic material prices.The mean drag power from the rotor blades

    reduces output by 4.5 per cent of the ideal Betz

    figure. The drag from the diagonal ties (shown inFig. 6) with streamlined fairings would reduce it byabout 1 per cent and the skin drag of unfouledrings by a further 2.5 per cent. The drag loss of thelower ring is likely to be less than that from the tipvortex, which it suppresses. In combination thesegive an estimated performance coefficient of 0.51.

    This coefficient should apply across a wide range ofsolidities, flow velocites, and tip-speed ratios,provided that the appropriate pitch control is used.

    Fig. 5 (a) Flapwise blade force in kilo Newton to give the required change in momentum plotted

    against blade rotation; (b) The ideal pitch angle in degrees and a compromise (dashed) to

    avoid excess acceleration plotted against blade rotation; (c) Useful and wasteful (dashed)

    forces in kilo Newton against blade rotation; and (d) Power into or out of the pitch

    actuation system of one blade in kilowatt with the mean value dashed

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    Fig. 6 Plan view (top) and elevation (below) of floating 45 MW vertical-axis tidal-current

    generator with ring-cam high-pressure oil power-take-off

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    It was reassuring to note that, if all the drag coeffi-cients are set to zero, the MathCad model predicts aperformance coefficient very close to the 16/27 figureof a perfect Betz rotor. Halving the value of the drag

    coefficient improves the performance coefficient by3 per cent. The addition of a blade pitch-error of 18reduces the performance coefficient by ,0.2 percent indicating a wide plateau of good operation.

    At an open stream flow of 3 m/s the prediction forthe head difference across the turbine is 0.4 m. Close-packed units filling most of the flow window in highimpedance channels will behave more like turbinesin ducts and so the Betz limit will not be applicable.

    With more blades or larger chords the performancecoefficient should reach about 0.75.

    There is a wide range of equally good choices ofblade number, blade chord, and tip-speed ratio

    with just two design boundaries. The first boundaryis that the angle of incidence is never above thestall angle at any point of the rotation. If stall wereto arise then the chord or number of blades wouldhave to be increased so as to allow a smaller angleof incidence for the same force. Therefore thenumber and chord should be chosen such thatthe stall angle in not exceeded. Higher numbersmake for a good structural truss. Higher chords giveblades that have good beam strength and so can belighter than slender blades. It might be helpful tokeep foil chords low enough for transport in sea

    containers.The second design boundary requires that no point

    on any blade ever experiences a negative pressurecoefficient high enough to induce cavitation. Pressurecoefficients depend on the curvature of the foil atthe nose, its angle of incidence and the magnitudeof the resultant velocity. Fortunately the highest vel-ocities are associated with small angles of incidence.Cavitation can be reduced somewhat by modifiednose curvature, lower tip-speed ratios, or the use oflarger chords, which need smaller angles of incidenceto produce the required forces. For this set of designchoices the worst cavitation pressure was 73 kilo Pas-cals on a blade at 24.58 from the cross-current diam-eter into the up-current sector.

    In the case of an isolated rotor there will be the extracomplication that the upstream foils will induce achange of flow direction, giving a diverging fanlikeflow. However, the effect of this will be to changethe angles of incidence to the down-stream bladesby a predictable amount and so will be easy to correct.

    A likely installation scenario is that a rotor would befirst installed and operated as an isolated machineand later joined by close neighbours, which will coun-ter the diverging flow. Rotors at the end of a row will

    experience increased flow velocities but these willbe reduced when there are enough banks built inseries to give an impedance which approaches the

    channel value. Rotors may also have to be removedfrom time to time, with effects on the pitch-controlstrategy of those on either side of the gap. All theseconsiderations point to the need for retrospective

    modifications of the pitch-control algorithms.

    7.1 Pitch actuation

    Advanced algorithms for pitch control require a suit-able pitch actuator. If the foil bearings are placed for-

    ward of the centre of pressure there will be a pitchingmoment tending to bring the blade noses in to theresultant velocity. For more than half the rotationperiod the required movement of the foil is in thesame sense as the hydrodynamic torque on it, soblade pitch movement will be generating ratherthan absorbing power. Figure 5(d) shows the instan-

    taneous power to or from one blade actuator throughone cycle of rotation together with the mean output.The power output could be increased by moving theblade pitch axis nearer to the nose.

