Risks associated with wind-turbine blade failures

Risks associated with wind-turbine bladefailures

J.F. Macqueen, J.F. Ainslie, D.J. Milborrow, D.M. Turner andProf. D.T. Swift-Hook

Indexing terms: Wind power, Hazards

Abstract: The CEGB is investigating the potential of large wind turbines for generating electricity. The paperconsiders the risk to people and property, in the unlikely event of a serious structural failure of the main rotor.The greatest risks are found very close to the machine, typically within one blade diameter of the tower base.Outside this area, the overall probability of being struck by a blade is around 10"7 per year for a fixed building.For people who are mobile, the risks are substantially less. The range obviously depends on the initial speed,which is shown to be limited by aerodynamic effects to around Mach 0.8 or 0.9. It also depends on theconfiguration of the fragment during its flight. General reasoning suggests that gliding effects are unlikely tooccur; the fragment tumbles and this simplifies the calculation considerably. Blade or fragment throw distanceswould typically be a few hundred metres or up to 800 m for a once-in-fifty-years high-wind runaway. Probabil-ities of impact for a projectile are typically below 10"5 per square metre within two or three hundred metres(and 10~6/m2 for high-wind runaway over a maximum range of 800 m). The possibility of a stable flightconfiguration, though very remote, does exist. Calculations incorporating the effects of low drag and high lift,which would apply in such circumstances, predict ranges of more than 2 km. However, the risk levels arereduced by an order of magnitude, as compared with tumbling fragments, due largely to their inverse depen-dence on the area of the potential hazard zone.

List of symbols

English symbolsAAfCCDCLD,D

HkL,LII'MMG

1/4

mN

PR

U(V)V[V=(u,v,Vf

W{W)x = (x, y, z)

target-area/risk-zone-areaflat face (reference) area of fragmentblade chorddrag coefficientlift coefficientdrag forcegravitational accelerationhub heightvertical unit vectorlift forcecentre of gravity to 1/4-chord distancecentre of pressure to 1/4-chord distanceMach numberpitching moment1/4-chord momentmass of fragmentaerodynamic force normal to bladefaceprobability of impactvertical-velocity/horizontal-speeddistance from fragment mass centre tohub centreradial distancemaximum radial distance or rangeradial boundstimespeed (velocity) through airspeed (velocity) over groundrelease speed of fragment centre ofgravitywind speed (velocity) over groundposition of fragment

Paper 2902A, first received 10th October and in revised form 26th October 1983The authors are with the CEGB Technology, Planning and Research Division, Cen-tral Electricty Research Laboratories, Kelvin Avenue, Leatherhead, Surrey KT227SE, England

Greek symbolsa, a'yX

peQ)l,a)2,a)3

= aerofoil angle of attack= chance of a thrown fragment gliding= lift parameter= drag parameter (tensor)= air density= azimuthal direction of throw= inclination of rotor to vertical= angular velocity components of frag

ment

1 Introduction

The CEGB is investigating the potential of large windturbines for generating electricity (Milborrow, 1982a). Thechoices of machine design and site location will be madewith full consideration of the safety implications for thepublic and CEGB operating staff. The most serious failurefrom the safety point of view is the detachment of a bladeor blade fragment which could be thrown a considerabledistance and could damage people or property.

This paper sets out the operating experience of largemodern wind turbines around the world. It then considersthe consequences of such failures in terms of throw dis-tances and the risk of being hit by such a blade or frag-ment. An analytical approximation to the risk for a giventarget size and location is presented.

2 Relevant operating experience

To generate realistic amounts of power for injection intoan electricity grid, wind turbine designs have developed inrecent years towards low-solidity rotors of two or threeblades with a high tip-speed ratio. Typical examples arethe Boeing MOD-2, Hamilton Standard and Taywood3 MW machines (BWEA, 19826).

The MOD-0 wind turbine built by NASA was the firstlarge US wind turbine of modern design, having a two-blade rotor of 38 m diameter and a rated power of 100 kW(BWEA, 19826). It has been generating with blades ofvarious types since its construction in 1975. It has been

574 IEE PROCEEDINGS, Vol. 130, Pt. A, No. 9, DECEMBER 1983

used very successfully as a test bed to develop bladedesigns, some of which are now regarded as very prom-ising and are being used in operational wind turbines.Although faults have been found from time to time andcorrected, it has never lost a blade.

The MOD-OA designs were developed from the originalMOD-0, and four such wind turbines have been built inthe USA by Westinghouse: the first in 1978, with a ratedpower of 200 kW or more. Routine inspection, in 1978, ofthe turbine at Clayton, New Mexico, revealed cracking inthe aluminium skin near the roots of both blades. Theblades were modified structurally and reinstalled (Glasgowand Robbins, 1979). Other machines have operated atBlock Island in Rhode Island, Calebra in Puerto Rico andOahu in Hawaii. The last machine has operated with avery high load factor since it was commissioned in 1981(Goodman and Vachon, 1982).

The MOD-1 60 m diameter 2 MW wind turbine wasinstalled by GE (GE, 1979) in 1979. Engineering problemsand environmental effects (principally infrasound)restricted its operation to about 0.2 GWh.

Three MOD-2 units have been built by Boeing in theGoodnoe Hills, near Goldendale in Washington State, thefirst being commissioned in 1980. The rotors are 91 m indiameter and the rated output of each is 2.5 MW. In June1981, the first unit suffered a malfunction and overspedduring a load-dropping test. The hydraulics failed tooperate the pitch control system, and so the rotor acceler-ated from its rated 17.5 rev/min up to 29 rev/min, when thegenerator seized. The malfunctioning valve did then acti-vate and the rotor was brought to rest safely (Vachon,1982). Boeing proceeded to carry out a full safety analysisof the system backed by their aerospace experience. Thewind turbines have been modified accordingly. Holesdrilled in the shafts of the MOD-2 machines initiatedcracking, as stress analysis predicts, and the shafts arebeing replaced.

The two 40 m diameter, three-bladed wind turbines atNibe (Denmark) are similar to each other (Jensen, 1982);they have slightly different rotor designs and controls, butboth are rated at 630 kW. The 'A' machine was grid-connected in 1979, followed by the 'B' machine in 1980.Routine inspection and maintenance is a key part of thephilosophy for their safe operation, and, in 1981, incipientcracking was found in the rotor blades of one of the tur-bines; the rotors of both units have since been strength-ened.

The Tvind wind turbine, built in 1978, has a diameter of54 m and a rated power of 2 MW. The output from thisunit has, however, been severely limited due to therestricted capacity of the local grid (Vachon, 1982).

More recently, several other large wind turbines havebeen built, notably two Boeing MOD-2s, two HamiltonStandard wind turbines (WTS3 and WTS4), a KaMeWaWTS75 and Growian 1 in Germany. Experience fromthese machines is very limited as yet, with only a few thou-sand hours running time between them.

Although other smaller and/or earlier wind turbines areof interest for specific components, they are not directlyrelevant to modern megawatt-size designs. For instance,the only other large machine was the Smith-Putnam unitbuilt on Grandpa's Knob in 1945 (Putnam, 1948), whichfailed after six months when a blade was thrown off. Thatmachine was not aerodynamically optimised (e.g. theblades were not tapered) and was designed before fatiguewas properly understood. The fracture after about1000 000 cycles is entirely predictable with present knowl-edge of materials.

Analyses have been performed of failure modes andeffects for a number of large aerogenerator systems, includ-ing the 200 kW MOD-1 (GE, 1979), the 2.5 MW MOD-2(Lynette and Poore, 1979) and the 3.7 MW unit describedby British Aerospace (1980). These studies reveal that fail-ures capable of leading to detachment of a blade fragmentcan arise in many subsystems of the aerogenerator. Thetwo key systems for preventing such failures are:

(a) a reliable control system to identify the fault situ-ation rapidly and to react accordingly

(b) a braking system to bring the rotor safely to rest.

