Davis and Oates 



T = T„ uy - — i^^ . (52) 



% 



Combining the above effects we have 



T = (1 + k) 



(i + G-G„)" 



(l + k) 



(l + u-uJ"J 



(53) 



If we assume small perturbations (the above expressions will not hold for large 

 speed fluctuations) expand the R.H.S. of the equation and neglect all but the first 

 term in the binomial expansion 



n(n- l)u2 

 (1 + u)" = (1 +nu) + ^ — ! + .... 



We have 



and 



T = Vl+k)[l-n(G-Gj] I (54) 



CT(l + k)[l-n(G-G^)] . (55) 



i/'v^^s^ 



The complete set of equations may now be written in the following normal- 

 ised form: 



Normalised Euler Equations for Small Perturbations 



Linear Motions and Forces 



o ^ - Thrust - Drag 2 /cc\ 



2/xu - — Cl e (56) 



Angular Motions and Moments 



i i . Rolling moment ^^^^ 



624 



