Im trying to understand why does L/D MAX, (the top of the polar curve that computes CL & CD ratio for any airfoil) is also the lowest point of the total drag curve. Im guessing the reason is that CD curve is not just about induced drag as I thought.
Airfoil drag is "parasitic" (or better: everything but induced) drag.
It consists of shear drag and pressure drag, the latter mostly from local flow separation. Both are only present when viscous flow is assumed. Airfoil drag is for the wing section without taking tip effects into account, presuming an infinitely wide wing. This kind of theoretical wing has no induced drag (d'Alembert's paradox).
L/D max is the point on the polar curve where the angle to the origin of the coordinate system is steepest. This is not the point of the lowest drag coefficient! Maybe you mean the point of lowest drag for a full airplane – but that is another story, with more than just the airfoil polar. Now induced drag is part of overall drag and due to its inverse relationship with speed, a distinct minimum can be found when lift is held constant.
Drag polar of the NACA 23012 airfoil (picture source, colored comments own work)
I'm trying to understand why does L/D MAX, (the top of the polar curve that computes CL & CD ratio for any airfoil) is also the lowest point of the total drag curve.
The graph in another answer shows how to find the max ratio of Cl / Cd, which is arithmetically equal to the max ratio of L/D.
The concept of minimum Drag (as opposed to minimum Drag coefficient) can be confusing. If we are talking about a Cl vs Cd graph obtained in a wind tunnel with constant airspeed, whether for an airfoil or for a whole airplane, we could say that Drag is minimized when Cd is minimized. This is obviously not the point where the Cl / Cd ratio is maximized.
But the situation is completely different in actual flight, where Lift is constrained to be equal to Weight (or in the case of a steady-state glide, constrained to be equal to Weight * cos ((arctan (D/L))), which is nearly equal to Weight), and the airspeed varies accordingly. In this case, we can show that Drag is minimized when the L/D (and Cl / Cd ) ratio is maximized, even though this is not the point where the Drag coefficient is smallest.
In the context of actual flight, we need to talk about the L/D or Cl / Cd ratio of the whole aircraft. Therefore there's really no context in which it makes sense to say that Drag is minimized when the Cl / Cd ratio of the airfoil is maximized.
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