Why is the use of tail-down force so prevalent in aircraft design? Why not use canards to avoid induced drag?
If it were so simple ...
To achieve natural longitudinal stability (the aircraft stays at the trimmed speed, even after disturbances like gusts), the rear lifting surfaces need to have a lower lift per area than the forward surfaces. Why? In a gust, the aircraft's angle of attack changes on all surfaces nearly at the same time. By having less lift per area, the relative lift increase due to an increase in angle of attack is higher for the rear surfaces, so now they gain relatively more lift increase than the forward surfaces. This creates an imbalance which lifts the tail up, until the old angle of attack (and, consequently, the old speed) has been reached again.
A negative tail loading is a sign of high stability. This creates more drag, but allows the pilot to take the hands off the stick, to read his maps, check something or have a cup of tea. But its effect on induced drag can actually be helpful. You might be surprised, so please bear with me!
What is induced drag, anyway? It is the consequence of creating lift over a limited span. The wing creates lift by deflecting air downwards. This happens gradually over the wing's chord, and creates a reaction force orthogonally to the local speed of air. This means the reaction force is pointing up- and slightly backwards. This backwards component is induced drag! The lengthwise distribution of the surfaces which do the downward deflection is of little importance (for a very technical explanation: See here, where they talk about the Treffz plane): If you have a highly loaded canard wing, its downwash will hit the wing eventually, creating a lot of backward-tilted lift there. The canard by itself will not cause so much induced drag, but will mess up the airflow over the wing. Behind the airplane it does not matter if you fly a canard or a conventional configuration, what matters is over how much span you distribute lift creation (for a constant amount of lift at a given speed).
You probably know that an elliptic distribution of circulation over wingspan produces the smallest induced drag. Now imagine that your wing has more a triangular than an elliptic distribution. The downward lift on the tail will reduce this hump of lift in the middle, making the distribution closer to that ideal elliptic distribution behind the whole airplane. The induced drag of the whole airplane is lowered by the tail!
Another explanation: Since the wing creates a strong downwash at its center, the tail flies in an airflow which points slightly downwards. Negative lift there (being approximately orthogonal to local airflow) will actually point slightly forward, so your negatively loaded tail produces a small amount of thrust!
Black: Total force, Blue: Lift, Red: Drag
And if you think that a triangular lift distribution is unusual, please read this NACA report by R. T. Jones. It takes wing weight into account, and this changes the picture how the lift distribution for minimum induced drag should look.