Dynamics cheat sheet

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9
( )
C mα = a (h − h nwb ) − a t ¯VH 1 −
∂ɛ ∂C
∂α + mp
∂α
C mα = a wb (h − h nwb ) − a t V H
(
1 −
∂ɛ
∂α
)
+
∂C mp
∂α
C m0 = C macwb + C mop + a t ¯VH (ɛ 0 + i t ) [ 1 − at S t
a S
¯C m0 = C macwb + ¯C mop + a t V H (ɛ 0 + i t )
( )]
1 −
∂ɛ
∂α
∂C m
∂α
Two versions of
one for α wb and one one
uses α
C m0 is total pitching
moment coef. at zero
lift (does not depend on
C.G. location) but ¯C m0
is total pitching moment
coef. at α wb = 0
(not at zero lift). This
depends on location of
C.G.
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¯Cm0p = C m0p + (α − α wb ) ∂Cmp
∂α
h n = h nwb + at ¯V
( )
a H 1 −
∂ɛ
∂α −
1 ∂C mp
a ∂α
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= h nwb +
a t (
a wb
[1+ a t S t
a wb S
1− ∂ɛ
∂α
)] ¯VH
(
1 −
∂ɛ
∂α
)
−
1
a wb
[1+ a t S t
a wb S
(
)] ∂Cmp
1− ∂ɛ ∂α
∂α
Used to determine h n
19.3 definitions
1. Remember that for symmetric airfoil, when the chord is parallel to velocity vector, then the angle of attack
is zero, and also the left coefficient is zero. But this is only for symmetric airfoil. For the common campbell
airfoil shape, when the chord is parallel to the velocity vector, which means the angle of attack is zero,
there will still be lift (small lift, but it is there). What this means, is that the chord line has to tilt down
more to get zero lift. This extra tilting down makes the angle of attack negative. If we now draw a line
from the right edge of the airfoil parallel to the velocity vector, this line is called the zero lift line (ZLL)
see diagram below.
Just remember, that angle of attack (which is always the angle between the chord and the velocity vector,
the book below calls it the geometrical angle of attack) is negative for zero lift. This is when the airfoil is
not symmetric. For symmetric airfoil, ZLL and the chord line are the same. This angle is small, −3 0 or so.
Depending on shape. See Foundations of Aerodynamics, 5th ed, by Chow and Kuethe, here is the diagram.
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