So the 7E7 gets the Comets´ nose section, and the nice rounded VC-10 horizontal stabilizer, guess I know where all the british aircraft designers went to after their compamies were shut down
Old Aero Guy,
as induced drag is nothing that can be calculated for one wing alone, you can´t state that the canard works with higher induced drag just because of it´s lower span. Aspect ratio is the important value, not span.
You can state in general, that for static stability reasons wing loading of the canard must alwys be higher as the wing loading of the main wing. This means your canard always operates at higher Cl than the main wing.
This implies, that the high lift devices on the canard must be able to allow higher Cl than on the main wing, so you probably end up with slats and tripple slotted flaps, making elevator design a real challenge. If you look at the Tu-144 canard, it has double slotted slats, and tripple slotted flaps, a maintenance nightmare !
Comming back to induced drag, as Cl is influencing the induced drag to the second, one can assume that therefor the induced drag should be very high. But looking at the theory in detail, you see that induced drag is coming from the difference in local angle of attack in comparison to the angle of attack at CG. Multiplying Cl with the differential angle gives you induced Cd, and differential angle is a function of Cl and aspect ratio. As the wing tip vortices induce a downdraft on the wing, differential angle is negative, therefor the induced force is in drag direction. For any multiple wing system, differential angle is not only influenced by the wing´s Cl, but also by the Cl of all other wings in the same flow field. And the main wing induces an updraft on the canard, resulting in a positive differential angle, or an induced force in thrust direction. Therefor the main wing produces ´induced thrust´ on the canard, making it indeed more efficient than it would be in free stream. On the other hand the canards downdraft produces enormous additional induced drag on the main wing inner part, but also produces ´induced thrust´ on the outer main wing. As for structural reasons the inner main wing normally carries more load as the outer, and the outer wing updraft induced by the canard is lower than the inner wing downdraft, overall influence on the main wing is negative.
Canard configuration aerodynamics is nothing easy (I´ve worked on it for about 7 years) and it is hard to give a general statement whether it is the ´better´ configuration. It all depends on the overall layout of the plane.