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by turbine over defined time period; modulus of elasticityE1longitudinal elastic modulus of uniaxial composite plyE2transverse elastic modulus of uniaxial composite plyE{}time averaged value of expression within brackets
expected value of significant wave height conditional on a hub‐height mean wind speed
ftip‐loss factor; Coriolis parameter; wave frequency; source intensityf( )probability density functionf1(t)support structure first mode hub displacementfj(t)blade tip displacement in jth modefin(t)blade tip displacement in ith mode at the end of the nth timestepfJ(t)blade j first mode tip displacementfpwave frequency corresponding to peak spectral densityfT(t)hub displacement for tower first modeFforce; force per unit lengthFxload in x (downwind) directionFYload in y directionFtforce between gear teeth at right angles to the line joining the gear centresF(μ)flow expansion function determining the radial distribution of the radial component of induced velocity normal to the wake axisF( )cumulative probability distribution functionF(x|Uk)cumulative probability distribution function for variable x conditional on U = Ukgacceleration due to gravity; vortex sheet strength; peak factor, defined as the number of standard deviations of a variable to be added to the mean to obtain the extreme value in a particular exposure period, for zero up‐crossing frequency, vgpeak factor as above, but for zero up‐crossing frequency nGgeostrophic wind speed; shear modulus; gearbox ratioG12shear modulus of composite plyG(f)transfer function divided by dynamic magnification ratioG(t)t second gust factorhheight of atmospheric boundary layer; duration of timestep; thickness of thin‐walled panel; maximum height of single gear tooth contact above critical root section; height of centre of buoyancy above centre of gravity for a spar buoyh(ψ)root vortex influence functionHhub height; wave height; hub height above mean sea levelH11 year extreme wave heightH5050 year extreme wave heightHjkelements of transformational matrix,
H, used in wind simulationHi(n)complex frequency response function for the ith modeH(f)frequency‐dependent transfer functionHssignificant wave heightHs11 year extreme significant wave height based on 3 hour reference periodHs5050 year extreme significant wave height based on 3 hour reference periodHBbreaking wave heightIturbulence intensity; second moment of area; moment of inertia; electrical current (shown in bold when complex)Iambient turbulence intensityI+added turbulence intensityI++added turbulence intensity above hub heightIbblade inertia about rootIrinertia of rotor about horizontal axis in its planeIrefreference turbulence intensity, defined as expected value of hub‐height turbulence intensity at reference mean wind speed of 15 m/sIulongitudinal turbulence intensityIvlateral turbulence intensityIwvertical turbulence intensityIwaketotal wake turbulence intensityi, j
kshape parameter for Weibull function; shape parameter for GEV distribution; integer; reduced frequency, (ωc/2W); wave number, 2π/L; surface roughness; turbulence energy (
Section 4.7.3)kigeneralised stiffness with respect to the ith mode, defined as
Kconstant on right hand side of Bernouilli equationKCKeulegan–Carpenter numberKPpower coefficient based on tip speedKSMBsize reduction factor accounting for the lack of correlation of wind fluctuations over structural element or elementsKSx(n1)size reduction factor accounting for the lack of correlation of wind fluctuations at resonant frequency over structural element or elementsKv()modified Bessel function of the second kind and order vK(χ)function determining the induced velocity normal to the plane of a yawed rotorLlength scale for turbulence (subscripts and superscripts according to context); lift force; wave length
integral length scale for the along‐wind turbulence component, u, measured in the longitudinal direction, xmmass per unit length; integer; depth below seabed of effective monopole fixity; inverse slope of log‐log plot of S‐N curvemaadded mass per unit span of blademigeneralised mass with respect to the ith modemT1generalised mass of tower, nacelle, and rotor with respect to tower first modeMmoment; integer; tower top mass; mass of floating structure
mean bending momentMpeak quasi‐static mudline momentM1(t)fluctuating cantilever root bending moment due to excitation of first modeMTteeter momentMXblade in‐plane moment (i.e. moment causing bending in plane of rotation); tower side‐to‐side momentMYblade out‐of‐plane moment (i.e. moment causing bending out‐of‐plane of rotation); tower fore–aft momentMZblade torsional moment; tower torsional momentMYSlow‐speed shaft moment about rotating axis perpendicular to axis of blade 1MZSlow‐speed shaft moment about rotating axis parallel to axis of blade 1MYNmoment exerted by low‐speed shaft on nacelle about (horizontal) y axisMZNmoment exerted by low‐speed shaft on nacelle about (vertical) z axisnfrequency (Hz); number of fatigue loading cycles; integer; distance measured normal to a surfacenzero up‐crossing frequency of quasi‐static responsen1frequency (Hz) of first mode of vibrationNnumber of timesteps per revolution; integer; design fatigue life in number of cycles for a given constant stress rangeN(r)centrifugal forceN(S)number of fatigue cycles to failure at stress level Spstatic pressurep()probability density functionPaerodynamic power; electrical real (active) power
associated Legendre polynomial of the first kindq(r, t)fluctuating aerodynamic lift per unit lengthQrotor torque; electrical reactive powerQaaerodynamic torque
rate of heat flow
mean aerodynamic lift per unit lengthQDdynamic factor defined as ratio of extreme moment to gust quasi‐static momentQgload torque at generatorQLloss torque
associated Legendre polynomial of the second kindQ1(t)generalised load, defined in relation to a cantilever blade by Eq. (A5.13)rradius of blade element or point on blade; correlation coefficient between power and wind speed; radius of tubular tower; radius of monopiler′radius of point on blader1, r2radii of points on blade or bladesRblade tip radius; ratio of minimum to maximum stress in fatigue load cycle; electrical resistanceReReynolds numberRu(n)normalised power spectral density, n.Su(n)/
, of longitudinal wind speed fluctuations, u, at a fixed pointsdistance inboard from the blade tip; distance along the blade chord from the leading edge; separation between two points; Laplace operator; slip of induction machine; spacing of columns of a semi‐submersibles1separation between two points measured in the along‐wind directionSwing area; autogyro disc area; fatigue stress range; surface area
S(apparent) electrical power (bold indicates a complex quantity)S()uncertainty or error bandSjk(n)cross‐spectrum of longitudinal wind speed fluctuations, u, at points j and k (single‐sided)SM(n)single‐sided power spectrum of bending momentSQ1(n)single‐sided power spectrum of generalised loadSu(n)single‐sided power spectrum of longitudinal wind speed fluctuations, u, at a fixed point
single‐sided power spectrum of longitudinal wind speed fluctuations, u, as seen by a point on a rotating blade (also known as rotationally sampled spectrum)
cross‐spectrum of longitudinal wind speed fluctuations, u, as seen by points at radii r1 and r2 on a rotating blade or rotor (single‐sided)Sv(n)single‐sided power spectrum of lateral wind speed fluctuations, v, at a fixed pointSw(n)single‐sided power spectrum of vertical wind speed fluctuations, w, at a fixed pointSηη (n)single‐sided power spectrum of sea surface elevationttime; gear tooth thickness at critical root section; tower wall
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