For an aircraft in straight and level flight, lift-induced drag is the horizontal component of the force perpendicular to the wing chord. Positively cambered aerofoils generate lift starting at small negative angles of attack. So, could the horizontal component of the force generated by the wing point forward?
Can induced drag be negative?
Not for the full configuration, but for parts of it.
Induced drag is part of the reaction force when a stream of air is deflected. This reaction force is split into one component, called lift, orthogonal to the initial flow direction and one parallel, called drag.
Regardless of upward or downward lift, this definition will only result in positive drag. The lowest induced drag possible is zero when zero reaction force is created. Any nonzero reaction force creates positive drag.
For a thought experiment, let's split the deflection into tiny segments, each deflecting the stream a bit more. The initial amount of deflection creates almost no drag. The next bit, however, will already start with a small deflection and add its bit to it. Relative to the initial flow direction, here the flow has already an angle and the reaction force, being orthogonal to the local flow angle, will already have positive drag. The further down we now go, each section will add more drag. The drag component of the reaction force will never be negative.
The only situation where local induced drag is positive is when the local flow hits the lift-creating surface such that bending the flow brings it closer to its initial direction of flow. This is possible on the horizontal tail of a longitudinally very stable conventional design which creates a downforce and flies in the downwash of the wing.
For an aircraft in straight and level flight, lift-induced drag is the horizontal component of the force perpendicular to the wing chord.
No answer has yet explicitly pointed out, that this definition of "induced drag" is incorrect. It would be interesting to know where you encountered it. In horizontal flight, lift-induced drag is the horizontal component of the net force generated by the wing.
Not on fixed wing aircraft, but this does happen with rotor wing aircraft and it’s the principal driving mechanism for auto rotation. The section of a rotor blade known as the driven region has an effective force of lift tipped in the direction the rotor spins, driving the rotor blades by means of the air moving through the rotor disc.
Let's approach this from another direction.
Assume that it's possible to find a wing position that generates thrust rather than drag. Thrust or drag is a matter of airflow over the surface, to generate thrust we must have a net forward airflow. Put an indicated air speed sensor in front of the wing, what does it say? Negative.
Can a plane fly backwards? No, it would stall. Thus our initial premise must be wrong--it's impossible to have a net thrust from the airframe overall. (It is possible to have it for part of the airframe.)
The understanding of the relationship of drag and thrust in aircraft design is crucial to the development of efficient fuel saving aircraft.
From the aircraft reference, thrust is force towards the line of flight, drag is resistance (from the air) to this path. Because they are directly linearly opposed, thrust = - drag is mathematically correct, and can be derived from the steady state formula thrust + drag = 0.
Realizing this (simple) relationship can help explain other phenomena, such as "autorotation", extremely low net drag of airfoils, the benefits of slats, and (putting them all together), the design of soaring birds.
All gliders seek to find an updraft greater than their rate of descent. The broad, highly cambered wing of the eagle is exactly what airliners emulate when preparing to land, allowing them to slow to around 1/3 of their cruising speed.
But what of the slotted wingtips? Could they be using the updraft to provide thrust? This seems to work fairly well for auto rotating helicopters, so...
By changing relative wind away from flight path, drag on a part of the aircraft can produce thrust force (negative drag) to the line of flight. This is accomplished by producing a localized horizontal lift component to the line of flight.
Importantly, to preserve the strict definitions, drag opposes thrust, but localized lift from induced drag can produce a thrust force in the direction of flight.
Now, to get to the point of the question, the Blackbird, and sailing against the wind in general, the key is to extract mechanical energy from a drag force and use it to create a more efficient thrust force in the direction of travel.
Back to thrust = - drag
Let's add in:
thrust = -drag × conversion efficiency
The simplest model would be an anemometer. Mechanical energy is extracted by the difference in drag coefficient between the closed and open end of a cup. You could make a Blackbird using a giant anemometer, and it would roll in any direction when there was sufficient wind.
with the wind, faster than the wind
A bit more challenging. Now we can take the extracted energy and use it to turn a rotating airfoil, a propeller. Airfoils can generate many times more lift force per unit of drag.
So we turn to iceboats, which can easily sail faster than the wind by minimizing drag. Energy input from the wind is amplified by the sail airfoil, creating a thrust force that "runs away" until the total drag (from the entire craft) = thrust (steady state).
The Blackbird propulsion seems to be a form of "autorotation" (with the inner part of the prop blade absorbing drag energy and the outer part lifting).