    The energy produced can be recycled to return a foilto its optimum position during the rest of the cycle. It

    would be possible to use a combination of switchingvalves, cross-connections, and pressure accumulatorsto achieve the required control. However, an extre-mely versatile system, which can apply any comput-able control strategy, can be implemented by digitalpoppet-valve machines, [16, 17]. The block diagram

    in Fig. 7 shows a three-bank machine controllingtwo rams and a link to a common accumulator. Athree-bank poppet valve machine for this powerrating would easily fit in the rotor rings.

    Digital hydraulic machines have two electromag-netically controlled poppet valves on each chamber.Radial geometry allows them to share a commonshaft, which in this case might be started by an elec-tric motor/generator. No magnet can ever overcomethe force of hydraulic pressure on a poppet valve butvalves can be moved at times when there is nopressure difference across them. The correct timingof valve operation allows individual chambers to beidle, to pump or to motor. The unit can changebetween these modes in one half revolution of theshaft, much faster than any swash-plate machine.

    At angles of a few degrees either side of the 0 and180 positions, both rams will be allowed to act asunloaded pumps, sending oil freely to the low-pressure tank, and the blade will head directly intothe local current. After a few degrees the hydrodyn-amic pitch moment will rise and bank 1 of themachine will act as a motor, giving way reluctantlyto a rising pressure from ram A with the level of reluc-tance set by a computer. Meanwhile bank 2 can send

    oil back to the cylinder of ram B at very low pressure.The required energy balance can be maintained byusing bank 3 to pump oil to the high-pressure

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    accumulator, thus storing most of the energy gener-ated by the blade movement. At some angle beyondthe upstream direction the blade will reach its maxi-mum pitch angle and it will be necessary to move itback against the pitching moment, which by thistime is fortunately reducing. This will be done bydrawing power from the high-pressure accumulatorto drive bank 3 as a motor while bank 1 pumps oilback to ram A and ram B sends oil back to the low-pressure tank.

    The electrical machines are needed to perform asmotors only for the initial start. They can be a mixof DC brushless and AC induction types. Once thesystem is running they can be used to generatepower for control logic, instrumentation, communi-cations, hydrostatic bearings, compressors for inflat-ing air bags which can lift the rotor clear of the

    water, dolphin repulsion, anti-fouling, or cathodicprotection. The direct connection of the two ramsto the low-pressure tank can be used as a fail-safepanic measure.

    In this condition the blades will move to align withthe local flow whatever its direction, and there will beno lift and very low drag. This is useful for towing tosite and for installation. It also provides a way to dis-connect the power input that is faster, cheaper, andmore reliable than any braking system and that

    would be needed following any loss of the networkconnection.

    7.2 The seabed attachment

    The seabed attachment affects the entire design of

    tidal stream turbines and is highly dependent onlocal geology. For a vertical-axis rotor, a systemknown as a tri-link which consists of three rigid legs

    with spherical end-bearings can be used. Theseare shown in plan and elevation in Fig. 6. This willgive the rotor freedom to heave, pitch, and rollbut will prevent surge, sway, and yaw. Good tidal-stream sites, which are open at both ends, are likelyto be swept clear down to solid rock or verylarge boulders. However, closed estuaries such asMorecambe Bay will have thick layers of mobilesediment. An even more difficult seabed would beloose sediment containing large boulders or rockoutcrops and the worst would be loose sand contain-ing obstructions like abandoned trawling gear ormines. In two wars Britain and Germany deployed600 000 mines. Only 180 000 have so far beenaccounted for. Many will have been put nearScapa Flow, close to promising tidal-stream sites.

    A thorough survey with seabed-penetrating radar isindicated.

    For the easiest case of good rock the preferredchoice, shown in Figs 6 and 8, is a set of three conicalfabrications pulled down into a conical crater by

    post-tensioned steel strands protected from cor-rosion by alkaline grout. The size of the cone is setby the strength of the rock. For the Pentland Firththe seabed rock is red sandstone with a bendingstrength in the plane of the strata of 37 MPa. With amaximum stress of 10 MPa and the pre-stressfactor of 0.4, the diameter of a 608 cone for a60 MW rotor would be 4 m. Cones can be made ofCor-ten (a corrosion-resistant but easily weldablesteel) with an anti-fouling treatment.

