The longitudinal dynamics of the F-4C can be described with the following transfer function
$$\frac{\theta(s)}{\delta_e(s)}=\frac{32.2(s+.0162)(s+1.46)}{(s-.0378)(s+.0516)(s+1.74\pm4.08j)}$$
This has a well-damped 2nd-order short-period response. The Phugoid mode has 2 real parts, with one unstable tuck mode.
To get the root locus plot via Matlab we must convert the complex values into real values
The short-period roots are stable and well damped for low to moderate gain values. High pilot gain could still drive the roots to be unstable. With only springs, there would be a residual stick oscillation in the open-loop response.
Slight Negative damping would be controllable, but if the gain required was too high, PIO susceptibility would increase. This might happen during a Bellows failure. If the bellows failed, the system roots would be unstable and the pilot would be unable to stabilize it without driving the short-period unstable. A decreased damping would decrease the gain required to make the roots unstable, therefore increasing the PIO susceptibility.
The worst case, with no stick feel system, would require the pilot to pay attention to both the pitch attitude, as well as the stick position. While possible, this will require all of the pilot’s attention. If the pilot were to focus only on pitch attitude, they would drive the system unstable.
With a bobweight we get the following transfer function.
Which has the root locus response
- airforcetestpilotschooledwardsafbcaVolumeIIFlying1988[^1]