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