    The conical holes in the rock would be producedby equipment mounted on a Bryden Sea Snail [18],

    a novel seabed vehicle, which gains its down-thrustfrom the water flow and has proved to be muchmore effective than clump anchors. The snail

    Fig. 7 Block diagram of the pitch-control system with a multi-bank poppet-valve machine

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    would be fitted with a rock drill which can beinclined at 608 to the horizontal and also rotatedabout the vertical axis. This would produce a ringof inclined holes which would nearly meet at the

    centre. These would be filled with explosives. A ringof low energy propellant will produce a bubble cur-tain to contain the effects of the blast. A similarmethod can clear debris from the crater.

    The outer surface of the lower cone slope wouldbe fitted with stiffeners in the form of lengths ofangle iron. They will initially be filled with clayand will later form passages for post-tensioningtendons. Across the cone would be a conicalsocket, set at an angle to be perpendicular to themooring leg. The weight of steel would be about12 tonnes. A float on the top of the cone wouldgive it enough buoyancy to allow placement with

    an inflatable vessel. The float would be released,and concrete weighing about 20 tonnes would bepumped inside the cone and in the rough spacesbetween the cone and the surrounding blast-craterin the rock. The total weight will keep the coneand additional tooling in place.

    Drilling holes and placement of post-tensioningtendons can be done with a robot-like machine

    which can sit on the upper cone and be indexedabout its vertical axis. A ring of 45 holes will be drilledthrough the clay in the angle-iron stiffeners and thena further 20 m into the bed rock. Eight lengths of

    50 mm diameter, 3 m drill tube will be held in a rotat-ing can like the chamber of a revolver. It would besequentially fed downward at 308 from the verticaland returned to the can when the hole has reachedfull depth. A design for this machine will be pre-sented in a future paper.

    A plastic hose on the indexing head will be feddown to the bottom of the holes and grout pumpedinto the bottom three-quarters of the depth ofeach hole. The rest of the hole and the passagesthrough the cone will be filled with a non-settingalkaline, hydrophobic, conformable paste, perhapsbased on lithium grease, with a density above thatof sea water. The non-adhesion of the top quarterof the tendon above the grout level is desirable tostore elastic energy and to maintain a constanttension to avoid fatigue.

    The tendons would be 15 mm diameter, seven-strand wire. This can safely be wrapped round andpaid out from a 3.5 m diameter drum, but this wirediameter is rather small for a rock drill hole. Threestrands will be passed into each of the 45 holesdrilled to 50 mm diameter. The odd number meansthat the holes will miss each other. The final toolon the indexing head will crop the strands, place a

    triplex collet over their ends, pull them to the work-ing tension and finally fit a protective cap. This com-plex tool will require advanced robotic techniques,

    but its cost can be written off over many hundredsof installations.

    When a leg is in compression the typical maximumforce of about 20 MN from a 45 MW rotor will go

    safely straight down into the rock and increase thecompressive stress at the cone-to-rock interface.When a leg is in tension the hold-down force mustexceed the vertical component of the leg tension

    which could reach 14 MN. The system has thesame features as a post-tensioned concrete structureand the upward force is supplied by a reduction ofthe compressive stress between cone and rock. Thiscontact has much less elasticity than the long ten-dons and so the tendon stress remains constantand fatigue is avoided. Furthermore, all tendons

    will have been fully tested during the post-tensioningprocess before the turbine is installed.

    The lower end of each leg, shown in Fig. 8, will befitted to the cylinder of a large hydraulic ram. Therod of the ram will be fitted to the outer of aplain spherical bearing such as the SKF GEC 1250FSA [19]. This has a dynamic rating of 35.5 MNand a static rating of 52 MN. It can take rotationof 38 either side of centre. The pressure in theram will be an accurate measure of the force onthe leg. If oil from each side of the ram piston isfed to the appropriate side of the bearing it canpartly offset the contact force without going allthe way to the higher leakages of a full hydrostatic

    bearing. The small exit flow from the bearingmust be scavenged and returned to the system.

    The inner of the plain bearing will carry a femalecone with a 458 half angle which turns into a muchmore acute angle, probably 2.58. The choice of thisangle is important because it will form the contact

    with a male cone permanently placed on theseabed. The axes of the cones will lie perpendicularto the direction of the leg. The female cone will con-tain a set of reinforced-textile air-bags made of amaterial similar to that used for fire hoses. These

    will act as cushions when inflated but will vent airand slowly collapse as the cones approach oneanother. The outer end of the female cone will bebell-mouthed.