The defence-in-depth philosophy adopted nowadays is todesign the wind-turbine system and to provide routineinspection protocols to preclude failures due to fatigue andcorrosion (Bridson and Worthington, 1980). Redundancyis included wherever practical.

Good design and construction practice have limited thenumber of operational problems encountered, but thosethat have occurred have demonstrated:

(a) the success of good routine maintenance in identify-ing areas of overstressing and possible failure before failureoccurs

(b) the importance of a reliable control system andactuators to keep the wind turbine under control at alltimes.

An indication of the risk levels associated with large windturbines is provided in the Swedish studies reported byEggwertz et al. (1981). These authors point out thatpresent design codes with conservative component reliabil-ities are sufficient to ensure only 'one serious structuralfailure in some 10000 WECS' with assumed lives of105 hours of continuous service (i.e. 10 years continuousoperation or 30 years at normal wind-turbine load factors).This corresponds to a failure rate of less than 10"5 peryear for an individual wind turbine.

3 Basis of blade-throw calculations

Having shown that the probability of a blade throw issmall, with relevant experience showing no such events inmany thousand hours of operation, it is appropriate toconsider the conditional probabilities should such an eventactually occur.

Simple ballistic analysis shows that a projectile thrownwith speed V under gravity g has a maximum range ofV2/g on level ground. Very high initial speeds would bereached, if a rotor could accelerate until the centrifugalforce exceeded the breaking stress. Paradoxically, thestronger the blades were made to avoid breaking, thehigher would be the initial velocity when a break even-tually occurred.

Air resistance has three effects, two which dramaticallyreduce the range and one which increases it. First, itensures that a rotor cannot accelerate further as the tip-speed approaches Mach 1, which is close to 340 m/s atambient temperature. This immediately limits our con-sideration to 10 km throw range and provides a conve-nient worst-case initial speed to use in our calculations.Secondly, the drag acts to limit the range: it is a nonlinearforce, varying as the square of the speed in air of the frag-ment, and so has its greatest effect at the highest speedsand on the greatest ranges. Thirdly, however, drag cancarry a blade or fragment along with the wind, so addingto the range. This will be especially noticeable in very highwinds which are most likely to produce conditions such asoverspeed or overstressing, which could cause a break inthe first place.

IEE PROCEEDINGS, Vol. 130, Pt. A, No. 9, DECEMBER 1983 575

The effects of air resistance can be incorporated into theanalysis by means of a drag factor \i. The drag force is nU2

against the direction of the air-flow velocity U; lift is atright angles to this and can be simply included as addi-tional terms of a tensor ft. The aerodynamic forces are thensimply expressed as fiUU, and the equation of motion isjust

dU/dt=g- ftUU (1)

The velocity through the air U is the difference betweenthe velocity over the ground V and that of the wind W:

U= V -W (2)

where velocity is related to position x in the usual way

dx/dt = V (3)

These three equations can readily be solved, subject toinitial conditions, if /i can effectively be reduced to a scalarconstant. In general, it cannot; it varies as the attitude ofthe projectile varies. However, if fragments tumble in theair, the various coefficients vary cyclically and, providedthe tumbling period is short compared with the total flighttime, a good approximation to the trajectory is given bytaking an averaged drag factor. Lift will average out tozero overall as the blade or fragment tumbles, and so thetensor nature of the drag factor disappears with the off-diagonal terms. The drag coefficient will vary, as a bladetumbles, from very low values for normal aerodynamicattitudes (say 0.01 or less at zero incidence; Goldstein,1938) to a maximum value which can exceed 2 at rightangles to this (Hoerner, 1958). An average scalar drag coef-ficient of around unity is then appropriate, // in eqn. 1reduces to a scalar constant, and the whole calculation isimmensely simplified. We must, therefore, first of all estab-lish the 'runaway' speed, the maximum initial speed withwhich a blade can be thrown, to provide initial conditionsfor our calculations. Then we must consider the questionof tumbling which can simplify the whole analysis. The sol-ution of the equations can then follow.

4 Initial conditions

4.1 Runa way speedsThe accident which befell the American MOD-2 windturbine in 1981, when the rotor accelerated from 17 to29 rev/min, highlighted the propensity of rotors to'runaway', should they become disconnected from a loadsource. The MOD-2 rotor oversped by some 70%, rea-ching a tip speed around 140 m/s before damage to thegenerator, and consequential vibration, activated safetysystems which should have prevented the occurrence(Vachon, 1982). An appreciation of the likely limitingspeed is needed so that the maximum throw distances offragments shed from the blades can be calculated.

4.2 Aerofoil dataFor a typical large wind-turbine blade, say MOD-2 forexample, the Reynolds number is around 8000000 innormal operation. Mach numbers are around 0.25, butunder runaway conditions the transonic region is of inter-est with higher Reynolds numbers. The aerofoil datacovering such ranges of Reynolds numbers is limited tosubsonic velocities; for transonic velocities, Reynoldsnumbers only up to 2000000 (Gothert, 1944) are available.Furthermore, such data as there are cover only a smallrange of conventional 'flying' angles of incidence. Substan-tial extrapolations are therefore necessary in several direc-tions.

The transonic data, on which this analysis is based,derive from Gothert (1944). For Mach numbers whichcorrespond to typical wind-turbine operating conditionsaround 0.25, his Reynolds number 2000000 correspondsto one-quarter scale. In the region well below stall, it isknown that aerofoil characteristics do not change mark-edly above 2000000. Transonic data that is available forthe 23015 section, used in the MOD-2 blade-tip region,shows that the transonic characteristics change as theaerofoil moves to higher Reynolds numbers, e.g. to the full-scale wind-turbine aerofoils that are of interest. The lift/drag ratios which these data yield are slightly higher thanquoted by Graham, Niteberg and Olson (1945), but thediscrepancy is small.

This provides the necessary extrapolation to high Re inthe transonic range, but Gothert (1944) only coveredangles of incidence up to 8°. Stivers (1953) covered muchwider ranges of angle into the transonic region (but atlower Re) and his results show that:

(a) lift coefficients level off at stall and do not fall withhigher angles of incidence, above Mach 0.7

(b) drag coefficients rise rapidly above Mach 0.75, but(c) different sections give similar data below stall if the

angle of attack is measured from the zero-lift angle,although

(d) different sections give similar data above stall for thesame absolute angle of attack.

It seems reasonable to assume that lift and drag coeffi-cients follow Stivers' (1953) trends as the angle of incidencevaries.

4.3 Aerodynamic theoryThe maximum speed of a runaway wind-turbine rotor,subject to no restraint, is reached when the driving torquefalls to zero. Conventional subsonic performance theorypredicts the existence of a limiting speed where the per-formance curve (power coefficient against tip-speed/wind-speed ratio) intersects the speed ratio axis. Publisheddata for the MOD-2 rotor (Boeing, 1979) show that thisoccurs at a tip-speed/wind-speed ratio around 17. Itfollows that, in a 10 m/s wind, an unrestrained rotor wouldaccelerate to 170 m/s. This limitation arises due to abalance of forces on the rotor. At high tip-speed/wind-speed ratios, the relative flow angle in the outer portions ofthe blade becomes very small and consequently aerofoilangles of attack are also small. The resolved component ofthe lift is therefore smaller than the drag, so that the nettorque in this region is negative and the total torque onthe blade can fall to zero.

Evaluation of the operating conditions at any givenradius and Mach number necessitates an iterative pro-cedure which takes into account tip losses, rotor geometryand aerofoil characteristics. Rotor performance can be cal-culated by a radial integration of these elemental torques.

