394 CHAPTER 13 Airframe Loads
Fig.13.11
(a) Sharp-edged gust; (b) graded gust; (c) 1−cosine gust.
The “sharp-edged” gust was replaced when it was realized that the gust velocity built up to a
maximumoveraperiodoftime.Airworthinessrequirementsweremodifiedontheassumptionthatthe
gustvelocityincreasedlinearlytoamaximumvalueoveraspecifiedgustgradientdistanceH.Hence,
the“graded”gustofFig.13.11(b).IntheUnitedKingdomHistakenas30.5m.Since,asfarasthe
aircraftisconcerned,thegustvelocitybuildsuptoamaximumoveraperiodoftime,itisnolonger
allowable to ignore the change of flight path as the aircraft enters the gust. By the time the gust has
attaineditsmaximumvalue,theaircrafthasdevelopedaverticalcomponentofvelocityand,inaddition,
maybepitching,dependingonitslongitudinalstabilitycharacteristics.Theeffectoftheformeristo
reducetheseverityofthegust,whereasthelattermayeitherincreaseordecreasetheloadsinvolved.
To evaluate the corresponding gust loads, the designer may either calculate the complete motion of
theaircraftduringthedisturbanceandhenceobtainthegustloadsorreplacethe“graded”gustbyan
equivalent “sharp-edged” gust, producing approximately the same effect. We shall discuss the latter
procedureingreaterdetaillater.
Thecalculationofthecompleteresponseoftheaircrafttoa“graded”gustmaybeobtainedfrom
itsresponsetoa“sharp-edged”or“step”gust,bytreatingtheformerascomprisingalargenumberof
small“steps”andsuperimposingtheresponsestoeachofthese.Suchaprocessisknownasconvolution
orDuhamelintegration.Thistreatmentisdesirableforlargeorunorthodoxaircraftwhereaeroelastic
(structuralflexibility)effectsongustloadsmaybeappreciableorunknown.Insuchcases,theassumption
ofarigidaircraftmayleadtoanunderestimationofgustloads.Theequationsofmotionaretherefore
modifiedtoallowforaeroelasticinadditiontoaerodynamiceffects.Forsmallandmedium-sizedaircraft
havingorthodoxaerodynamicfeatures,theequivalent“sharp-edged”gustprocedureissatisfactory.