    7.3 Installation

    Conventional marine installation uses tugs and tow-lines. An inelastic cable connecting two objects,

    which are far enough apart to be in waves of oppositephase can experience a tension, which is the relativeseparating acceleration (possibly twice the accelera-tion of the water in a wave) times the mass plusadded hydrodynamic mass of the lighter object.

    Even higher tensions can result if a cable is allowedto go slack and then retighten after the build-up ofkinetic energy. An elastic cable can store energy,

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    which will be half the square of the peak tensiontimes the spring rate of the rope. If the cableshould ever break it will release this stored energyin a frighteningly short space of time.

    Cables can apply only tension and in only onedirection. They are slow to make changes in thatdirection. To connect or disconnect heavy cables atsea requires intelligent communication and the con-trol of large forces and heavy objects at both ends ofthe cable, but vessels in distress often have no powerto move heavy objects and sometimes not even acrew. The only attractive things about a cable arethat the tug can be at a safe distance from a danger-ous client vessel which is burning or about to explodeand that the cable can be coiled for compact stow-age. Everything else about towing cables is bad.

    Conventional tugs must be able to make trans-ocean crossings lasting many days in any weatherand must provide acceptable living conditions forquite large crews. This makes hire expensive, typi-cally tens of thousands of pounds a day for an unpre-dictable number of days. Furthermore, availability

    and hire costs vary widely depending on weather,demands of other work, and the location of the tug.The vessels have to be paid for as they move between

    jobs and when they have no work. Until the oil hasgone, the marine renewables cannot compete withthe charter prices of oil firms. A single installationcycle can be a large fraction of initial capital costand early devices may need many cycles of removaland reinstallation.

    A better system would place the tug and the struc-ture being towed close enough to be in the same

    wave phase and arrange that their phase and ampli-tude responses to wave spectra are similar. This

    would produce a large reduction in the forcesbetween them. The driver vessel should be able toapply force in any direction through a short connect-ing link and change it quickly. The system shouldallow instant connection and disconnection withintelligence at only one place and no need for hand-ling heavy weights.

    The drag of a hydrofoil at zero angle of incidence isabout one fortieth of the drag of a circular cylinder

    which would just fit inside it. If the rotor foils arefree to point into the direction of the local water vel-ocity, turbines will be quite easy to tow. However,

    with fuel and a Diesel engine on board, a pair of ver-tical-axis rotors could act like ocean-going vessels

    with an astonishing bollard pull and extreme agility

    Fig. 8 Composite views of the sea-bed connection showing cones, post-tensioning tendons,

    33 KV loops with exo-skeleton and breakable contacts

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    in any direction. A single rotor could do quite well iffitted with some torque reaction. An installationvessel using very large inflated tubes, GPS-linked3608 variable-pitch vector-thrusters and, a quick-dis-

    connect magnetic coupling has been described [20].Each can produce a thrust of 200 kN so a group offour could install a large rotor, even without assist-ance from the rotor itself.

    Before the installation, one inflatable vessel willarrive at the site, where there will be three markerbuoys with lines running down to caps protectingthe male cones on the seabed. The buoys will becaptured and their lines will be made fast to thevessel. The lines will contain air hoses leading tothe inside of the caps so that they can be releasedby compressed air. Device arrival will be timed for

    just after the seabed cone-caps have been removed.

    The turbine will be accurately positioned over itsdesignated site with help from a carrier-phase differ-ential GPS navigation system. Analysis of recordsfrom acoustic Doppler instruments shows that sev-eral sites never have completely slack water butrotors can hover accurately enough for the lowerends to make connection with the seabed attach-ment points.

    When the rotor has reached approximately the cor-rect position and the support vessels have rotated itto the correct azimuth angle, the legs can be loweredby partial filling with water. Three winches will con-

    trol the lowering of each leg. One winch will take themain weight of the leg. The other two can pull the legoutwards or inwards. The third degree of freedomneeded for full positioning control can come fromthe ram at the lower end of each leg. The end bearing

    will be fitted with acoustic sensors to give the final,high-precision position relative to datum points onthe male cone. The rams can allow some inaccuracyin the positioning of the seabed attachment. Theycan provide controlled yielding to wave loads. Theycan even generate a moderate amount of wavepower from long period swell.