The application of these techniques to rotors operatingnear the sonic region has been discussed by Pankhurst andHaines (1945). Although they concluded that their applica-tion was valid, there is the question of interference betweenradial elements when shock waves are present, whichwould degrade the performance and reduce the runawayspeed. Our estimates ignoring such effects are, therefore,likely to be pessimistic.

4.4 Performance curves approaching sonicThe performance of a rotor was calculated first at lowMach numbers, for comparison with manufacturers' data.There was close agreement between the two data sets asshown in Fig. 1.


Performance curves have also been derived for tipspeeds approaching sonic, using data derived as describedin Section 4.2. These curves are shown in Fig. 1, and it can

0.5

-0.15 10 15tip-speed/wind-speed ratio

Fig. 1 Influence of tip Mach number on performanceA this analysis, + Boeing (1979)

be seen that above Mach 0.82 there is no positive torque atall. This can, therefore, be taken as the maximum possiblerunaway speed for such a rotor (MOD-2). Aerofoil charac-teristics change rapidly at speeds approaching sonic, pro-ducing correspondingly rapid changes in performance, andso the critical or maximum Mach number can be specifiedwith only a small margin of error.

The performance curves obtained in Fig. 1 have beenused to derive the complete relationship between windspeed and runaway tip speed over the full range of windspeeds shown in Fig. 2. The runaway tip speed cannot

300

</>200e

100

limit at M =0.82

subsonic slopedefined for tip speed ratio 17.5

0.8

0.6

04

0.2

10 20 30wind speed,m/s

50

Fig. 2 Runaway speeds for the MOD-2 rotor

exceed the limiting Mach number (0.82 in this case or276 m/s), but it could well fall off from its peak value athigher wind speeds. However, estimates are not reliable inthat region, because of the large extrapolations requiredfrom existing data in the stalled region, and our pessimisticestimates assume the limiting value at higher wind speeds.

4.5 Other aerofoilsThese results are specific to the particular aerofoil rotortaken as an example (23 000 series and Boeing MOD-2),and different aerofoils on different machines would, inprinciple, give different limits. Accordingly, a sensitivityanalysis was carried out. Most aerofoil characteristics dete-riorate rapidly above Mach 0.75, and so the general trendswere repeated in all the cases considered. The highest

runaway limit found using pessimistic assumptions wasMach 0.93.

4.6 Runaway limitsThis analysis has shown that, in normal operating winds, arunaway rotor can accelerate to around 17 times the windspeed. As the wind speed increases, so does the runawaytip speed, but there is an upper limit in the region ofMach 0.8 or Mach 0.9 (270 m/s to 305 m/s) set by trans-onic effects around the aerofoil.

For the Boeing MOD-2 design, the limit is 153 m/s atthe site mean wind speed, with an absolute limit in highwinds of Mach 0.82 or around 275 m/s. The highestrunaway tip speed found for conventional rotor designswas 0.93 or around 310 m/s (Milborrow, 1983).

5 Tumbling

Having established the worst initial speeds to be expectedin the unlikely event of losing a blade or blade fragment,the question of tumbling remains. Various approacheshave been made to this problem. To take a sophisticatedexample, the Swedes, notably Montgomerie (1982), havefollowed (numerically) complete aerofoil trajectories,attempting to calculate all the aerodynamic forces with sixdegrees of freedom at each step. More simplistically,experiments dropping rulers in a wind tunnel lead to thesame conclusion: calculations and experiments both seemto show that tumbling is to be expected.

The only cause for concern with this conclusion is therealisation that it must, in principle, be possible, by carefuldesign of a well balanced projectile and with careful initialprojection, to avoid tumbling and even to obtain lift,which can extend the range. A javelin, a discus, a sycamoreseed and a paper dart are just three examples of suchsystems that come readily to mind.

However, any fragment breaking loose from a windturbine is most unlikely to have the carefully arrangedinitial projection essential in such cases, as it will separatewith angular momentum from the rotor plus any otherrotation acquired during break-up. Furthermore, even ifthe initial projection imparted no rotation, it is difficult toconceive that a fragment breaking loose from a windturbine would be suitably balanced to avoid tumbling.Geometrical asymmetries along the blade, such as varyingchord length or twist, will give rise to span-wise torques;pitching moments will arise about the span-wise axis of theblade, and a fragment will usually break off with asym-metries such as ragged edges or protruding spars. Theseeffects, together with velocity shear and turbulence in theair stream, certainly favour a tumbling mode of flight.

5.1 Two-dimensional analysis of tumblingTo quantify the implications of tumbling or otherwise forthrow distance calculations, it is helpful to consider theaerodynamic forces acting on a two-dimensional bladefragment. This can be done most easily in terms of thecentre of pressure (Milne-Thomson, 1966) through whichthe lift L and drag D forces act. The aerodynamic forcenormal to the blade face (or more precisely, in two dimen-sions, the chord line) is

N = L cos a + D sin a

and the pitching moment about the centre of gravity is

MG = (/ - l')C(L cos a + D sin a) (5)

where C is the blade chord and a the angle of attack, / and/' are the chord-wise distances of the centres of gravity, and


pressure from the quarter-chord expressed as a fraction ofthe chord. It is common aerodynamic practice to calculatethe centre of pressure /' in terms of the quarter-chordmoment M1/4, using the relation

M1/4 = —l'C(L cos a + D sin a)

thus /' is a function of a, the angle of incidence.One can now express the pitching torque MG as

MG = M1/4 + ICN (6)

Particular values of a may correspond to vanishing MG,implying an equilibrium orientation of the fragment. Thiswill be stable equilibrium, if

MG = 0 and dMJda < 0 (7)

These conditions may be satisfied if the total aerodynamicforce acts along the chord line (so that N vanishes), or ifthe centre of pressure coincides with the centre of gravity(and N dx'/da > 0).

The stability of a blade fragment to pitching oscillationscan be characterised using a pitching-moment potentialdefined by

£(a) = - MG(a') da'Jo

(8)

which defines the potential difference between 0° and aincidence. The existence of this potential function providesa useful criterion for discussing the stability of the bladefragment at a given angle of attack in flight.

5.2 Application of two - dimensional analysisAerofoil data for lift and drag can be used in the equationsof Section 5.1 to locate the stable angles as a function ofthe position of the centre of gravity, and results are plottedin Fig. 3A for a typical symmetrical section (NACA 0012)

°7

Ill04Q. O -O UO

0 20 40 60 80 100 120 140 160angle of zero moment,degrees

Fig. 3A Variation of angle of zero moment with position of centre ofgravityNACA 0012, aspect ratio = 10

whose lift and drag coefficients are shown in Fig. 3B. Inpractice, the centre of gravity of a blade fragment will liebetween 30% and 60% of the chord behind the leadingedge, and, in this case, one stable angle will exist in thestalled region between 0 and n, and a corresponding stableangle between n and 2n. There is a possibility of a stableangle close to 0° incidence for a cambered aerofoil.

Fig. 4 shows the potential energy of rotation, E(a) fromeqn. 8, as a fraction of the initial translational kineticenergy for the full range of possible orientations a. Thereare four regions in this E against a plot. In region A, tum-bling always occurs because the initial spin energy is suffi-cient to overcome the aligning forces which create thepotential well. In region B, the aerofoil does not start withsufficient rotational energy to escape from the potentialwell, but oscillates from one side to the other. For this

region, however, the well is 'wider' than 180°, so that theoscillations cover a full range of lift and drag coefficients,

2.0

1.0

-1.003 0.4 0.5

location of blade centre of gravity,chord lengths behind leading edge

Fig. 3B Lift and drag coefficient at the stable angle, as functions oflocationa Drag coefficientb Lift coefficient

•rt/2 tt 3ir/2aerofoil angle of incidence

2u

Fig. 4 Pitch potential well, showing the tumbling and flight moderegionsNACA 0012 profile

span = S)chord = C)Centre of gravity is 0.4C behind leading edge

S= 10C

just as if complete tumbling had occurred. These cases can,therefore, be treated along with region A as tumbling.

