Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

14.4 Prediction of Aircraft Fatigue Life 413

The gust damage/km at different forward speedsVeis then found using Eq. (14.21) with the appro-
priatevalueofufasthelowerlimitofintegration.Theintegralmaybeevaluatedbyusingtheknown
approximateformsofN(Su,e)andE(ue)fromEqs.(14.15)and(14.17).FromEq.(14.15),

Sa=Su,e=

S′∞,m

Kn

(

1 +C/

√

N(Su,e)

)

fromwhich

N(Su,e)=

(

C

Kn

) 2 (

S′∞,m

Su,e−S′∞,m

) 2

whereSu,e=k 1 VeueandS′∞,m=k 1 Veuf.Also,Eq.(14.17)is

E(ue)=

r(ue)

1000 l 10

or,substitutingforr(ue)fromEq.(14.18),

E(ue)=

3.23× 105 u−e5.26

1000 l 10

Equation(14.21)thenbecomes

Dg=−

∫∞

uf

1

2

(

Kn

C

) 2 (

Su,e−S′∞,m

S′∞,m

) 2 (

−3.23×5.26× 105 u−e5.26

1000 l 10

)

due

SubstitutingforSu,eandS′∞,m,wehave

Dg=

16.99× 102

2 l 10

(

Kn

C

) 2 ∫∞

uf

(

ue−uf

uf

) 2

u−e6.26due

or

Dg=

16.99× 102

2 l 10

(

Kn

C

) 2 ∫∞

uf

(

u−e4.26

u^2 f

−

2 u−e5.26

uf

+u−e6.26

)

due

fromwhich

Dg=

46.55

2 l 10

(

Kn

C

) 2

u−f5.26

or,intermsoftheaircraftspeedVe,

Dg=

46.55

2 l 10

(

Kn

C

) 2 (

k 1 Ve

S∞′,m

)5.26

perkm (14.26)