    Force from the leg will pass to the seabed throughthe contact between male and female cones lookinglike a rather over-designed butterfly net (see Fig. 8).During the final approach, air will be released fromthe annular cushion bags of the female cone. Theinitial force collapsing the cushion bags can comefrom the weight of the leg. After the 2.58 cones arein contact, the space between them will still be fullof sea-water containing sediment and animal life.This can be cleared with a flow of filtered sea waterand then air, both at pressures set below that which

    would separate the cone contact. This will befollowed by flushing with fresh water to remove salt

    residue, air to remove most of the fresh water, ethylalcohol to remove the last of the water, and a sprayof biocompatible, electrically insulating corrosion

    inhibitor. Pressure can then be reduced to the levelat the surface allowing the 7 bar water pressure tohold the cone closed against the full leg force withno reliance on friction at the 2.58 cone contact.

    Drying air will be circulated to leave conditions suit-able for high-voltage connections.The proposed transmission voltage is 33 kV, so

    60 MW will need 1049 A per phase or, say, 1200 fora reasonable power factor. The turbine side of theconnection will consist of three coaxial conductorsinsulated with 18 mm of Teflon leading to three50 mm thick 200 mm diameter discs with rimsmachined to 22 mm curvature leaving a 6 mmcylindrical track. This gives a potential contact areaof 3700 mm2. If an even contact pressure can beachieved the current density at the contact face willbe 0.3 A per square millimetre. All this will be

    potted into a 200 mm probe, housed in a tubeattached to the top of the female cone.

    The seabed side of the connection consists of threehollow annular shells with a wall thickness of1.5 mm, with a slightly elliptical section having aminor diameter of about 100 mm and an innermajor diameter which is 0.1 mm clear of the innerprobe assembly. The three shells will be housed

    within the male cone. A sealing piston-plug with O-rings will block the entry to each side of the electricalcontact but can slide towards the seabed side onceconditions are dry. Pressure will be applied to the

    probe in the female cone and will advance it, pushingaway the piston-plug which was sealing the malecone. When the discs of the turbine side are aligned

    with the seabed rings, oil pressure will be appliedto the inside of the elliptical section annuli. This

    will distort them to the circular shape and make auniform high-pressure contact. The complicatedshape of the elliptical section annulus can be madefrom electroformed nickel. This has a rather highelectrical resistivity but plating with 0.2 mm ofcopper will reduce the dissipation in the annulus toless than 20 W at 600 A.

    When a turbine has to be removed, air will bepumped into the mooring legs to give them somesmall positive buoyancy and a tension will be appliedby winches on the power torus. Hydraulic pressureapplied to the underside of the probe piston willpull it back into its housing dragging the male conepiston-plug after it and leaving both entries sealed.High pressure air will be injected into the spacebetween the cones to supply a large force to breakthe contact. It is important that all three legsdisconnect simultaneously. The Morse tapers usedfor large twist drills have half-angles of about 1.58but, interestingly, are not all quite the same angle.

    They need a sharp tap to break contact. Such a tapcould be provided by an air cylinder driving ahammer head.

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    It should be ensured that the cone contact doesnot corrode while a turbine is absent. It can be pro-tected by lowering a cap in the form of a similarfemale cone. This can be done by three of the inflat-

    able vessels described above.Electrical cables and hydraulic hoses which areforced to bend are a notorious source of poorreliability. The problems are invariably found at theends where bending is concentrated. The problemcan be reduced if the cables and hoses are formedinto loops of a generous diameter by an exo-skeleton which forces the cable to enter the loopalong a defined tangent and spreads the necessarybending evenly over the full circumferential lengthof the loop. Figure 8 top right shows such a mechan-ism at the ends of the rams. Four metres of ram travel

    will need a change of about 158 in 2.25 turns of the

    outer loops and 308 spread over 4.5 turns of thecentre loop. If the loops are 2 m in diameter thesechanges in curvature would produce less than 1000microstrain at the outer sheath of a 50 mm cable.This would be low enough for a steel pipe and sothere should be an infinite fatigue life.

