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118 Empennage
14-3.1 Lift
The tail lift is defined in terms of lift-curve slope CLα and maximum lift coefficient CLmax (based
on tail planform area). The three-dimensional lift-curve slope is input directly or calculated from the
two-dimensional lift-curve slope:
CLα =
cℓα
1+cℓα(1 + τ)/(πAR)
where τ accounts for non-elliptical loading. The effective angle-of-attack is αe = αtail + i − αzl, where
αzl is the angle of zero lift; in reverse flow (|αe| > 90), αe ← αe − 180 signαe. Let αmax = CLmax/CLα be
the angle-of-attack increment (above or below zero lift angle) for maximum lift. Including the change of
maximum lift angle caused by control deflection, Amax = αmax +Δαmaxf and Amin = −αmax +Δαmaxf.
Then
⎧
CLααe +ΔCLf
Amin ≤ αe ≤ Amax
⎪⎨
π/2 −|αe|
(CLαAmax +ΔCLf )
αe >Amax
CL =
π/2 −|Amax|
⎪⎩
π/2 −|αe|
(CLαAmin +ΔCLf )
αe 90), αe ← αe −180 signαe. For angles of attack less than a transition angle αt, the drag coefficient
equals the forward-flight (minimum) drag CD0, plus an angle-of-attack term and the control increment.
Thus if |αe| ≤αt, the profile drag is
and otherwise
CDp = CD0 (1 + Kd|αe| Xd )+ΔCDf
CDt = CD0 (1 + Kd|αt| Xd )+ΔCDf
CDp = CDt +(CDV − CDt) sin
π
2
|αe|−αt
π/2 − αt
Optionally there might be no angle-of-attack variation at low angles (Kd =0), or quadratic variation
(Xd =2). In sideward flight (defined by (v B x ) 2 +(v B z ) 2 < (0.05|v B |) 2 ), the drag is obtained using
φv = tan −1 (−v B z /v B y ) to interpolate the vertical coefficient: CDp = CD0 cos 2 φv + CDV sin 2 φv. The
induced drag is obtained from the lift coefficient, aspect ratio, and Oswald efficiency e:
CDi = (CL − CL0) 2
πeAR
Conventionally the Oswald efficiency e can represent the tail parasite-drag variation with lift, as well as
the induced drag (hence the use of CL0). Then
D = qSCD = qS
is the drag force. The other forces and moments are zero.
CDp + CDi