In the early Action and Superman volumes, Superman is described as "Leaping over skyscrapers", and similar such terms. He is also portrayed as running from place to place, which begs the question, if you can fly, why run? Apparently he could leap over skyscrapers, but long distance air travel was something else again. The old TV show also began with "Able to leap tall buildings in a single bound".
Seems from all this that Superman didn't really "fly" - i.e. he had no scheme to give him lift, or any sort of propulsion system - he just made very long, strong (strong enough to reach escape velocity from the earth and much larger worlds as well), high jumps, and was able to navigate using aerodynamic principles - similar to a flying squirrel or fish, as opposed to a bird or bat.
Even though later on we find that he did travel long distances by air, couldn't we explain all of Superman's maneuvers as extraordinary powerful and carefully calculated leaps and bounces?
The proof would be from situations where he demonstrates acceleration without a boost from some external source of energy: If it's all leaping, even if it's incredibly powerful, he would be constantly decelerating to some extent.
Is there any proof that he could actually fly using some sort of propulsion system, like an airplane or a bird, and not just engage in mighty, calculated leaps? Would constraining Superman's ability to jump (hard to imagine how...) result in him not being able to "fly"?
This question is definitely not a duplicate. I am not asking how he flies, I am asking if he actually flies. See accepted answer, from before this question was mistakenly closed.