Dynamics cheat sheet

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C Lwb = ∂C L wb
∂α wb
α wb
= a wb α wb
C Lt = a t α t
C mp = C m0 p + ∂C mp
∂α α
α t = α wb − i t − ɛ
ɛ = ɛ 0 + ∂ɛ
∂α α wb
C Lt = a t α t
[ (
= a t α wb 1 − ∂ɛ ) ]
− i t − ɛ 0
∂α
a wb is constant, represents
∂C L wb
∂α wb
and C m0p
is propulsion pitching
moment coeff. at zero
angle of attack α
main relation that associates
α wb with α t . α wb
is the wing-body angle
of attack, ɛ is downwash
angle at tail, and
i t is tail angle with horizontal
reference (see diagram)
Lift due to tail expressed
using α wb and
ɛ (notice that α t do not
show explicitly)
(
4 a = a wb
[1 + at S t
a wb S 1 −
∂ɛ
∂α) ] a defined for use with
overall lift coefficient
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C L =
a wb α { }}
wb
{
C Lwb
+ St
S C L t
= a wb α wb + St
S a t
= aα
= (C L ) αwb =0 + aα wb
[
αwb
(
1 −
∂ɛ
∂α
)
− it − ɛ 0
]
overall airplane lift using
linear relations
6 α = α wb − at S t
a S (i t + ɛ 0 )
overall angle of attack
α as function of the
wing and body angle of
attack α wb and tail angles
cl_apha.vsdx
Nasser M. Abbasi
021 214
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C m = C m0 + ∂Cm
∂α α = C m0 + C mα α
C m = ¯C m0 + ∂Cm
∂α α wb = ¯C m0 + C mα α wb
overall airplane pitch
moment. Two versions
one uses α wb and one
uses α
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