regular waves; time stepTcmean period between wave crestsTppeak wave period, 1/fpTzmean zero crossing wave periodufluctuating component of wind speed in the x direction; induced velocity in upstream direction (as in Figure 4.5); perturbation velocity in x direction (downstream, as in Figure 4.11); in‐plane plate deflection in x direction; gear ratio; water particle velocity in x directionu*friction velocity in boundary layerU∞free‐stream velocityUfree‐stream velocityU, U(t)instantaneous wind speed in the along‐wind direction
mean component of wind speed in the along‐wind direction – typically taken over a period of 10 min or 1 hUaveannual average wind speed at hub heightUDstreamwise velocity at the rotor discUiturbine lower cut‐in wind speedUWstreamwise velocity in the far wakeUe1extreme 3 s gust wind speed with 1 year return periodUe50extreme 3 s gust wind speed with 50 year return periodUturbine upper cut‐out wind speedUrturbine rated wind speed, defined as the wind speed at which the turbine's rated power is reachedUrefreference wind speed defined as 10 min mean wind speed at hub height with 50 year return periodU1strain energy of plate flexureU2in‐plane strain energyvfluctuating component of wind speed in the y direction; induced velocity in y direction; in‐plane plate deflection in y directionVairspeed of an autogyro; streamwise velocity at rotor disc, U∞(l – a) (Section 7.1.15); voltage (shown in bold when complex)VArreactive power volt‐amperes‐reactiveV(t)instantaneous lateral wind speedVAapparent power electrical volt‐amperesVffibre volume fraction in composite materialwfluctuating component of wind speed in the z direction; induced velocity in z direction; out‐of‐plane plate deflection; weighting factor; water particle velocity in z directionw(r)blade shell skin thickness (Section 6.4.2)Wwind velocity relative to a point on rotating blade; electrical power lossxdownwind coordinate – fixed and rotating axis systems; horizontal co‐ordinate in the direction of wave propagation; downwind displacementx(t)stochastic component of a variablexnlength of near wake regionxmode of distribution
1first mode component of steady tip displacementXelectrical inductive reactanceXncoefficient of nth term in Dean's stream functionylateral coordinate with respect to vertical axis (starboard positive) – fixed axis systemylateral coordinate with respect to blade axis – rotating axis systemylateral displacement; reduced variate of distribution; height above seabedzvertical coordinate (upwards positive) – fixed axis system; height above ground datum; height above water level; delay operatorzradial coordinate along blade axis – rotating axis systemzground roughness lengthz1number of teeth on pinion gearz(t)periodic component of a variableZsection modulus; externally applied load on flanged jointZelectrical impedance (bold indicates a complex quantity)
Greek
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
