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While I was watching a cockpit video of an A330 landing in which the pilot was frenetically moving its sidestick, I wander what was the reaction time of this flight by wire system. Indeed, the time for transmiting the signal from the sidestick to flight computer, the time for computer to interpret all its inputs (pilot's input, probes,...) and to decide to act on flight control surfaces, the aircraft's reaction is not instantaneous.

Then, I realize that whatever the transmission system, there are delay between pilot's input and air control surfaces movement (material's elasticity, time for hydraulic fluid to transmit pressure, other mechanism I can't imagine).

Thus my question is: is there a maximal delay between pilot's input and flight control surface deflection to certify an aircraft?

If needed, for the FBW system, a direct law can be considered (no complex computation as flight control surface movement is proportional to input)

If needed, the question can be restricted to airliners flying under FAA and EASA jurisdictions.

EDIT: given the first feedback (comments, edits, answer), I want to highlight this question is not restricted to flight-by-wire (transmitting pilot's input through mechanical links may also induce delay)

Excessive phase lag is a direct contributor to Type I Pilot-Induced Oscillation (PIO). Phase lag comes from:

• Rigid body dynamics of the aircraft (e.g. delay between elevator surface and pitch rate response)


• Actuators (finite acceleration time between input and desired surface angle)


• Structural compliance (e.g. cable friction)


• Transport delay in signals


• Finite computational bandwidth (e.g. loop closure bandwidth)

From NASA Report 4683, PIO susceptibility can be expressed assuming the pilot is compensatory; that is, in a full blown PIO, the pilot input and the aircraft response would be exactly in phase, except for a constant time delay (across frequencies). This model is expressed as:

$$G(s)=fracKse^-tau_e s$$

where $tau_e$ is the effective time delay.

From its research, it found that an effective time delay larger than 0.3 sec leads to PIO issues. Therefore, I would say that 0.3 sec is the upper bound of the overall time delay of the total aircraft (in another word, its phase rate), end to end.

There is quite some experience in this in Level D simulators, which have computer generated responses that must match those of the original aircraft, within tight tolerances.

A couple of decades ago, the gold standard for Unix real time host computers was 30 Hz. So 30 times per second, all of the following was computed:

• Surface deflection from stick input, including cable stretch, oil flow simulation etc.


• Aerodynamic hinge moments on the surface.


• Hydraulic hinge moments exerted by the actuators.


• Aerodynamic forces amd moments on the aeroplane.


• Inertial response of the aeroplane.


• Visual system response.


• Motion system response.


• All other system states and responses.

With an update rate of 30 Hz the standard was deemed acceptable for Level D zero flight time training, which implies a time delay of 1 frame = 0.0333 sec. So we know that this is fast enough: frequency rate 30 Hz, time delay 0.0333 sec.

As an aside, for present day computers this iteration rate is something to smile at, the code that ran @ 30Hz on a state of the art realtime unix machine runs @ 3000Hz on a Macbook Pro now.

This is a classic problem in control system theory. The condition to be avoided at all costs is the case where the pilot's control actions get out of phase with the movements of the plane, so the sidestick-action makes the oscillations worse instead of damping them out.

The two ways that could happen are 1) if there are significant processing time delays in the control system connected to the sidestick and 2) if there are significant delays in the pilot's reactions.

As pointed out above, the control system time lags are tiny compared to the time constants of the plane's responses to aileron movement, etc. and the significant time lag in the overall system consisting of plane + pilot + computer control system is in the PILOT, not the control system.

This gives rise to something called PID or pilot-induced oscillation, where the response time lag of the pilot pushes the whole system into divergent oscillation- as for example in the case of a pilot porpoising a plane down the runway after bouncing off the runway on his or her initial touchdown.

I do not know if computerized flight control systems contain subroutines that prevent PID but perhaps Peter Kaempf knows!