Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

396 CHAPTER 13 Airframe Loads

small.Theincreaseinwinglift Listhengivenby

L=

1

2

ρV^2 S

∂CL

∂α

u

V

=

1

2

ρVS

∂CL

∂α

u (13.22)

where∂CL/∂αis the wing lift–curve slope. Neglecting the change of lift on the tailplane as a first
approximation,thegustloadfactor nproducedbythischangeofliftis

n=

1

2 ρVS(∂CL/∂α)u

W

(13.23)

whereWistheaircraftweight.ExpressingEq.(13.23)intermsofthewingloading,w=W/S,wehave

n=

1

2 ρV(∂CL/∂α)u

w

(13.24)

This increment in gust load factor is additional to the steady level flight valuen=1. Therefore, as a
resultofthegust,thetotalgustloadfactoris

n= 1 +

1

2 ρV(∂CL/∂α)u

w

(13.25)

Similarly,foradowngust

n= 1 −

1

2 ρV(∂CL/∂α)u

w

(13.26)

If flight conditions are expressed in terms of equivalent sea-level conditions, thenVbecomes the
equivalentairspeed(EAS),VE,ubecomesuEandtheairdensityρisreplacedbythesea-levelvalue
ρ 0 .Equations(13.25)and(13.26)arewritten

n= 1 +

1

2 ρ^0 VE(∂CL/∂α)uE

w

(13.27)

and

n= 1 −

1

2 ρ^0 VE(∂CL/∂α)uE

w

(13.28)

WeobservefromEqs.(13.25)through(13.28)thatthegustloadfactorisdirectlyproportionaltoaircraft
speedbutinverselyproportionaltowingloading.Itfollowsthathighspeedaircraftwithlowormoderate
wingloadingsaremostlikelytobeaffectedbygustloads.
The contribution to normal acceleration of the change in tail load produced by the gust may be
calculated using the same assumptions as before. However, the change in tailplane incidence is not
equaltothechangeinwingincidenceduetodownwasheffectsatthetail.Thus,if Pistheincrease
(ordecrease)intailplaneload,then

P=

1

2

ρ 0 VE^2 ST CL,T (13.29)