The figure of 1.32 we have been talking about is derived exactly from the mathematics of the drag curves, as has been shown above. It is actually the fourth root of 3, rounded up a bit. HOWEVER, this is true for aircraft only if the drag co-efficients used in the formulae are constant over the range of speed we are talking about.
So long as the co-efficients are constant then for all cases of Cdp and Cdi the 1.32 relationship will apply. That is for all values of Cdp and Cdi from zero to infinity and any combination of these.
There are two well known cases where the co-efficients are not constant, and 1.32 no longer applies. These are at the rise in Cdp when wave drag comes in and in the "laminar bucket", an area around best L/D for some airfoils where wing laminar flow gives a local improvement in Cl/Cd
When the derived curves are drawn a tall and narrow total drag curve shows a poor L/D ratio and a fat low curve a good L/D ratio. In both cases, so long as the co-eficients are constants the tangent from the origin will meet the total drag curve at 1.316 times Vmd
Dick W