Dynamics cheat sheet

1
C L = ∂C L
∂α α
= C Lα α
= aα
C L is lift coefficient. α is angle
of attack. a is slope ∂C L
∂α
which
is the same as C Lα
2 C Lw = C Lwα α wing lift coefficient
3 C D = C Dmin + kC 2 L
drag coefficient
4 C mw = C macw + (C Lw + C Dmin α w ) (h − h nw ) + (C L α w − C Dw ) z¯c pitching moment coefficient
due to wing only about the
C.G. of the airplane assuming
small α w . This is simplified
more by assuming C Dw α w ≪
C Lw and (C L α w − C Dw ) ≪ 1
5 C mw = C macw + C Lw (h − h nw ) simplified wing Pitching moment
C mwb = C macwb + C Lwb (h − h nw )
6
= C macwb + ∂C L wb
∂α wb
α wb (h − h nw )
= C macwb + a wb α wb (h − h nw )
simplified pitching moment coefficient
due to wing and body
about the C.G. of the airplane.
α wb is the angle of attack
7 C Lt = Lt
1
2 ρV 2 S t
C Lt is the lift coefficient generated
by tail. S t is the tail area.
V is airplane air speed
8 L = L wb + L t total lift of airplane. L wb is lift
due to body and wing and L t
is lift due to tail
9 C L = C Lwb + St
S C L t
coefficient of total lift of airplane.
C Lwb is coefficient of lift
due to wing and body. C Lt is
lift coefficient due to tail. S is
the total wing area. S t is tail
area
10
1
M t = −l t L t = −l t C Lt 2 ρV 2 S t pitching moment due to tail
about C.G. of airplane
11 C mt = Mt = − lt¯c
S t
1
2 ρV 2 S t¯c S C L t
= −V H C Lt pitching moment coefficient
due to tail. V H = lt¯c
S t
S
is called
tail volume
12
V H = lt¯c
S t
S
¯V H = ¯l t¯c
S t
S
introducing ¯V H bar tail volume
which is V H but uses ¯l t instead
of l t . Important note. V H
depends on location of C.G.,
but ¯V H does not. ¯lt = l t +
(h − h nwb ) ¯c
95