A while back I did a couple of posts about Danny Macaskill, a highly talented cyclist who can do things with a bike that I can’t even imagine doing. I recently saw a post on Rhett Allain’s Dot Physics about the Physics of the Ninja Warrior Salmon Ladder and it reminded me of Danny Macaskill (who is the bicycle equivalent of a ninja warrior). In particular, the way the ninja climbing the salmon ladder seem to be pulling themselves up by their bootstraps, similar to how Danny Macaskill can make a bike jump in the air. Take a look at the video.
It almost looks like the ninja (I gotta admit I feel kinda silly calling them a “ninja” but I’m willing to give them the benefit of the doubt; never piss off a ninja) is continuing to pull himself up the whole time, but it turns out he is alternating between pulling himself up and falling down. Let me show you what I mean with a few free-body diagrams.
When the ladder rung is firmly seated in the notch, the ninja pulls himself up. There is a net upward force on the ninja during this part of the climb, but the rung itself is stationary.
Once the ninja has pulled themselves up so they have a slight upward velocity, they can take their weight off of the bar and push up on it. But as soon as they take their weight off of the bar the net force on the ninja is downwards so they start falling.
So, even though it looks like the ninja is continually moving up, they are actually falling while the bar is in the air. Here is a screenshot from Tracker showing the position of the bar and the center-of-mass of the ninja
The graph for the rung at the top left shows the bar moving up and then dropping back down into the notch. The bottom graph represents the ninja, and shows a slight upwards velocity at the start (graph is moving up slightly) following by the ninja falling and then slowing themselves down once the bar has caught in the notch.
If you go back and look at the Bootstrap post about Danny Macaskill, you can see the way to get a bike to leap into the air is using the same physics as is used to climb the salmon ladder. Does anybody know why it is called a salmon ladder? Last time I checked salmon don’t climb this way.