By F. G. Irving
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Extra info for An Introduction to the Longitudinal Static Stability of Low-Speed Aircraft
CONDITIONS FOR STATIC STABILITY 31 Criterion of Static Stability The condition for static longitudinal stability is therefore that, at the equilibrium condition, the slope of the CMG~CL curve should be negative. When assumption (6) above is valid, the CMG-CL curve is linear: Fig. 3 shows some departure from linearity at high lift coefficients, as would occur in practice near the stall, since the above assumption then ceases to be valid. In practice, further departures from linearity occur due to the flexibiUty of real aircraft structures.
It is called the "modified tail volume coefficient", symbol V. 8) therefore becomes CMG = CMo + (h-h0)CLV'CLT. 9) apply whether the aeroplane is in trim or not. 10) MG = 0 and CMa = 0. 38 LONGITUDINAL STATIC STABILITY Inserting this condition in eqn. 11) ΙΊ and C„-^±£=^. Π) must be positive for positive static stability. This quantity is simply obtained by differentiating eqn. 13) since, by definition, An important feature of aeroplane static stability is immediately apparent. e. g. is sufficiently far forward, the static margin will be positive.
So far, it has only been assumed that a change in CL is accompanied by a change in C L T , SO that dCLJdCL has a value. In order to consider static stability in more specific terms, this quantity must be considered in more detail. The Influence of the Tail lift-curve Slope From eqn. e. CL = CLwb + CLT^. e. dCLvvb/da) is denoted by a, this becomes CL = aa + C L T ^ . 18) It should be noted that the mean airstream velocity at the tail V may be different from the forward speed of the aeroplane V. If CLT were based on V, a factor (V'/V)2 would appear in eqn.