Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

13.4 Gust Loads 393

andforverticalequilibrium

Lcosφ=W (13.18)

or

L=Wsecφ (13.19)

FromEq.(13.19),weseethattheloadfactornintheturnisgivenby

n=secφ (13.20)

Also,dividingEq.(13.17)byEq.(13.18)

tanφ=

V^2

gR

(13.21)

Examination of Eq. (13.21) reveals that the tighter the turn the greater the angle of bank required to
maintainhorizontalflight.Furthermore,weseefromEq.(13.20)thatanincreaseinbankangleresults
inanincreasedloadfactor.Aerodynamictheoryshowsthatforalimitingvalueofn,theminimumtime
takentoturnthroughagivenangleatagivenvalueofenginethrustoccurswhentheliftcoefficientCL
isamaximum—thatis,withtheaircraftonthepointofstalling.

13.4 GustLoads............................................................................................

InSection13.2,weconsideredaircraftloadsresultingfromprescribedmaneuversinthelongitudinal
planeofsymmetry.Othertypesofin-flightloadarecausedbyairturbulence.Themovementsoftheair
inturbulencearegenerallyknownasgustsandproducechangesinwingincidence,therebysubjecting
theaircrafttosuddenorgradualincreasesordecreasesinliftfromwhichnormalaccelerationsresult.
Thesemaybecriticalforlarge,high-speedaircraftandmaypossiblycausehigherloadsthancontrol
initiatedmaneuvers.
Atthepresenttime,twoapproachesareemployedingustanalysis.Onemethod,whichhasbeenin
useforaconsiderablenumberofyears,determinestheaircraftresponseandloadsduetoasingleor
“discrete”gustofagivenprofile.Thisprofileisdefinedasadistributionofverticalgustvelocityover
agivenfinitelengthorgivenperiodoftime.ExamplesoftheseprofilesareshowninFig.13.11.
Earlyairworthinessrequirementsspecifiedaninstantaneousapplicationofgustvelocityu,resulting
inthe“sharp-edged”gustofFig.13.11(a). Calculationsofnormalaccelerationandaircraftresponse
were based on the assumptions that the aircraft’s flight is undisturbed while the aircraft passes from
still air into the moving air of the gust and during the time taken for the gust loads to build up; that
theaerodynamicforcesontheaircraftaredeterminedbytheinstantaneousincidenceoftheparticular
lifting surface; and finally that the aircraft’s structure is rigid. The second assumption here relating
the aerodynamic force on a lifting surface to its instantaneous incidence neglects the fact that in a
disturbance such as a gust there is a gradual growth of circulation and hence of lift to a steady state
value (Wagner effect). This, in general, leads to an overestimation of the upward acceleration of an
aircraftandthereforeofgustloads.