Download - NASA

Aircraft 61
where Δz F = z F − z F cg. In hover and low speed, the download is calculated: F I z = k T (C IF F F ), the
downward component of the aerodynamic force in inertial axes. Download can be expressed as a fraction
of the total rotor vertical force, or as a fraction of gross weight. The aerodynamic model also calculates
the interference velocities caused by this component at all other components: v F int = CFB v B int.
Equations for the aerodynamics models are defined for all angles in radians. Input values of angles
will, however, be in degrees.
The aircraft neutral point is calculated from the airframe aerodynamics with all controls set to zero.
The neutral point is here defined as the longitudinal position about which the derivative of the pitch
moment with lift is zero. Hence SLna = SLcg − ΔM/ΔL, with the change in lift and moment calculated
from the loads at angles of attack of 0 and 5 degree.
7–8 Trailing-Edge Flaps
The lifting surfaces have controls in the form of trailing-edge flaps: flap, flaperon, and aileron for
wings; elevator or rudder for tails. The aerodynamic loads generated by flap deflection δf (radians) are
estimated based on two-dimensional aerodynamic data (as summarized in refs. 1 and 2). Let ℓf = cf /c
be the ratio of the flap chord to the wing chord. The lift coefficient is cℓ = cℓα(α + τηδf ), where
η ∼ = 0.85 − 0.43δf is an empirical correction for viscous effects (ref. 1, eq. 3.54 and fig. 3.36). Thin
airfoil theory gives
τ =1− θf − sin θf
π
∼=
sin( π
2 ℓf
n )
with θf = cos −1 (2ℓf − 1) (ref. 1, eq. 3.56 and fig. 3.35; ref. 2, eq. 5.40). The last expression is an
approximation that is a good fit to the thin airfoil theory result for n = 1/2, and a good approximation
including the effects of real flow for n = 2/3 (ref. 2, fig. 5.18); the last expression with n = 2/3 is used
here. The increase of maximum lift coefficient caused by flap deflection is less than the increase in lift
coefficient, so the stall angle-of-attack is decreased. Approximately
Δcℓmax ∼= (1 − ℓf )(1+ℓf − 5ℓ 2 f +3ℓ 3 f )
Δcℓ
(ref. 1, fig. 3.37). Thin airfoil theory gives the moment-coefficient increment about the quarter chord:
Δcm = −0.85 (1 − ℓf ) sin θf δf = −0.85 (1 − ℓf )2 (1 − ℓf )ℓf δf
(ref. 1, eq. 3.57; ref. 2, eq. 5.41); with the factor of 0.85 accounting for real flow effects (ref. 2, fig. 5.19).
The drag increment is estimated using
ΔCD =0.9 ℓ 1.38
f
Sf
S sin2 δf
for slotted flaps (ref. 1, eq. 3.51). In summary, the section load increments are:
Δcℓ = cℓα
Δcℓmax = Xf Δcℓ
cf
c Lf ηf δf
Δcm = cf
c Mf δf
The decrease in angle-of-attack for maximum lift is
Δαmax = − Δcℓ − Δcℓmax
= −(1 − Xf ) Δcℓ
cℓα
cℓα