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What are the forces felt on the flight yoke/stick based on the deflection of control surfaces and the aerodynamic forces acting on the control surfaces with respect to different aircraft attitudes?

For example: At low airspeed, the controls usually feel soft and sluggish, and the airplane responds slowly to control applications. At high speed, the controls feel firm and the response is more rapid.

Are there any equations that represent the same and how is the force exerted on the flight control yoke calculated?

My question is based on the control loading system of professional grade flight simulators for general aviation aircraft. I want to design a force feedback mechanism for a flight simulator to enhance realism.

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  • $\begingroup$ This is very much application specific. For example in a 177 the elevator "feels" a lot different than a 172 at just about any speed. This is due to the design of the stabilator vs elevator. I don't think there is a generic "Xft-lbs per knot" if that is what you are looking for. Professional grade simulators only simulate one kind of aircraft, so they can base it off of specific aerodynamics. $\endgroup$
    – Ron Beyer
    Jan 8 '20 at 13:21
  • $\begingroup$ Lets say I simulate this for only light category aircraft. Can I then generalize the aerodynamics then? $\endgroup$ Jan 8 '20 at 14:48
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I've worked with control loading systems quite a bit. What you describe is a reversible system, where the flight crew feels the aerodynamic forces acting on the primary control surfaces (elevator, ailerons, rudder).

From old paper format uni book on stability & control by prof. Gerlach

  1. In the aircraft, the pilot pulls on the flying control, which is connected via a steel cable to the control surface, which then deflects. Airflow blows back on the deflected surface, with a force proportional to deflection of the surface. In the picture above $H_e$ is the hinge moment on the elevator, the aerodynamic part of which is $$H_{ea} = C_{he} \cdot ½ \cdot \rho \cdot {V_h}^2 \cdot S_e \cdot \bar{c_e}$$ with $C_{he}$ = moment coefficient, $\rho$ = air density, $V_h$ = airspeed at horizontal tail, $S_e$ = elevator area, $\bar{c_e}$ = mean aerodynamic chord of elevator.

    The hinge moment coefficient is a function of trim tab deflection and angle of attack, and is measured in flight tests. Figure below shows $C_{he}$ for the Fokker F27. same as above

    On ground, at airspeed zero, $H_{ea}$ is zero but there is contribution of friction, bob weight and down spring.

Same as above

  1. In the simulator, the same flight control is installed as in the aeroplane, but now is attached to an active actuator that is programmed to push back at the stick with the same force that would be experienced in the simulated flight state in the aeroplane. The actuator features an inner (control) loop and an outer (force feedback) loop.

Force vs. position and position vs. time measurements are taken from flight measurements, which must be tightly reproduced in the simulator in order for the sim to be certified. Reversible controls of small, simple aeroplanes are much harder to simulate than the irreversible, hydraulically actuated flight controls of larger planes, since these do not change as a function of flight state.

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  • $\begingroup$ Have fun simulating friction! $\endgroup$
    – JZYL
    Jan 8 '20 at 14:23
  • $\begingroup$ First of all, thank you for such a beautiful explanation. I understand the concept of reversible flight controls. if you could also guide me as to how I familiarize myself with all such equations that exists and also how can I get access to the flight measurements part as well. $\endgroup$ Jan 8 '20 at 15:07
  • $\begingroup$ @JZYL We’ve dome so for numerous aircraft, at both the stick position and the surface position. Total simulated friction must match that of the measured aircraft, friction balance between fwd/aft appears during matching step responses and hydraulic system malfunctions. $\endgroup$
    – Koyovis
    Jan 8 '20 at 19:21
  • $\begingroup$ @DhruvBhatt Studying aerospace engineering helps with the equations. The flight measurements are Intellectual Property of the company that mounted the necessary transducers on the plane and carried out the measurements during the course of a couple of weeks, in case of reversible controls. Irreversible control forces can be measured on ground with a hydraulics chart attached, using a dedicated force measurement set. $\endgroup$
    – Koyovis
    Jan 8 '20 at 19:31
  • $\begingroup$ Can the flight measurements be extracted using a flight simulator software such as P3D or XPlane? $\endgroup$ Jan 9 '20 at 5:40

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