13.4 Gust Loads 395Although the “graded” or “ramp” gust is used as a basis for gust load calculations, other shapes
ofgustprofileareincurrentuse.Typicaloftheseisthe“l−cosine”gustofFig.13.11(c),wherethe
gustvelocityuisgivenbyu(t)=(U/2)[l−cos(πt/T)].Again,theaircraftresponseisdeterminedby
superimposingtheresponsestoeachofalargenumberofsmallsteps.
Although the “discrete” gust approach still finds widespread use in the calculation of gust loads,
alternative methods based onpower spectralanalysis are being investigated. The advantage of the
powerspectraltechniqueliesinitsfreedomfromarbitraryassumptionsofgustshapesandsizes.Itis
assumedthatgustvelocityisarandomvariablewhichmayberegardedforanalysisasconsistingofa
largenumberofsinusoidalcomponentswhoseamplitudesvarywithfrequency.Thepowerspectrumof
suchafunctionisthendefinedasthedistributionofenergyoverthefrequencyrange.Thismaythenbe
relatedtogustvelocity.Establishingappropriateamplitudeandfrequencydistributionsforaparticular
randomgustprofilerequiresalargeamountofexperimentaldata.Thecollectionofsuchdatahasbeen
previouslyreferredtoinSection12.2.
Calculationsofthecompleteresponseofanaircraftanddetailedassessmentsofthe“discrete”gust
andpowerspectralmethodsofanalysisareoutsidethescopeofthisbook.Moreinformationmaybe
foundinRefs.[1–4]attheendofthechapter.Ourpresentanalysisisconfinedtothe“discrete”gust
approach,inwhichweconsiderthe“sharp-edged”gustandtheequivalent“sharp-edged”gustderived
fromthe“graded”gust.
13.4.1 “Sharp-Edged” Gust
Thesimplifyingassumptionsintroducedinthedeterminationofgustloadsresultingfromthe“sharp-
edged”gusthavebeendiscussedintheearlierpartofthissection.InFig.13.12,theaircraftisflyingat
aspeedVwithwingincidenceα 0 instillair.Afterenteringthegustofupwardvelocityu,theincidence
increasesbyanamounttan−^1 u/V,orsinceuisusuallysmallcomparedwithV,u/V.Thisisaccompanied
by an increase in aircraft speed fromVto (V^2 +u^2 )
1(^2) , but again this increase is neglected sinceuis
Fig.13.12
Increase in wing incidence due to a sharp-edged gust.