In regions C and D, there is insufficient energy to escapefrom much narrower potential wells, so that flutter isstable with small amplitude oscillations (less than 70°either way) about the equilibrium positions. Lift and dragcoefficients will vary around those corresponding to equi-librium and, to first order, their average values can betaken as the equilibrium ones.

The analysis applies to any fragment, but the worst caseseems likely to be with an aerofoil cross-section which isnot only the one most likely to arise in practice, but whichis known to be capable of producing much more lift thanother, random, sections.

Angular motion of the aerofoil within the potential wellhas been examined using a simple numerical model. Thishas shown that, for realistic blade-design parameters (suchas those for the British Aerospace 3.7 MW machine), oscil-lations about a stable angle will have periods of between1 s and 4 s. For typical blades or aerofoils with theircentres of gravity placed realistically (40% or 50% of thedistance from the leading edge), complete rotations occurwith periods less than 2 s. Although the lift and drag coeffi-cients can vary rapidly with time for a tumbling blade,over a complete rotation the time averaged lift coefficientis very close to zero and the time averaged drag coefficient


lies between 0.6 and 1.3. The maximum flight time of ablade or fragment without drag is y/2 V/g or (2 rjg)i/2 forrange rm; for initial velocities of Mach 0.8 or 0.9, this isaround 40 s, many times the tumbling period. With drag,which reduces the range rm by an order of magnitude asshown in the following Section, flight times are no greaterthan about 13 s, but this is still many times the largesttumbling period. Thus an average drag coefficient and zerolift can be used with some confidence in a projectile anal-ysis for the great majority of cases.

However, for small initial energies, there is a regionabout the stable angle corresponding to an aerodynami-cally stable attitude, with significant lift and moderatedrag. For example, an aerofoil fragment from the BritishAerospace 60 m 3.7 MW design would have a lift coeffi-cient of about 0.8 and a drag coefficient of 0.4 at its stableangle.

5.3 Lift and drag coefficientsTo summarise, in the event of a blade failure one expectsany thrown fragment to tumble during its flight. In thesecircumstances it is calculated that a lift coefficient of zero(CL = 0) and a drag coefficient of approximately unity(CD = 1) is appropriate.

However, there may be improbable combinations ofconditions at the moment of release, which would allow afragment to adopt a stable flight condition (the 'paper dart'scenario) with moderate drag and substantial lift. In thatcase, data from realistic blade designs suggest CD = 0.4and CL = 0.8 as appropriate values for the drag and liftcoefficients.

6 Blade throw: calculations with tumbling

This Section and Section 7 are concerned with calculationsof the thrown distance of detached fragments, and the dis-tribution of risk within the maximum throw circle sur-rounding the wind turbine.

6.1 The drag parameterIn view of the preceding discussion, it is most appropriate,first of all, to make blade throw calculations on the basisthat any thrown fragments tumble and the net effect of liftis small. With these averaging simplifications the equationscan be solved quite easily. The tensor /i in eqn. 1, strippedof any off-diagonal terms because lift is zero on average,represents a purely drag effect and can be reduced to ascalar n the drag parameter.

Thus the drag term in eqn. 1 is simplified to —fiUU.This drag, like gravity g, acts on unit mass of the fragment;it depends on the reference face area Af (usually taken asthe flat plan area) and mass mf of the fragment, the dragcoefficient CD (discussed above and equal to unity, onaverage) and the density p of the air (1.2 kg/m3). Theprecise definition of \i in terms of these physical quantitiesis (Milne-Thomson, 1966)

Table 1: Drag parameters for four rotor designs

^ = 2pCD(Af/mf) (9)

Drag parameters fi are presented in Table 1 for fourmachines (BWEA, 19826) of relevance to the CEGB; thesystems concerned are the British Aerospace design(proposed for construction in the Orkneys), the BoeingMOD-2 system, the Hamilton Standard WTS-4 and theMOD-5A which is a General Electric (USA) designconcept. Generally, the ratio of area to mass will increaseinversely with the linear dimensions of the fragment, asreflected in Table 1, and the effect of drag becomes moreimportant for small fragments. Consequently, a tip frag-

Unit type

British AerospaceBoeing MOD-2Hamilton WTS-4General Electric

M0D-5A

Area A f

(wholeblade)

m 2

6095

104

170

Mass mf

(wholeblade)

kg16,00016,00012,000

27,000

Drag parameter fj(Co = 1)

(wholeblade)

m - 1

24 x10""40 x10""56x10-"

40x10""

(tipfragment)

m - 1

63x10-"40x10""75 x10""

75x10""

ment, although released with a higher initial speed than awhole blade, will be more rapidly slowed down, and somay travel little further.

The equations of motion, eqns. 1-3, describe the trajec-tory of the fragment under the action of gravity and drag,when initial conditions, specified at the instant of fracture,are given. These prescribe the position and velocity of thefragment mass centre; as can be seen from Fig. 5, they

(release speed)

mass cenireof detached fragment

Fig. 5 Definition sketch for fragment throw

depend straightforwardly on the hub height of the turbine,the distance of the fragment mass centre from the hub, theinclination of the blade to the vertical and its rotation rate.Computer programs have been developed to solve theequations for any combination of initial conditions.

There are three questions which must be addressedwhen a blade fragment is thrown. First, how far can itpossibly go? Secondly, how far is it likely to go? Thirdly,what is the chance that a particular point on the groundwill be hit? These questions can be answered to someextent with the model just described.

The physical size of the wind turbine will only influence,to a small extent, the distance reached by any projectiles; itis the tip speed that mainly determines throw distance andthat is related to wind speed rather than rotor size.However, to focus the discussion, sizes appropriate to theMOD-2 (Vachon, 1982) can be taken (91 m diameter, 61 mhub height).

As the rotor turns, the inclination of the blades to thevertical changes cyclically. The break is as likely to happenat one inclination as another. By following a series ofthrows at equally spaced angular intervals through onecomplete rotation, estimates of the maximum throw dis-tance and the distribution of impacts on the ground can beobtained using the computational model.


The fracture may occur close to the tip, at the bladeroot or at some intermediate position along the bladespan. The data in Table 1 suggest that the smallest (and,therefore, most pessimistic) drag parameter /x for a tip frag-ment is 0.004 m" 1 ; for a whole blade the lowest drag par-ameter is 0.002 m~l.

6.2 Throw distances and impact probabilities fortumbling fragments

The maximum throw distance will be attainable when aparticularly high wind, say the once-in-fifty-years gust of40 m/s, has accelerated the rotor to its maximum speed,when the tip is travelling at almost the speed of sound(340 m/s), and a fracture occurs as a blade or fragment iscarried away by the wind. Calculations show that, for a

10"

ua.VI

- 810

range/maximum range

10"

10-7

range/maximum range

Fig. 6 Releases in extreme conditions with zero lift

a Tip fragmentRelease velocity = 340 m/s, wind speed = 40 m/s, hub height = 61 m, releaseradius = 46 m, drag = 4 x 10~3/rn, lift = 0, maximum risk = 2.776 x 10" i /m2,maximum range = 795 m.b Complete bladeRelease velocity = 170 m/s, wind speed = 40 m/s, hub height = 61 m, releaseradius = 23 m, drag = 2 x 10~3/m, lift = 0, maximum risk = 2.648 x 10"5/m2,maximum range = 799 m.

(small) tip fragment under these extreme conditions, themaximum throw distance is some 800 m (or nearly ninerotor diameters). A complete blade shed under the sameextreme conditions (for which the mass centre speed is170 m/s) will travel virtually the same distance, owing tothe reduced drag referred to in Table 1.

