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K=~:} a"==n_Ae aw2=~A
1.1CIA
e= R u .+ 1R)7rA
R = ai}~ + a217j + a3AI + a4
ai - 0.0004 a2 ~ -0.0080 a3 - 0.0501 a4 - 0.8642
We have
i. AA
Ai -
'I cos ALE
ao
CLr,e = ~+ _
Substituting ao - 0.1 *57.3 - 5.73/rad and A - 6, we get CUr,e = 0.0767/deg
or 4.3943/rad. With this, CL -. CIAr.ea - 0.3834. Further using Ac/4 = 0 and
A = 1.0, we get R - 0.9632, e - 0.9812, and K - 0.9942.
We have B = ~- = 1- Substituting, we get (CnplCL)C =O =
(Crip/CL)CL~.M = -0.6 and- (Cnp)W~ -0.2285. Therefore, the stnip theory
prediction of -0.08317/rad is in error by as much as 63%.
Now let us calculate (Clr)W and (Cnr)W. The strip theory gives
CL 0.1*-5~0.16
(Clr)W= 3 = 3 1667lrad
~CDJ 0.0011*5+0.022 (
(Cr)W= 3 =- -0.009/rad
3
Nowlet us estimate (Clr)W and (Cnr)W using Datcod methods.
(Clr)W = c,(C/,).,_ .M + (A2 )~7rad
Num (
(g C~=O,M = D<. (g ),.=o.v=o
EQUATlONS OF MOTION AND ESTIMATION OF STABILITY DERiVATIVES 435
B2) 'AB+2cosAc/4 :an2Ac/4)
Num=1+2B~AABl2B /,)+(7~ :,,)(~ ')
:cosAc/4) ,AB+4~osA 4 8 )
A+2cosAc/, tan2Ac/4'
Den:l+ -.,,,)(- -)
A+4cosA.c/, 8 /
We have r : O, ALE - Ac]4 = O, A - 6, and M -. 0.15. Substituting and
simplifying, we get (Clr)W - 0.1051/rad, Thus, the str:ip theory prediction of
0.1667 differs by as much as 50o/o compared to the Datconl result.
We have
(Cnr)W = (C/: )cl- + (g )CDO
Assuaung g=0 from Fig. 4.29, we get (Cnr/CZ) = -0.02 and (Cnr/CD) =
-0.20. We have CL = 0.3834 and CDO -. 0.022. Substituting, we get (Cnr)W =
-0.0073/rad. In this case, the strip theory result of -0.009/rad differs from the
Datcom result by about 25%.
Example 4.14
Estimate the low-speed vertical tail contributions (Clp)V, (Cnp)V, (Clr)V, and
(Cnr)V at an angle of attack of 5 deg using the following data: lift-curve slope
au - 0.07/deg, leading-edge sweep ALE - 0, vertical tail length /u =' 9.0 m,
wing mean aerodynamic chord c - 3.0 m, wing span b = 15 m, zy = 0.9 m, ratio
of vertical tail area to wing area Sy]S - 0.20, wing aspect ratio A = 6, and wing
taper ratio A, = 0.5.
Solution. We have
(l+?dp T7v=0.724+~06S3S~+2f4 +0.009A
Cyp.v = -kay 1 + ?dp)-7,SS
z N zU COS CL - /v sin a
(qp)V={2(b)( b )ICyp,v
(Cnp)V=-(;)(l,,osa+zusm,)( b )Cyp.v/rad
(C,r)V = b2(lv cos a + zl sinu)(ZU cos a - ly sin ty)Cyp.v
(Cnr)V = b2 (lv cos a + zu SiIICL,)?Cyp.V
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