    The rod of the ram can be protected by a rubberBelofram rolling seal, which works like a stockingpartly turned inside out. This is contained by a canat the end of the ram rod which runs back over thecylinder body. This rod-can will carry a bearing toallow the ram end to rotate independently of the

    exo-skeleton linkage so that rolling of the rotor willnot be transferred to the seabed attachment. Threehelical loops between the legs and the ram end willallow the 33 kV cables and control hoses to toleratethis rotation.

    7.4 Structural forces

    A close analysis of the complete force path through astructure is an important part of the design process.The dominant hydrodynamic flap-wise force on theblades will have its largest component radial to therotor, either inwards or outwards, and will be com-bined with the smaller, useful tangential component.The flap-wise forces will produce reversing bendingmoments in each blade but, because of the supportat both ends and the short length, these are notserious. The forces at each blade end will passthrough pitch bearings to vertical spars runningfrom top to bottom of the rotor. At an open streamcurrent velocity of 4 m/s, 7 m blades with a 2 mchord would experience a peak bearing load of alittle over 200 kN well within the infinite fatiguelife of SKF spherical roller bearings. A hydrostaticbearing pressurized by filtered sea water with pads

    that can tilt through 28 is also possible.There is plenty of room inside an 18 per cent thick-

    ness foil section for a 300 mm diameter tubular spar

    with a wall thick enough to take all the foil forces inshear, as well as vertical forces due to heaveacceleration.

    Blades are separated by faired rings which are

    braced diagonally by sloped cross-ties like somedesigns of gasometer. This braced structure isstrong in torsion and shear and so there is no pro-blem about passing torque from the lowest bladeset up to the power torus. The vertical componentof the diagonal wires will induce compression inthe vertical spars but they are short enough not tobuckle. However, the cross-ties give no strength inthe radial direction. This must come from the separ-ating rings, which will suffer the most critical stressesin the structure. For large rotor diameters the ringcan be split into inner and outer parts, separatedby diagonal webs to increase the section moment

    (see Fig. 6). All torsion and shear forces pass to the ring-cam

    in the power torus. The cam is made as a necklaceof post-tensioned cam sections with junctionsplaced at the cam troughs. The pump must oper-ate as a bearing as well as a power conversionmechanism. The critical stress is the Hertzian con-tact stress between rollers and cam. At full workingpressure this will be 750 MPa, well below valuesused in smaller pumps and railways. Many hun-dreds of contact lines are used in parallel. Anyfaulty lobes or rollers can be identified by a

    change in the rolling noise signature and canthen be disabled by software. The torque is trans-ferred by roller forces on the cam slopes, and goesfrom the roller through hydrostatic oil films thatare pressurized by the piston. The radial pistonforces are taken by bulkhead frames into thebody of the power torus. The tangential forces gothrough swinging struts. Torque presented by thering-cam will be of the order of 108 N/m.

    The circular shape of the power torus is maintainedby tension spokes like those of a bicycle wheel or ofthe London Eye. The upstream arc of the powertorus will be in compression like the stones of anarch and will induce radial outward forces along thediameter perpendicular to the flow direction just asan arch induces in its abutments. These forces willbe resisted by spokes. The downstream arc will bein tension which can be taken by spokes and by ahoop tension member which pulls the arch elementstogether. Up to this point the forces have been welldistributed though many short parallel paths butnow they must be collected round the circumferenceand concentrated at the three points where the post-tensioned concrete mooring legs are connectedthrough plain bearings. Post-tensioned concrete is

    excellent for taking both tension and compressionswithout fatigue. The slope of the legs produces anunwelcome vertical component, upward on one leg

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    and down on a second, which has to be resisted by achange in the water plane area of the power torusrequiring a small tilt.

    At the bottom of the leg the forces go through

    hydraulic rams which give a chance for accurateforce measurement by a pressure transducer,through another plain-bearing universal joint,through the cones of the seabed attachment andinto the pre-compressed rock of the Pentland Firth.For such long legs (about 0.8 of the rotor diameter),buckling is more of a consideration than directstress. One leg will be in tension and one in com-pression with a change at the next tidal phase. Buck-ling will be complicated by any out-of-straightness ofa leg and by bending moments on the leg caused bythe current. It would be interesting to see if slip form-ing can give a small deliberate curvature so that

    whichever leg is in compression is straightened bythe current force.