Fig. 6 shows graphically the area-weighted probabilities(chance/m2 per throw) of impact for a tip fragment and acomplete blade. These results have been obtained from aprogram IMPACT (Macqueen, 1983), which runs in aHewlett-Packard desk-top computer. Close to the tower ofthe wind turbine, the probability density is relatively high,but one rotor diameter away from the tower this falls toaround 10~ 6 / m 2 o v e r t n e whole range, until, close to themaximum range in both cases, it rises again.

This peak in area-weighted risk at the outer limit of theimpact area is due to the form of the probability distribu-tion, which is roughly an inverse sine—exactly so in theabsence of drag. The analytic simplicity of the zero-dragproblem will be utilised in Section 7.3.

These worst-case conditions of 40 m/s wind and high-speed runaway correspond to an unlikely combination ofcircumstances. The wind turbine would normally expect tohave been shut down by its control and braking systems,long before such a high wind speed could arise, and so itmust be presupposed that the failures of the control andbraking systems have occurred at the same time as theonce-in-fifty-years wind. Such a coincidence should be veryunlikely. It will be more typical to suppose that a modestoverspeed, to say 10% above the rated tip speed of100 m/s, has occurred in a typical wind of 10 m/s whenfailure occurs.

Results shown in Fig. 7 for a tip fragment and a wholeblade give the area-weighted risks as the chance per squaremetre per throw (/m2/throw) in these more typical circum-stances. For a tip fragment, the maximum throw is 371 mwith probabilities well below 10~5/m2/throw within thatrange (except very close to the tower). For a whole blade,the maximum throw is 261 m; probabilities are againbelow 10~ 5 / m 2 A n r o w within most of that range.

The program IMPACT looks at the likelihood ofimpact under a single given set of circumstances of windspeed and break position, as can be seen in Figs. 6 and 7.It does not take into account the consequences of anysliding along the ground after impact, and it assumes thepoints of impact are distributed equally in all directionsround the turbine tower. These simplifications are current-ly being addressed using a Monte-Carlo simulation code,RISKIT, running on an IBM 370 mainframe. Several thou-sand throws can be followed, with initial conditions forwind speed and direction, rotation speed, angle of rotorinclination and the radial break position being selectedwith given probability distributions.

Results from RISKIT, of course, exhibit differences andasymmetries which are not evident from Figs. 4 and 5, butthe estimates of risk level are comparable.

6.3 Overall risk levels for a tumbling bladeThe risk levels derived from IMPACT (chance/m2/throw)must be compounded with the chance of a blade failure ona machine in the first place, which, as discussed in Section2, should be below 10"5 throws per machine per year(Eggwertz et al., 1981), and by the probability of theassumed wind speed occurring. For the high-wind-speedcalculations giving the greatest ranges, one year in fiftymust be taken, while normal winds (10 m/s) occur everyyear. The overall probabilities are, therefore, in the regionof 10"10 per square metre per year for 'typical' throw dis-


tances and 0.2 x 10 12 per square metre per year for themaximum ranges encountered in 'extreme' conditions.

10"

10

10"

- 6

10- 6

range /maximum range

range/maximum range

Fig. 7 Releases in normal conditions with zero lift

a Tip fragmentRelease velocity =110 m/s, wind speed = 10 m/s, hub height = 61 m, releaseradius = 46 m, drag = 4 x 10~3/m, lift = 0, maximum risk = 2.674 x 10~3/m2>maximum range = 371 m.b Whole bladeRelease velocity = 55 m/s, wind speed = 10 m/s, hub height = 61 m, releaseradius = 23 m, drag = 2 x 10~3/rn. lift = 0, maximum risk = 3.31 x 10~3/m2,maximum range = 261 m.

the effective impact area of a tumbling blade. Blade frag-ments could be very small (a bolt or rivet or ice) but asignificant component would be a complete blade tip (say15% of the blade length as used for aerodynamic controlin the MOD-2), with an effective area of 20 m2.

Such areas are large compared with likely individualtargets. The target size will not, therefore, significantlyaffect the total area (projectile plus target area), and, to thisextent, the risks are independent of target size.

Taking these effective areas with the 'typical' probabil-ities in the region of 10~10/m2/year gives the chance ofbeing hit by a whole blade as around 10 " 7 per year (within261 m range) or by a blade fragment (20 m2 say) as2 x 10" 9 per year (within 371 m range).

Over the 'once-in-fifty-years' ranges the correspondingprobabilities are extremely low: 2 x 10"1 0 per year for awhole blade and 4 x 10"1 2 per year for a fragment, up to800 m range.

6.4 The risk levels put into contextThe implications of these risk levels must be seen in thecontext of other engineering and social risks. Consider, forexample, the risks associated with a natural phenomenonsuch as lightning. Records indicate that lightning strikesover the UK occur at a rate of 10"6/m2 per year; thisfigure can be compared with the impact risk levels of10"1 0-10"1 2/m2 per year calculated above. The attractinginfluence of an upright human would mean that, in theabsence of any action to take shelter, the risk to a humanof being struck by lightning could be as great as 3 x 10"5

per year; in practice, protective action is taken, and therisk of death by lightning strike is reduced to 10 " 7 peryear (Kletz, 1981).

Thus the overall probability of being struck by a wholeblade, within about 210 m of the wind turbine, is just com-parable with that of death by lightning. The probability ofbeing struck by blade fragments, or by a whole blade, atdistances in excess of 210 m is less than the risk associatedwith lightning—in the cases considered, the reduction is byseveral orders of magnitude.

Similar calculations have been performed for ice frag-ments, which might accumulate on the rotor in certainconditions. A pessimistic assumption is that the ice slidesoutwards from the hub to the rotor tip, where it is releasedwith twice the tip speed. The calculations show that, forflat square fragments (say 1 m square by 100 mm thick),the thrown distance is typically 400 m or so, and less than800 m in worst-case high-speed-runaway conditions. Thesefigures are comparable with those for a tip fragment.

These calculations cover the overwhelming majority ofcases in which the blade or fragment tumbles. It remains toconsider flighted fragments that do not tumble—the 'paperdart' case or systems (like the sycamore seed) with liftinduced by autorotation.

These risks of being hit (chance/m2) actually relate tothe (point) centres of gravity of projectiles hitting a squaremetre of target, with the risks for larger or smaller targetsbeing proportional to their area. In fact, a 'hit' would becounted if any part of a blade or fragment landed on thetarget, and so the appropriate area is the sum of the pro-jectile and target area.

The effective area of a blade is difficult to specify accu-rately. End-on it would present only a few square metresas a minimum. As it tumbles, it sweeps out a much largerarea, more than 1600 m2 for a single MOD-2 blade, butonly a fraction of this area could 'hit' a target. In roundfigures, 1000 m2 is probably a substantial over estimate of

7 Blade throw calculations with lift

First, the straightforward 'dart' situation with lift and dragcan be disposed of by observing that no blade or likelyblade fragment is well balanced enough to behave like apaper dart. Asymmetry will cause tumbling in one or otherdirection. However, it is then instructive to ask whethertumbling is upwards or downwards, clockwise or anti-clockwise, and it is immediately clear intuitively that theremay be an intermediate equilibrium orientation at whichtumbling does not occur.

This possibility has been discussed quantitatively inconnection with eqns. 5-7. Under these circumstances, lift


need not average to zero and extended ranges are possible.This unfortunate combination of circumstances seemsmost unlikely, but clearly needs to be investigated moreclosely. Similar remarks apply to the possibility of autoro-tation; it is most unlikely to develop because no wind-turbine blade or fragment is sufficiently well balanced, ingeneral, to achieve it. However, it is worth observing thatthe effect of any such flight is to spread the danger morethinly, not to increase its total.

7.1 The lift force—a worst caseThe aerodynamic forces have been described, through eqn.1, by means of a tensor and the velocity U through the air.The treatment of drag alone can be accomplished, asshown in eqn. 9, by reducing the tensor to a scalar (thedrag parameter fx). When lift is incorporated, however, thesituation is a little more complicated.

