Michael Graham - Wind Energy Handbook

αangle of attack – i.e. angle between air flow incident on the blade and the blade chord line; wind‐shear power law exponent; exponent of reduced variate in three parameter Weibull distribution; exponent of JONSWAP spectrum peak shape parameter; direction change of geostrophic wind relative to surfaceαxmeridional elastic imperfection reduction factorβinclination of local blade chord to rotor plane (i.e. blade twist plus pitch angle, if any); pitch angle ( Sections 8.3.5& 8.3.16) radius of environmental contourβrprobability weighted moment raised to power rγyaw angle; Euler's constant (= 0.5772); JONSWAP spectrum peak shape parameterγLload factorγmfpartial safety factor for material fatigue strengthγmupartial safety factor for material ultimate strengthΓblade circulation; vortex strengthΓ()gamma functionδlogarithmic decrement of combined aerodynamic and structural damping; width of tower shadow deficit region; depth of surface irregularity; width of jet slot; wake velocity deficitδ3angle between axis of teeter hinge and the line perpendicular to both the rotor axis and the low‐speed shaft axisδalogarithmic decrement of aerodynamic dampingδslogarithmic decrement of structural dampingΔ1 − ν12ν21; discrete jump (e.g. ()− − ()+)εproportion of axial stress to total stress; eddy viscosityεturbulence dissipationε1, ε2, ε3proportion of time in which a variable takes the maximum, mean, or minimum values in a three‐level square waveζteeter angleηellipsoidal coordinate; shaft tilt; one eighth of Lock number (defined in Section 5.8.8); skewness parameter; water surface elevationηbcrest elevation above still water level for a breaking waveθblade pitch angle; wind speed direction change; random phase angle; azimuthal direction; cylindrical panel coordinate; brake disc temperatureκvon Karman's constantκ(t − t)auto‐correlation functionκL(s)cross‐correlation function between velocity components at points in space a distance s apart, in the direction parallel to the line joining themκT(s)cross‐correlation function between velocity components at points in space a distance s apart, in the direction perpendicular to the line joining themκu(r, τ)auto‐correlation function for along‐wind velocity component at radius r on stationary rotor auto‐correlation function for along‐wind velocity component as seen by a point at radius r on a rotating rotorκu(r1, r2, τ)cross‐correlation function between along‐wind velocity components at radii r1 and r2 (not necessarily on same blade), for stationary rotor cross‐correlation function between along‐wind velocity components as seen by points (not necessarily on same blade) at radii r1 and r2 on a rotating rotorλtip speed ratio; latitude; ratio of longitudinal to transverse buckle half wavelengths; relative shell slenderness; curling factor of breaking waveλrtangential speed of blade element at radius r divided by wind speed: local speed ratioλ(d)ratio measuring influence of loading near cantilever root on first mode resonance ( Section 12.7.4)λ*(d)approximate value of λ(d)Λyaw rateμnon‐dimensional radial position, r/R; viscosity; coefficient of frictionμi(r)mode shape of ith blade modeμ1(y)mode shape of first mode of offshore support structureμi(z)mode shape of ith tower modeμT(z)tower first mode shapeμTJ(r)normalised rigid body deflection of blade j resulting from excitation of tower first modeμzmean value of variable zνellipsoidal coordinate; mean zero up‐crossing frequency; rank in series of data points; kinematic viscosity; Poisson's ratioν12, ν21Poisson's ratios for uniaxial composite plyξdamping ratioρair density; water density normalised cross‐correlation function between along‐wind velocity components as seen by points (not necessarily on same blade) at radii r1 and r2 on a rotating rotor σblade solidity; standard deviation; stress mean stressσcrelastic critical buckling stressσMstandard deviation of bending momentσM1standard deviation of first mode resonant bending moment, at blade root for blade resonance, and at tower base for tower resonanceσMBstandard deviation of quasi‐static bending moment (or bending moment background response)σMhstandard deviation of hub dishing momentσMTstandard deviation of teeter moment for rigidly mounted, two bladed rotor standard deviation of mean of blade root bending moments for two bladed rotorσQ1standard deviation of generalised load with respect to first modeσrrotor solidity at a given radius, r, i.e. Bc/(2πr)σustandard deviation of fluctuating component of wind in along‐wind directionσvstandard deviation of wind speed in across‐wind directionσwstandard deviation of wind speed in vertical directionσx1standard deviation of first mode resonant displacement, referred to blade tip for blade resonance and to nacelle for tower resonanceτtime interval; non‐dimensional time; shear stressυPoisson's ratioϕflow angle of resultant velocity W to rotor plane; velocity potential; blade azimuth ( Section 8.3.11)Φ()standard normal distribution functionΦ(x, y, z, t)velocity potential due to unit sourceΦWagner (impulsive heave motion) function ( Sections 4.5.3and 4.6.2)χwake skew angle: angle between the axis of the wake of a yawed rotor and the axis of rotation of rotor; buckling strength reduction factor; fibre inclination to blade panel axisχM1weighted mass ratio defined in Section 5.8.6ψblade azimuth; angle subtended by cylindrical plate panel; stream function parameter with respect to fixed reference frame; wake amplification factor stream function parameter with respect to frame of reference moving at same speed as wave crests and troughsψuu(r, r', n)real part of normalised cross‐spectrumΨKussner (indicial gust) functionωangular frequency (rad/s)ωddemanded generator rotational speedωinatural frequency of ith mode (rad/s)ωggenerator rotational speedωrinduction machine rotor rotational speedωsinduction machine stator field rotational speedΩrotational speed of rotor; Earth's rotational speed

aaerodynamicBbaselineccompressiveddisc; drag; designemotion due to elastic deformatione1extreme value with return period of 1 yeare50extreme value with return period of 50 yearsextextremeffibreimode ijmode jJblade JkcharacteristiclliftmmatrixMmomentmaxmaximum value of variableminminimum value of variablenvalue at end of nth timestepQgeneralised loadRvalue at tip radius, RsstructuralttensileTthrustudownwind; ultimatevlateralwverticalwwakexdeflection in along‐wind direction

orotationally sampled (applied to wind speed spectra)

Figure C1Coordinate system for blade loads, positions, and deflections (rotates with blade).