We all know that given a normal swing set we can pump our way to heights slightly above the horizontal bar to which our seat is attatched via the chains that hold said seat to said bar. We also know that this is easier for smaller swing sets than larger ones.

This is due to two reasons. First, one can only impart a fixed amount of energy for each pump (cycle). Second, the larger the swingset, the longer the arc, and the more air friction (drag) one encounters per cycle.

What I would like to know is how high can the average human pump a swing?

Assumptions:

1. Atmospheric conditions - sea level, standard day.

2. Average body weight - let's call it 150 lbs.

3. Maximum pump height would be to the height of the overhanging bar from which the chains are suspended.

4. The swinger would be seated, using the "head/torso back, feet/legs forward" method at the back limit of the arc, and the "head/torso forward, feet/legs back" method at the forward limit of the arc.

5. Assume that the strength/rapidity of transition between the two positions is immaterial, average body composition, weight distrubtion, etc.

If my theory is correct, it wouldn't matter whether one is Spiderman or Amelda Lewis - there is a physical limit as to the length of the chain (distance between human center body mass and the overhead bar) due to the energy gain from shifting weight due to pumping and atmospheric friction.

One more assumption - let's assume that Spiderman doesn't give a massive tug on his swinging line during the bottom third of his swing to impart more kinetic/potential energy at the start of his next swing. I will stipulate that one can probably swing higher using a Spiderman setup than a sit in place swing. I base this off experience involving a plain rope swing (thick rope with a monkeyfist knot at the bottom) that was affixed to a branch perhaps 20 to 30 feet off the ground, roughly twice as high as most swing sets. No matter how hard we pumped that, and later, the seated swing my Dad set up on the same tree limb, we could never escape the bottom 60 degrees of arc. In fact, most of the time it seemed like I was fighting wind rush (atmospheric drag).

Any takers?

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I am Mugs, of the Alien clan of Usa, Nordamerica, a Terran, of Sol.

Mine: "Perception isn't reality. It's merely an abstraction thereof, and quite often not a very good one at that."

Heinlein's: "Staying young requires the unceasing cultivation of the ability to unlearn old falsehoods." "Freedom begins when you tell Ms. Grundy to go fly a kite."