The drag force acts in opposition to the direction of U,as indicated in Fig. 8. The lift force acts at right angles to

\

\

\

wind

W

,U=(u,v-W,w)

z,w

,u /

Fig. 8 'Worst-case' lift forceDrag vector D = —\i\JULift vector:

\L\ =W2

L • U=0

L • {U x k) = 0

U; apart from this constraint the direction in which it actsdepends on the orientation of the fragment. The magnitudeof the lift force, like that of the drag, is proportional to U2,as shown in Fig. 8. The 'worst case' which can be envis-aged is one in which the fragment orientation continuously(and maliciously) adjusts itself to maintain the upwardscomponent of the lift force L, and it is this case which isconsidered here, as illustrated in Fig. 8. Under these condi-tions the tensor fi can no longer be expressed as a scalar,but rather one obtains a diagonal matrix for /*, defined by

-H- kR

t* = -H- kR (10)-fi +

which is to be used in eqn. 1. The parameters k and R aredefined by:

R = vertical velocity/horizontal speed (11)

where CL is the lift coefficient. The drag parameter \x isdefined by eqn. 9; the quantity k in eqn. 1 will be termedthe lift parameter. It is mathematically important to notethat R is a function of the fragment velocity, and is notconstant during the motion.

The eqns. 1 and 10 can be solved numerically, and, inthis way, a worst-case estimate of the range which mightbe achieved by the trajectory of a thrown blade fragment,in a stable flight configuration, can be calculated. Aprogram LIFDRG, developed to run on a desk-top com-puter, has been used for these calculations.

7.2 Thrown distances and impact probabilitiesfor flying fragments

The lift CL and drag CD parameters for 'flying' fragmentshave been discussed in Section 5, where it was concludedthat CL = 0.8 and CD = 0.4 are appropriate values. Whenthese are translated into values for lift k and drag \i par-ameters (as defined by eqns. 9 and 11), using the data inTable 1 and the discussion of Section 6.2, one finds thatrepresentative values are

drag n =

lift k =

As in the case of tumbling fragments, it is instructive toconsider two situations which represent the limiting cir-cumstances for fragment throw; namely, sonic overspeed(340 m/s tip speed) in 50 year gusting winds (40 m/s) andmodest overspeed (110 m/s tip speed) in typical windspeeds (10 m/s).

The calculations for a tip fragment and whole blade re-leased under typical operating conditions are presented inFig. 9. It can be seen that the maximum ranges are almost400 m (whole blade) and over 800 m (tip fragment), whichare increased by 50% and 100% compared with the tum-bling results of Fig. 7. The impact-probability-densitylevels are less than lO"6/™2 per flight at distances greaterthan 100 m from the machine.

Corresponding calculations for extreme conditions arecontained in Table 2. The tip fragment can be thrown

Table 2: Comparison of tumbling and flying frag-ment results

816

1632

X

X

X

X

KT 4

10"4

10"4

10"4

m"1

m" 1

m" 1

m" 1

forfor

forfor

aa

aa

whole bladetip fragment

whole bladetip fragment

Problem parameters:

Wind speedTip speed

Drag Coefficient (CD)Lift Coefficient (CL)

Typical10 m/s

110 m/sTumbling1.00.0

(a) Maximum throw distance

TypicalExtreme

Whole bladeTumbling261 m799 m

Flying391 m

1649 m

Extreme40 m/s

340 m/sFlying0.40.8

Tip fragmentTumbling371 m795 m

Flying841 m

2245 m

(b) Maximum risk level/chance per m2 per throw, outside 200 m zoneWhole blade Tip fragmentTumbling Flying Tumbling Flying

Typical 10"5 10"8 2 * 10"6 10"6

Extreme 5><1O-6 2 x K ) - 7 2 x 10"6 2 * 10"7

These results are obtained with the programs IMPACTand LIFDRG.

almost 2.5 km, virtually three times as far as its no-liftcounterpart in Fig. 6a. A complete blade, under these sameconditions, could travel almost 1.75 km, roughly twice asfar in the no-lift case of Fig. 6b.

Table 2 provides a direct comparison of the throw dis-tances and impact risk levels for tumbling and flying frag-ments. Typically, the effect of flying is to increase the rangeestimates by a factor of between 2 and 4, and to reduce thecorresponding risk of impact by a factor between 2 and 25.


7.3 Useful analytic estimate for risk of impactThe probability-density distributions shown in Figs. 6, 7and 9 all exhibit the same general behaviour; the probabil-ity density (chance/m2/flight) is high close to the tower,

where

10- 4 -

10

10"

-7

0a

range/maximum range

10-7

range /maximum range

Fig. 9 Releases in normal conditions with lift

a Tip fragmentRelease velocity =110 m/s, wind speed = 10 m/s, hub height = 61 m, releaseradius = 46 m, drag = 1.6 x 10~3/m, lift = 3.2 x 10~3/m, maximum risk =2.648 x 10" i/m2, maximum range = 841 m.b Complete bladeRelease velocity = 55 m/s, wind speed = 10 m/s, hub height = 61 m, releaseradius = 23 m, drag = 8 x 10~*/m, lift = 1.6 x 10~3/m, maximum risk =2.674 x 10"5/m2, maximum range = 391 m.

falls to a minimum in the interior of the danger zone, andthen rises again as the maximum range limit isapproached. These features also apply to the ideal theoreti-cal case, a fragment thrown with no effect of either lift ordrag, and this simple case can be investigated analytically.

Consider the sector shown in Fig. 10a, with angularwidth 6 and radius r (^rm, the maximum throw distancefor a given set of circumstances). Then the probability thatthe thrown fragment will fall within this sector is givenapproximately (exactly in the absence of drag) as P(r; 6),

= ^ Z + -SH1- 1 - forr>0 (12)

It follows that the fragment will land in the annular sector,depicted in Fig. 9b bounded by rl and r2, with a likelihood

where

0 < r, ^ r2 ^ rn (13)

Consider, now, how one might estimate the probability ofhitting an isotropic target (i.e. one for which / ~ s in Fig.106) located within the danger zone, a circle of radius rm

centred on the wind turbine. A natural 'first guess' for thisprobability would be the ratio of the target area to thedanger area (nr2,); this area fraction is denoted by A in Fig.10b. However, a more accurate estimate for the impactprobability can be obtained from eqn. 13; for a given valueof A, the probability of impact, to the first order in A(supposed small) is given by P(A), where

P(A) =

(l/2n3)l/2A112 when 0 < r/rm

when r/rm ~ }

when r/rm ~ 1

(limit of danger zone)maximum range

(14)

mit ofdanger zone

Fig. 10 Definition sketch for probability estimates

a Probability of impact in a sectorb Probability of impact in annular sector

A =target area

danger area

These exhibit the following features:(a) the risk is high close to the wind turbine, and varies

as the square root of the target size(b) midway between the wind turbine and the limit rm of

the danger zone, the risk to a target is proportional to itsarea, in accordance with natural expectations

(c) targets close to the edge of the danger zone areexposed to a risk of impact which decreases with decreas-ing target size, but which is greater than would be expected


on the basis of the area ratio A by a factor of A 1/4 (whichis large for small targets).

These results are plotted in Fig. 11, for a range of values ofthe area ratio A and radial position r/rm. Particular cases,

\ A=A

0L-

lO"1I"8 KT7 10"6 1CT5 1O'A 1CT3 10'2

target area/danger area

Impact risk as a function of target size A and position r/rnFig.11Note: 0 < A < l/2n (also see Fig. 10)

corresponding to whole blades or tip fragments, flying ortumbling in normal or extreme conditions, are tabulated inTable 3. The risks to targets, supposed small in relation tothe whole-blade effective area (1000 m2) or the blade tip(20 m2), are shown close to the tower, at the limit of thepotential danger zone (up to radius rm away from the windturbine), and in its interior.

