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My take is this - to maintain height he would have to switch sides on the upswing. If he's attached to the side of a building he would hit that building first before achieving any upswing.

(Unless of course the web is pulling him in. Possibly it contracts after it hits the buildings, or it reels in somedow)

You can turn forward momentum directly into upswing. So if he does switch at the low and high point of a swing, it might work. At low point he would shoot bit backwards, at high point bit forwards.

He doesn't need to maintain height, but energy.

The thing is, he doesnt swing in a straight line. he goes forward but also in a zig zag path, so the web would end up getting longer and longer each time.

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