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Why are most canard fighter aircraft unstable? A stable design would let the canard provide lift. My guesses are:

  1. Increase pitch rate
  2. Decrease stability while supersonic (supersonic, the aircraft are stable)
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You want your control surface to create only little lift, so it has enough margin for maneuvering. This confirms your first guess.

Your second guess is also correct: Flying supersonically shifts the center of pressure back and increases stability. If the aircraft is unstable subsonically, it will suffer far lower trim losses supersonically.

Please read all about unstable designs in this answer. For conventional, stable configurations it makes most sense to put the control and damping surfaces at the back, and a canard is the better choice for unstable, highly maneuverable aircraft.

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Most modern fighter aircraft designs -not just canard-wing configurations- are designed to be (slightly) aerodynamically unstable. Stability is ensured through the action of the automatic control system, which issues commands to the control surfaces that stabilize the aircraft.

The unstable aerodynamic design together with the digital control system makes the aircraft more maneuverable.

A safety feature with the canard providing a downforce for trim, is that the wing stalls before the canard in high angle of attack situations, which ensures that the aircraft still has maneuverability post-stall.

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A canard surface operates in 'clean' air, not 'shadowed' by the wing, so maneuverability has priority over lift.

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