Thus, for example, the risk of being struck by a com-plete blade, thrown in typical operating conditions andtumbling, is less than 10"7 per year (10~5 throws peryear x 8 x 10 ~3) almost everywhere within the dangerradius of 261 m from the machine. The corresponding riskassociated with a tip-fragment release is less than 10" 9 peryear, everywhere within the danger limit of 371 m, exceptfor a small region within 40 m (a rotor radius), where therisk remains less than 10" 8 per year. These analytic esti-mates agree very well with those obtained from IMPACTand LIFDRG, following hundreds or thousands of individ-ual throws to build up the information.

In all cases, this analytic approximation, extrapolatedfrom the 'gravity-only' case, provides a good approx-imation to the computer simulation, and with a great dealless work. An efficient method of estimating risks requirestwo steps:

(a) Use the program LIFDRG to estimate themaximum throw range rm for a given blade fragment; thiswill involve simulating less than 50 throws, and with expe-rience 25 are sufficient, compared with the 500 or 1000 ofFigs. 6, 7 and 9.

(b) With this estimate of rm, the analytical approx-imations of eqns. 12-14 can be used to estimate the risk ofdelivering a hit to a given target A at a given fractionaldistance r/rm.

7.4 Overall risk levels for flying fragmentsAs in the treatment of tumbling in Section 6.4, it is impor-tant to set the risks arising from gliding (as opposed totumbling) fragments into perspective. The overall risk ofimpact from a gliding fragment is given by

overall chance = chance of a throw

x chance of a glide (given a throw)

x chance of being hit (given a glide)

The first of these factors has been discussed in Section 6.3,and is around 10 " 5 per machine per year, for typical con-ditions, or 2 x 10"7 per machine per year, for extremethrows. The third factor is obtained from the LIFDRGcalculations, discussed in Section 7.3, and presented inTable 2 and Fig. 9.

There remains the second factor, the chance that a frag-ment once thrown, will actually glide. This is expected tobe a small quantity, probably in the range 10~2-10~3

flights per throw, but strictly all that can be asserted, atpresent, is that it is less than unity; for the following dis-cussion, this probability will be denoted by y.

The overall probability that the centre of gravity of thefragment will strike a particular square-metre target cannow be calculated; one obtains, from Table 2 and the pre-ceding discussion:

overall risk =y x 10 ll m2/year/machine (typical)Ay x 10"1 4 m2/year/machine (extreme)

Thus, under typical conditions, the risk of being hit by acomplete gliding blade (with effective area of 1000 m2) isy x 10"8 per year per machine, at distances up to 400 m.The chance of being hit by a tip fragment (20 m2 area) is2y x 10"10 per year for a single machine up to 850 mrange; in an array of machines, with 500 m separation, this

Table 3: Estimates of risks to small targets, using the analytical approximation

Type offragment

whole bladewhole blade (1000 mwhole blade (1000 mwhole blade (1000 mblade tip (20 m2)blade tip (20 m2)blade tip (20 m2)blade tip (20 m2)

2)2)2)

Flightconditions

normal, tumblingnormal, flyingextreme, tumblingextreme, flyingnormal, tumblingnormal, flyingextreme, tumblingextreme, flying

Limit (rjofdanger

m261391799

1649371841795

2245

Ratio ofareasa

5 x 1 0 - 32x I O - 3

5x io~ 4

10-4

5 X 1 0 ~ 4

10-510-5io-6

Risk for various values of radial(r/r

8 x3 x8 x2 x8 x2 x2 x2 x

J

TO"3

10"310-4

io-4

10-510-510-51 0 - 6

r =

2>7 >2 >4>2 >4 >4 >4 >

U2 r

O O - 3 2c10"4 8<10~4 2<10"5 4(. 10"5 2< "\0~6 4

<10~7 4

position

X 10-3x 10-4

x 1 0 " 4

X 10"5X 10-5x 1 0 " 6

x 10"6

x 1 0"7

r — rm

3 x 1 0 - 32 x10"3

6 x10"4

2 x10" 4

10-4

3x10-53 x10"5

5 x i o - 6

These estimates of risk are obtained using the analytical approximation described in Section 7.3. The effective area of the whole blade is taken as103 m2 and of the tip fragment as 20 m2. Targets are supposed 'small' compared with these effective areas.


risk rises by (850/500)2 to 67 x 10 10 per year, due to theadditive influence of several machines within range of eachother.

For extreme conditions, the probability of being struckby a whole blade is 4y x 10" u per year, within 1650 m ofa single machine; this would rise by a factor of (1650/500)2

in an array of machines, to almost 5y x 10"1 0 per year.The corresponding figure for a tip fragment is 87 x 10"1 3

per year per machine up to 2250 m; in an array with500 m spacing, this risk level rise would increase by(2250/500)2 to almost 37 x 10" n per year.

Thus, in all cases considered, the risk levels are verylow, certainly well below the level of 10"7 per year associ-ated with death by lightning strikes. This conclusion isvalid irrespective of the choice of 7, the probability ofgliding.

7.5 Three-dimensional calculationsThe effect of lift has been included by considering a worstcase, as described in Section 7.1, based on conclusionsfrom a two-dimensional analysis of fragment stability. Thisis very likely, in practice, to result in substantial overesti-mates of the maximum throw distance.

A more detailed examination of the effects of the aero-dynamic forces has been performed using the full rigid-body equations, namely:

m dU/dt + mg = F

A dwjdt - (B - C)o)2 co3 = L

B dco2/dt — (C — A)CD1CO3 = M

C dcojdt - (A - B)(Dl(D2 = N

where g = (0, 0, g) is the acceleration due to gravity. U isthe velocity of the centre of gravity, with «,-, i = 1, 2 and 3angular velocities about the ith axis in the body, m is thefragment mass with A, B and C moments of inertia aboutthe axes 1, 2 and 3, respectively. F represents the aero-dynamic forces acting on the body with L, M and N as themoments of the forces about the three body axes. Theabove six-equation model is that used by Redmann et al.(1978) and Montgomerie (1982), and the system can besolved numerically, with some difficulty.

Sufficient data on the aerodynamic lift and drag areavailable only for true aerofoil sections—not for randomblade fragments. These data are obtained only for two-dimensional air flows, and do not take account of span-wise flows which may become important in the fully freeflight of a tumbling blade.

Experience with the model has not revealed any cases inwhich the blade remains in a stable configuration, with norotation about any axis. The conditions at the instant offailure appear sufficient to ensure this in almost every case,even for a symmetric aerofoil.

The most stable motion occurs when the blade con-tinues to rotate in a plane parallel to that of the rotorbefore failure, with only small oscillations about the othertwo axes (pitch and roll). Under these circumstances, thepredicted throw distance is at most 25% greater than thatobtained with the simple drag model of eqns. 1-3. This'stability' is very sensitive to assumptions about themoments of inertia of the blade.

Generally, the gyroscopic coupling present in eqn. 15 issufficient to ensure complete and rapid rotation about thepitching axis, consistent with the conclusions followingeqn. 8. In most cases, therefore, the blade does tumble inflight, and the agreement between this full aerodynamicanalysis and the gravity-with-drag formulation is good.

This conclusion is consistent with Swedish calculations(Eggwertz et al., 1981) which indicate that the effect of liftis to increase the range estimates by no more than 10%.The overall effect of lift can, therefore, be neglected on thebasis that it averages to zero through tumbling, or its effectis small. This type of analysis, although only applied torelatively few blade throw simulations at present, addsfurther conviction to the expectation that blade fragmentswill very rarely, if ever, achieve a stable 'gliding'orientation—corresponding to small values of 7 in Sec-tion 7.3.

