Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

13.4 Gust Loads 397

whereSTisthetailplaneareaand CL,Ttheincrementoftailplaneliftcoefficientgivenby

CL,T=

∂CL,T

∂α

uE

VE

(13.30)

in which∂CL,T/∂αis the rate of change of tailplane lift coefficient with wing incidence. From
aerodynamictheory,

∂CL,T

∂α

=

∂CL,T

∂αT

(

1 −

∂ε

∂α

)

where∂CL,T/∂αTistherateofchangeofCL,Twithtailplaneincidenceand∂ε/∂αistherateofchange
ofdownwashanglewithwingincidence.Substitutingfor CL,TfromEq.(13.30)intoEq.(13.29),we
have

P=

1

2

ρ 0 VEST

∂CL,T

∂α

uE (13.31)

Forpositiveincrementsofwingliftandtailplaneload

nW= L+ P

or,fromEqs.(13.27)and(13.31)

n=

1

2 ρ^0 VE(∂CL/∂α)uE

w

(

1 +

ST

S

∂CL,T/∂α

∂CL/∂α

)

(13.32)

13.4.2 The “Graded” Gust

The“graded”gustofFig.13.11(b)maybeconvertedtoanequivalent“sharp-edged”gustbymultiplying
themaximumvelocityinthegustbyagustalleviationfactor,F.Equation(13.27)thenbecomes

n= 1 +

1

2 ρ^0 VE(∂CL/∂α)FuE

w

(13.33)

SimilarmodificationsarecarriedoutonEqs.(13.25),(13.26),(13.28),and(13.32).Thegustalleviation
factorallowsforsomeofthedynamicpropertiesoftheaircraft,includingunsteadylift,andhasbeen
calculatedtakingintoaccounttheheavingmotion(i.e.,theupanddownmotionwithzerorateofpitch)
oftheaircraftonly[Ref.5].
Horizontalgustscauselateralloadsontheverticaltailorfin.Theirmagnitudesmaybecalculated
inanidenticalmannertothoseabove,exceptthatareasandvaluesofliftcurveslopearereferredto
the vertical tail. Also, the gust alleviation factor in the “graded” gust case becomesF 1 and includes
allowances for the aerodynamic yawing moment produced by the gust and the yawing inertia of the
aircraft.