"Now consider a wing together with a tailplane. The tailplane is positioned to generate a stabilising moment about the aircraft CG. The same vertical gust will increase the angle of attack of the tailplane and increase lift, which, when multiplied by arm 'y', will generate a negative (nose down) pitching moment about the aircraft CG.
If the tail moment is greater than the wing moment the sum of the moments will not be zero and the resultant nose down moment will give an angular acceleration about the CG. The nose down angular acceleration about the CG will return the aircraft towards its original position of equilibrium. The greater the tail moment relative to the wing moment, the greater the rate of acceleration towards the original equilibrium position. (Too much angular acceleration is no good).
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There are two moments to consider; the wing moment and the tail moment. The wing moment is a function of the change in wing lift multiplitd by arm 'y'. The lenght of both arms is dependent upon CG position. If the CG is considered in a more forward position, the tail arm is larger and the wing arm is smaller. A more forward CG position increases static longitudinal stability.
If the nose down (negative) tail moment is greater than the nose up (positive) wing moment, the aircraft will have static longitudinal stability."
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