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What was the discussion?
Different hull designs for different purposes. Flat bottomed boats for shallow water or stability for dorys in white water, rockers for riding waves, dual hulls for better efficiency and rising above the water, straight keels on Explorer canoes for better tracking on lakes, canoe rockers for white water, slicing bows........
Pros: There would be less friction on hard surfaces (think a sheet of flat ice) since there is less base material in contact with the snow. The skis would obviously track better on the flats where the surface was not perfectly smooth.
Cons: Turning the ski would be more difficult on anything but a perfectly smooth surface, which is why skis with one or more grooves in them (remember the Fischer President DHs?) are long gone. Well, except for the planks used in ski jumping.
I'm wondering why so many skis sold today do not have flat bottoms. I remember seeing one manufacturer claim that keeping their skis in the mold for a longer time while the resin cured was why they had a superior product, but I have no idea if the is true or if there is another reason. And if the bottoms are concave or convex, does that mean the entire ski has warped? If so, most skis sold today are warped.
Will the base flatten out on the snow from the skier's weight? If so, there would there be any friction advantage when the ski runs straight? When it is unweighted and turned, could the area under the runners (flat sections) get hung up in anything but a perfectly smooth and hard surface?
So is there an advantage to "purposely fabricate bases that are concave and two definite flat sections along the edges?" I don't think so because the skier's weight will flatten out too much of the ski, unlike the shape of a boat hull or canoe. And it is the canoe hulls that were used by certain Canadian tribes that are a perfect example of what makes the rocker ski work, but that is another story.
Actually, I think the friction would be about the same as the portions in contact would be more heavily weighted. I would also imagine that it would be hard, in practice, to keep everything even from ski to ski and side to side in terms of forces which might cause control issues as the more heavily weighted portions would have more drag. (assuming a skier running on "flat" bases on a smooth downhill). If this shape had an advantage in terms of friction, you would see it on WC speed skis where even tiny advantages make a difference.
If the skiers weight flattens the ski (and I am not sure it would), it is hard to imagine that it would be a smooth flattening over the whole length of the ski as the weighting shifts during the turn. I had a pair of old Atomic Beta Carvers that had some concave base shape develop over time and they could be somewhat erratic in performance.
Returning to the practical world, it is hard to see how the skis would be maintained over the long term. All of the grinding machines are designed for a flat base as far as I know. Might be a headache.