A Numerical Method for the Calculation of the Inertial Loads on an Airplane Page: 22
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22
Ci_i — C and ^7)
Cj_ = G+(% - 2113) (Yj_ - H2);
(il.) if R2 ^ < Yi ^ («2
Gi_i =• G "+* - ^3) (%_]_ - R2) , and
C cid)
C£ = G +-(% - D13) (Yi - K2)J
(5) finally, if R2 > Yi or Yi-1 > (**2 + 1y^ assume
= C, and
Gi - b-
Using the sain© type of proof as used in (5^)
(69)
rfpl = 'Pi • + Cl' Wp. (90)
ly (c+d)
In a nann0v similar to tnat used in (30)
y „ , 2 (!% (1Pi)2+ 3 C;-1 'V (91)
"pl 3 (ra^ - m3) dpi) -+■ 6 Gi-1
Also,
(92)
Api = Rx + Ypi tan ¥, and
Zpi = R3 + C/2 ■+ (7pi - H2) 112. (93)
Define,
ipit = 1Pi seo ¥■ (9W
Now define a set of orthogonal axes such that the beam lies
in the plane, with C,-^ also lying in the plane
and (Z - R3 -h C/2 +- Yi_1 Kg) lying in fche plane. So,
the co-ordinatel of the centor of gravity, *^2pi' f^pi* ^2pi,
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Williams, Glen R. A Numerical Method for the Calculation of the Inertial Loads on an Airplane, thesis, January 1958; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc107988/m1/27/: accessed July 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .