Dynamics cheat sheet

13 C mt = − ¯V H C Lt + C Lt
S t
S (h − h n wb
) pitching moment coefficient
due to tail expressed using ¯V H .
This is the one to use.
14 C mp pitching moment coefficient
due to propulsion about airplane
C.G.
15 C m = C mwb + C mt + C mp total airplane pitching moment
coefficient about airplane C.G.
16
C m = C mwb + C mt + C mp
[
]
= C macwb + C Lwb (h − h nw )
C L
+ [ − ¯V H C Lt + C Lt
S t
S (h − h n wb
) ] + C mp
{ ( }} ) {
simplified total Pitching moment
coefficient about airplane
S t
= C macwb + C Lwb + C Lt (h − h nw ) −
S
¯V H C Lt + C mp
C.G.
= C macwb + C L (h − h nw ) − ¯V H C Lt + C mp
17
∂C m
∂α
= ∂Cmac wb
∂α
C mα = ∂Cmac wb
∂α
18 h n = h nwb − 1 ∂C L
∂α
+ ∂C L
∂α
(h − h n w
) − ¯V H
∂C Lt
∂α
+ C Lα (h − h nw ) − ¯V H
∂C Lt
∂α
( ∂Cmacwb
∂α
− ¯V H
∂C Lt
∂α
)
+
∂Cmp
∂α
+ ∂Cmp
∂α
+
∂Cmp
∂α
derivative of total pitching moment
coefficient C m w.r.t airplane
angle of attack α
location of airplane neutral
point of airplane found by setting
C mα = 0 in the above
equation
19
∂C m
∂α
= ∂C L
∂α (h − h n)
C mα = C Lα (h − h n )
rewrite of C mα in terms of h n .
Derived using the above two
equations.
20 k n = h n − h static margin. Must be Positive
for static stability
19.2.1 Writing the equations in linear form
The following equations are derived from the above set of equation using what is called the linear form. The main
point is to bring into the equations the expression for C Lt written in term of α wb . This is done by expressing the
∂C Lwb
tail angle of attack α t in terms of α wb via the downwash angle and the i t angle.
∂α wb
in the above equations are
replaced by a wb and ∂C L t
∂α t
is replaced by a t . This replacement says that it is a linear relation between C L and
the corresponding angle of attack. The main of this rewrite is to obtain an expression for C m in terms of α wb
where α t is expressed in terms of α wb , hence α t do not show explicitly. The linear form of the equations is what
from now on.
# equation meaning/use
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