# Short-term or pitch (subsidence) mode

Instead of the SPPO, there are usually two aperiodic motions, one with a short time constant and one with a longer time constant, the former being masked by the latter. Just as the dynamic stability of the helicopter is directly related to its long-term modes the control response is characterized by the short-term modes. Whenever a pilot makes a control input the helicopter is excited dynamically and if left to its own devices will exhibit all the modes discussed above. However when the pilot wishes to manoeuvre the aircraft he will only be concerned with the response in the short term and therefore the short-term dynamic modes along with the control derivatives can be used to predict the handling qualities of the helicopter. In the matrix equations this means that for pitch subsidence everything but the third row and column can be ignored, so the equations of motion presented earlier reduce to:

q = Mq. q + MBl Bl + Mec.0c

With no collective input this becomes: q = Mq. q + MBl. Bl

q MBl

B = (s – Mq)

which describes a classic first-order type of response. Thus the time constant of the pitch subsidence mode is dependent solely on the value of Mq, the pitch damping derivative.