    7.5 Controls

    Digital hydraulics allows extremely flexible control ofthe torque from variable-displacement pumps,together with true synchronous generation. Initially,the requirement should be that, within the cavitationlimit, the speed of the rotor should be directly pro-portional to the mean current speed. As power willrise with the cube of current speed it follows that

    torque should rise with its square.The torque in Newton metres of an hydraulic

    pump is the product of the pressure in Pascalsto which it is delivering times its displacementper revolution in cubic metres divided by 2p. Adigital pump can have this displacement reducedfrom the maximum value by the selection of thefraction of the number of inlet valves which areallowed to close at bottom-dead-centre of thepiston strokes. Well-designed valve passages andhigh pressure allow the losses of a disabledchamber to be very low of the order of one-thousandth of the energy delivered by an operat-ing chamber.

    This freedom allows the inclusion of a pressureaccumulator to store useful amounts of energybetween the slow pump and the fast hydraulicmotor(s) that drive the generator(s). Even a fewseconds of storage will allow the system to ride outelectrical network transients. Gas accumulators canhold several minutes of output more thanenough time for the next fastest plant to respond.The rotation speed of the hydraulic motor and thesynchronous generator are locked to the frequencyof the network. The generator can export or import

    energy from that network according to the phase ofits armature relative to its rotating magnetic field.This angle, and the real output current, is set by the

    magnitude and direction of the torque supplied bythe hydraulic motor and this torque is set by the pro-duct of pressure and the enabled fraction of themotor cylinders.

    The pressure in the gas -accumulator depends onlyon the history of inflows and outflows. A digitalpoppet-valve machine can change from being a full-torque motor to idling to being a full-torque pumpin half a revolution only 20 ms for a motor drivinga four-pole electrical machine on a 50 Hz network.Subject to not exceeding the upper pressure limitand suffering from a reduced power rating at lowpressures, the instantaneous electrical output (orinput back from the network) can be left entirely tothe choice of the plant owner. Only batteries feedingswitching-mode four-quadrant DC to AC converterscan approach the frequency and phase response.

    The present networks are regulated by large centralplant and suffer problems at the distant periphery.Digital hydraulics and storage can make peripheralplant a valuable asset for grid stability.

    During normal operation, the rotor speed will bethe main control-parameter, with the product ofaccumulator pressure and enabled poppet-valvefraction being set to be directly proportional to it. Areduction in accumulator pressure, resulting per-haps from a short-term network demand, will pro-duce an increase in the enabled fraction to keepthe pump torque correct. Any change in current

    speed will produce a corresponding change in rotorvelocity, leading to a square-law change in therequired torque and so the correct match of tip-speed ratio. Pressure relief valves can protect theaccumulator for a short time, about three times theoil-tank circulation period.

    If rotor speed is following current speed, the bladepitch-angle variations round the circumference willbe the same for all current speeds. If they arechosen to put blades at the centre of the best operat-ing plateau, then local changes of velocity and direc-tion in turbulent flow will have little effect. However,they can be sensed by the pressures in the rams con-trolling pitch-angle, and perhaps in the pockets ofhydrostatic pitch bearings, so another control vari-able is available.

    For a cold start-up from zero rotor speed, all theblades will be heading freely into the current withtheir control rams retracted into the S-shapedguide tracks shown in Fig. 7. Blades on the withcurrent side will be pointing in the wrong direction.However, the pitch-control rams on a blade at 308into the against current sector can be advanced toengage in the sockets of the blade cross-arm andcan change the pitch angle to produce torque to

    start the rotor. Each foil can be engaged in turn asit enters the sector and pitched to increase rotortorque until the working speed is reached.

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    A second definition would be the ratio of blade areato the rectangular flow window and would be 0.49.

    With both variable-pitch blades and variable-speedrotors there can be quite a wide range of acceptable

    values of solidity. High values will be needed inhigh impedance channels, as the first installationsare joined by later ones and the Betz free-streambehaviour is replaced by closed-channel behaviour.It may be better to have higher solidity and lowerpitch-angle than to risk the stall from higher angles.

    Large numbers of small blades give a smoothoutput and lower local stress but are less effectiveas beams. Larger numbers also give benefits ofmass production. The load on a blade will rise withthe first power of chord, but its effectiveness as abeam to flapwise bending will rise with at least thecube. Chord values lower than the dimensions of

    an ISO sea container will be convenient for transport. A value of 2.3 m with 20 blades in one bank of a140 m diameter rotor seems attractive.

