# Short-term or the roll (subsidence) mode

In most aircraft, both fixed and rotary wing, the Dutch roll tends to have a reasonably long period and the spiral mode a long time constant. Damping in roll tends to occur rapidly with time constants of the order of 0.2 second. Hence the roll subsidence mode can be decoupled from the other motions. In the matrix equations this means that for roll subsidence everything but the second row and column can be ignored, so the equations of motion presented earlier reduce to:

P = Lp. p + La. A, + L0tr. 6tr With no pedal input this becomes:

P = Lp. p + La. A,

p = la

A, (s – Lp)

which describes a classic first order type of response. Thus the time constant of the roll subsidence mode is dependent solely on the value of Lp, the roll damping derivative. As forward speed increases the value of Lp will change. Typically the motion will remain heavily damped but the time constant will increase from that in the hover. It should be noted that a similar relationship can be generated for yaw control in the hover:

r = Nr. r + N0tr. 6tr

r = Netr

etT = (S—N)

4.11.4 Effect of aero-derivatives on dynamic stability modes

The lateral/directional dynamic response of a helicopter is governed by the values of the aerodynamic and control derivatives that make up the characteristic equation and stability matrices. As was the case with the longitudinal motion most of the important derivatives are speed dependent so it is instructive to examine the variation in the dynamic modes with airspeed as well as determining the effect of modifying single derivative values.