Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

412 CHAPTER 14 Fatigue

determinedasfollows.SubstitutingforthegustexceedanceE(ue)inEq.(14.21)fromEq.(14.17),we
obtain

Dg=−

1

1000 l 10

∫∞

uf

1

2 N(Su,e)

dr(ue)

due

due

or

Dg=

1

l 10

dgperkm (14.22)

inwhichl 10 isafunctionofheighthand

dg=−

1

1000

∫∞

uf

1

2 N(Su,e)

dr(ue)

due

due

SupposethattheaircraftisclimbingataspeedVwitharateofclimb(ROC).Thetimetakenforthe
aircrafttoclimbfromaheighthtoaheighth+δhisδh/ROC,duringwhichtimeittravelsadistance
Vδh/ROC.Hence,fromEq.(14.22),thefatiguedamageexperiencedbytheaircraftinclimbingthrough
aheightδhis

1

l 10

dg

V

ROC

δh

ThetotaldamageproducedduringaclimbfromsealeveltoanaltitudeHataconstantspeedVand
ROCis

Dg,climb=dg

V

ROC

∫H

0

dh

l 10

(14.23)

Plotting1/l 10 againsthfromESDUdatasheetsforaircrafthavingcloudwarningradarandintegrating
gives

(^3000) ∫
0
dh
l 10

= 303

(^6000) ∫
3000
dh
l 10

= 14

(^9000) ∫
6000
dh
l 10

=3.4

Fromtheabove

∫ 9000

0 dh/l^10 =320.4,fromwhichitcanbeseenthatapproximately95percentofthe
totaldamageintheclimboccursinthefirst3000m.
An additional factor influencing the amount of gust damage is forward speed. For example, the
changeinwingstressproducedbyagustmayberepresentedby

Su,e=k 1 ueVe (seeEq.(13.24)) (14.24)

inwhichtheforwardspeedoftheaircraftisinequivalentairspeed.FromEq.(14.24),weseethatthe
gustvelocityufrequiredtoproducethefatiguelimitstressS∞is

uf=S∞/k 1 Ve (14.25)