    Variable-pitch turbines can gracefully shed loadsdue to currents above their rated maximum velocity.This will improve capacity factor and reduce stress atquite a small cost in total annual energy.

    The very high power take-off torque needed bylarge, slow turbines is easily achieved in a rim-drivedesign. Ring cam hydraulics can also provide aconvenient bearing withlow losses andhighgeometri-cal tolerance. A quad ring cam with differentially-

    controlled pressures in each quadrant can withstandthe vertical wave loads as well as the downstreamforce.


    1. The impedance of a flow channel and the sourcedriving it are of great importance for calculationsof the maximum size of resource but little is yetknown about actual values. The L. Cf/Z. Cp ratiois proposed as an initial indicator of the resistiveimpedance. Many potential sites are likely tohave quite high ratios, suggesting that resourceestimates based only on the kinetic flux may below.

    2. Seabed pressure measurements of mean sealevel at points along a flow channel can be com-pared with flowrates at each cross-section to giveimpedance information both phase and ampli-tude for each section and branch.

    3. The phase lag between the water velocity relativeto the driving head is an indicator of the import-ance of the inertia of the water mass in the chan-nel. For the Pentland Firth, the 458 phase-shift

    between driving head and velocity suggest thatthe inertia of the water is also a strong controllingfactor.

    4. Spectral analysis of velocities at some sites showsodd-order harmonics of the strong 12.42 h M2component which are not present in the vel-ocities predicted by combining the astronomical

    forcing functions. These harmonics would beproduced by the selective reduction of thehigher velocities caused by a square law bottomfriction law.

    5. Vertical-axis rotors appear to be attractive in highimpedance channels because the rectangularflow window can fill a large fraction of the chan-nel cross-section with a wide range of depthsincluding the 70 m depth found in large partsof the Pentland Firth. By filling a large fractionand using contra-rotating rotors, sharp shearingvelocities in the turbine wakes are avoided.

    6. The performance coefficient of vertical-axis

    machines can be as good as for horizontal-axisones provided that the vertical-axis machineshave independent pitch control.

    7. The pitch angles can be calculated from the liftforces needed to give the required momentumchange in each flow slit.

    8. Pitch-changing of any desired sophistication canbe achieved with three banks of a poppet-valvemachine and will be a net generator of power

    which can be useful on the rotor. Only a smallamount of energy storage is needed on therotor for cold starting.

    9. Pairs of vertical-axis rotors can act as powerfuland agile tugs which can install and removethemselves. A single turbine can be installed

    with the help of small, inflatable vessels withmagnetic coupling and linked GPS navigation.

    10. The tri-link mechanism with rigid legs madefrom post-tensioned concrete with acousticend-guidance gives the correct freedoms andconstraints. It avoids the bending moments suf-fered by rigid towers and the problem of snatchloads suffered by ropes and cables. Preventionof buckling is the main design criterion but,

    with special slip-forming, the deliberate slightbending of a leg towards the upstream directionof the leg in compression can reduce problems ofbending moments induced by current.

    11. A combination of cones, spheres, cushion bags, water ballasting, and vacuum suction can givemechanical and high-voltage electrical connec-tions and disconnections in times of a few min-utes but will leave acceptably low seabedobstruction at the end of life.


    We are grateful to David Pugh for advice onimpedance measurement, Roger Proctor of the

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    Proudman Oceanographic Laboratory for numericalpredictions of Pentland Firth flow and Alan Owenof the Robert Gordon University for observationsfrom Burra Sound.


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    10 Nortek AS. Norwaves a Nortek newsletter, May 1999,available from

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    18 Owen, A. and Bryden, I. Prototype support structurefor seabed mounted tidal current turbines. Proc.IMechE, Part E: J. Process Mechanical Engineering,2005, 219, 173183.

    19 SKF. Plain bearings catalogue. The SKF Group, Sweden,available from

    20 Salter, S. H. A Purpose-designed vessel for the installa-tion of wave power devices. Sixth European Wave andTidal Conference, Glasgow, 2005.



    Cf bottom friction coefficientCp turbine performance coefficientL channel lengthPf, Pr bed friction power or rotor powerU current velocityW channel width

    Z channel depth

    r fluid density

    Vertical-axis tidal-current generators 199