Suppose that you, say, have both engines wrecked at the top of the climb by features like ash, vultures or overheating the engines... and find yourself at 40 000 feet with no prospect of relighting and 170 tons of fuel with absolutely no use except to power the postcrash fire.
When and where would you rather dump it?
L/D depends only slightly on weight.
If it did not depend on weight at all then the distance you could glide would be independent on the weight. Jets at cruise altitude are decent gliders... Azores Glider covered 140 km, so if the engines had failed for other reasons, and the tanks had been full, the same distance would have been covered, only faster.
But it does depend on weight.
For one, Mach number depends on true air speed. If the best glide speed for a fully loaded, 340 t airplane at altitude were, say, 0,84 M then after dumping the fuel, at 170 t empty weight, the best glide would turn out to be just 0,6 M.
Actually, lowering M improves L/D, at least in subsonic range (Not sure how to pick best glide speed and weight at the range 1...1,5 M. If you have 90 tons of fuel you do not want powering post-crash fire, would you start dumping right away at FL600 and M2,0, or after you have successfully gone to FL300 and M0,9, or at the end of the trip below FL100?).
Now, how about Reynolds number? At small Mach numbers, how does decreasing the weight and thus TAS affect L/D?
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