8 Risks to people and property

The risks, in this paper, have all been estimated 'per year',on the assumption that the target is at risk continuouslythroughout the whole year. This assumption is appropriatefor fixed items of property, such as buildings or oper-ational plant. It is unlikely to be appropriate for mobileitems or for people who will not normally stay withinrange for extended periods.

The exceptions might be operating staff or people livingpermanently in nearby buildings. Such persons will be pro-tected by the structure in which they spend the majority oftheir time, and their probability of injury or death will begreatly reduced thereby; perhaps by two orders of magni-tude if experience with lightning is anything to go by.

In particular, there will certainly be such reductions forthe extreme-range cases when once-in-fifty-years winds areinvolved. Flying windmill blades will be one of the leastconcerns for anyone caught out in such a storm!

Thus, the risk levels already established can be taken toapply to fixed property and buildings near wind turbines.For people, the risks are probably around two orders ofmagnitude less, permanent inhabitants or operating staffbeing most at risk. Visitors, agricultural workers or main-tenance staff are unlikely to spend more than a few dayswithin range, even though they may be in the open andunprotected by buildings, and their risks are, therefore,substantially less.

9 Conclusions

(a) Blade tips cannot overspeed beyond Mach 1.(b) Stable flight angles cannot be ruled out (as indicated

by the two-dimensional analysis) but seem very unlikely, inpractice, and on the basis of limited three-dimensionalnumerical analysis.

(c) For tumbling blades, average lift CL and drag CD

coefficients are 0 and 1; corresponding figures for flyingpieces are expected to be in the ranges 0.8-1.0 and 0.4-1.0.

(d) Tumbling fragments could go as far as 800 m inextreme conditions, but, more likely, 370 m or less.

(e) Gliding fragments could, correspondingly, go up to2250 m, but are more likely to travel less than 1650 m.

(/) In all cases, the probability of striking a fixed targetwith a blade fragment is less than 10"7 per year, thechance of being hit by lightning; in most cases and placesthe risk is much less than that.

(g) For people, the risks are probably at least twoorders of magnitude less than for fixed targets, and evenless than that for most people.

10 Acknowledgment

This paper is published by permission of the Central Elec-tricity Generating Board. The work was performed at theCentral Electricity Research Laboratories.

1EE PROCEEDINGS, Vol. 130, Pt. A, No. 9, DECEMBER 1983 585

11 References

BATCHELOR, G.K. (1967) An Introduction to Fluid Dynamics. Cam-bridge University Press.

Boeing Engineering (1979) MOD-2 wind turbine system: concept and pre-liminary design report (Vol. 1—Executive Summary). NASA LewisResearch Centre. Report CR-159609 (US DOE/NASA 0002-80/2),Cleveland, Ohio, USA.

BRIDSON, D.W. and WORTHINGTON, P.J. (1980) Structural designand maintenance policies for large wind turbines. Proceedings of the3rd International Symposium on Wind Energy Systems, 307-321,BHRA Fluid Engineering (Cranfield)/Technical University of Denmark(Lyngby)

British Aerospace (1980) Report on the work carried out in phase II ofthe 60 m horizontal axis wind turbine generator study. British Aero-space (Dynamics Group) Brochure No. 650 (Vol. 2 of 2), Internal pub-lication with limited circulation, Hatfield, UK

BWEA (1982a) Structures and materials. In Wind energy for the eighties,Peter Peregrinus, Stevenage, UK, 75

BWEA (19826) Large machines. In Wind energy for the eighties, PeterPeregrinus, Stevenage, UK, 169

EGGWERTZ, S., CARLSSON, I., GUSTAFFSON, A., LINDE, M.,LUNDEMO, C , MONTGOMERIE, B. and THOR, S.E. (1981) Safetyof wind energy conversion systems with horizontal axis. Technical noteHU-2229, Flygtekniska Forsoksanstalten, (Aeronautical ResearchInstitute), Bromma, Sweden

GE (1979) MOD-1 wind turbine generator; failure modes and effectsanalysis. NASA Lewis Research Centre Report NASA CR-159494(Contract NAS 3-20058, US Dept. of Energy Report DOE/NASA/0058-79/1), Cleveland, Ohio, USA

GLASGOW, J.C., and ROBBINS, W.H. (1979) Utility operational expe-rience on the NASA MOD-0A 200 kW wind turbine. NASA LewisResearch Centre Report NASA TM-79084 (US Dept. of Energy ReportDOE/NASA/1004-79/1), Cleveland, Ohio, USA

GOLDSTEIN, S. (1938) Modern Developments in Fluid Dynamics. Clar-endon Press, Oxford, UK

GOODMAN, F.R. and VACHON, W.A. (1982) United States electricutility activities in wind power. Wind Energy Systems, 2, 305 BHRA,Cranfield

GOTHERT, B. (1944) High speed measurements on sections of NACA230 with different thickness ratios. Translated by MAP Vokerrode, No.409C

GRAHAM, D.J., NITEBURG, G.F. and OLSON, R.N. (1945) A system-atic investigation of pressure distribution at high speeds over five rep-resentative NACA low-drag and conventional airfoil sections.

NACA-R832, National Advisory Council for Aeronautics, Washing-ton, DC

HEALY, T.I. and DODGE, D.M. (1982) Design lessons from the USDOE small wind systems development projects. Wind Energy Systems,1,351, BHRA, Cranfield

HOERNER, S.F. (1958) Fluid dynamic drag. US Library of CongressCatalogue No. 57-13009, Hoerner (Private Publication), New Jersey,USA

JENSEN, E. (1982) Structural measurements, particularly regardingfatigue on the two Nibe wind turbines. Wind Energy Systems, 1, 299,BHRA, Cranfield

KLETZ, T.A. (1981) The Mathematics of risk. Paper 52 (Section A),150th Meeting of the British Association for trie Advancement ofScience

LYNETTE, R. and POORE, R. (1979) MOD-2 failure modes and effectsanalysis. NASA Lewis Research Centre Report NASA CR-159632 (USDept. of Energy Report DOE/NASA/002-79/1), Cleveland, Ohio, USA

MACQUEEN, J.F. (1982) IMPACT and IMPCOL: Programs for calcu-lating risks of impact from detached wind turbine blade fragments.CERL Note TPRD/L/2426/P82

MILBORROW, D.J. (1982a) Windpower in the UK electricity supplyindustry. Electronics and Power, 29, 665

MILBORROW, D.J. (19826) Performance, blade loads and size limits forhorizontal axis wind turbines. Proc. 4th BWEA Wind Energy Conf,319, BHRA, Cranfield

MILBORROW, D.J. (1983) Wind turbine runaway speeds. Proc. 5thBWEA Wind Energy Conf. (Reading University), Cambridge Uni-versity Press

MILNE-THOMSON, L.M. (1966) Theoretical Aerodynamics. DoverMONTGOMERIE, B. (1982) Horizontal axis wind turbine blade failure,

blade fragment six degrees of freedom trajectory, site risk level predic-tions. Wind Energy Systems, 2, 389, BHRA, Cranfield

PUTNAM, P.C. (1948) Power from the Wind. Van Nostrand Inc., NewYork, USA

REDMANN, G.H. et al. (1978) Wind field and trajectory models fortornado-propelled objects. EPRI NP-748, Final report.

STIVERS, L.S. (1953) Effects of subsonic Mach number on the forces andpressure distributions of four NACA-64A series airfoil sections atangles of attack as high as 28°. NACA-TN 3162, National AdvisoryCouncil for Aeronautics, Washington, DC

VACHON, W.A. (1982) Wind turbine performance assessment. EPRIReport AP-2456 (Research Project 1996-1) prepared by Arthur D.Little Inc. (Cambridge, Mass., USA), EPRI, Palo Alto (California94304).


Documents

Risks associated with wind-turbine blade failures