Acrobat Landing: Can It Be Done?

[Himal kharel]

Suppose an acrobat is propelled upward in trampoline by 0 angular momentum i.e. perpendicular to trampoline. if by anyhow maneuvering his body can he land trampoline on this back?

 

[rcgldr]

The acrobat can't generate any net angualr momentum, but an acrobat could move his body a small amount by swinging his arms around in one direction, which would move his body in the other direction. This would be a very small effect. Acrobats generate angular momentum while in contact with the trampoline, during the upward part of the bounce. This angular momentum will be forwards or backwards and that angular momentum can also be used to generate twisting movements with body movements that offset the primary axis of rotation.

 

[Delta Kilo]

The acrobat can't generate any net angualr momentum, but an acrobat could move his body a small amount by swinging his arms around in one direction, which would move his body in the other direction. This would be a very small effect.

Small or not, this is exactly what stuntmen do when they play bad guys falling off buildings. Sometimes you can see it in the movies, especially in cheap ones: the guy who's just been kicked, stabbed and shot, falls off the roof and suddenly starts swinging his arms around like mad. He's doing it to avoid landing upside-down and breaking his neck.

 

[rcgldr]

Small or not, this is exactly what stuntmen do when they play bad guys falling off buildings. Sometimes you can see it in the movies, especially in cheap ones: the guy who's just been kicked, stabbed and shot, falls off the roof and suddenly starts swinging his arms around like mad. He's doing it to avoid landing upside-down and breaking his neck.

Normally the flailing of the arms is just for show. The intial fall motion determine the amount of angular momentum, and after that, the stunt person can pike or tuck to speed things up, or extend his arms to slow things down a bit. Stuntmen have enough experience to initiate the fall correctly, rather than trying to compensate for a mistake on the way down.

 

[A.T.]

Normally the flailing of the arms is just for show.

Probably mostly so. It is also sometimes said that cats use tail rotation in free fall in order to land on their feet. While it might be a factor, the contribution would be too small to turn the cat around 180° within a few feet falling distance.

The actual mechanism used by the cat to turn around while preserving angular momentum involves rotating the front & back body around non-parallel axes. An acrobat could potentially use the same technique:
http://pentagono.uniandes.edu.co/~j...inicursoJK-Uniandes/robotic examples/kane.pdf

 

[Delta Kilo]

I was referring to something like this:
This guy jumps into the water which is a lot less forgiving than airbags. See how he purposely rotates his arms to prevent landing on his back.

 

[A.T.]

I was referring to something like this:
This guy jumps into the water which is a lot less forgiving than airbags. See how he purposely rotates his arms to prevent landing on his back.

That is of course a pretty long fall, and he is merely stabilizing his orientation by making minimal adjustments to his angular velocity. A trampoline jumper would have use something similar to the falling cat, in order to turn 90° with zero net angular momentum, within just a few meters.

 

[rcgldr]

A trampoline jumper would have use something similar to the falling cat, in order to turn 90° with zero net angular momentum, within just a few meters.

A falling cat twists up to 180° by circling the front and rear halves of it's body while bent at the middle, it doesn't significantly change it's end over end rate of rotation. High divers normally do a double flip using the amount of pike to control the rate of rotation, although the woman does a back gainer from 120 feet in this video:

http://www.youtube.com/watch?v=EPS1q3QBBDo&feature=related

If you want to see some wall and trampoline stuff, do a youtube search for Oli Lemieux, most of them have bad music though.

 

[A.T.]

A falling cat twists up to 180° by circling the front and rear halves of it's body while bent at the middle, it doesn't significantly change it's end over end rate of rotation.

Not sure what you mean by "end over end rate of rotation" but here is a nice video to demonstrate what I mean:

https://www.youtube.com/watch?v=t84a0L76ju4

From this perspective:
- Both body halves rotate CCW around two non parallel axes.
- The plane in which the two axes lie counter-rotates CW around a horizontal axis trough the center of mass.

The second rotation is hard to see, but note how the "bend" (intersection of the two axes) moves in relation of the COM: below -> left -> above

 

[rcgldr]

Not sure what you mean by "end over end rate of rotation" but here is a nice video to demonstrate what I mean.

By "end over end" I mean flipping like a front or back flip as opposed to twisting which is what the cat does in the video. Angular inertia for twisting is much less than for flipping (end over end). A person whirling arms won't generate a lot of flipping motion, but can generate some twisting motion. By bending at the waste and trying to whirl the legs and upper body, similar to the cat's movement, a person can twist while in mid air more effectively than trying to whirl arms.

Getting back on topic, a stuntman uses a controlled fall that initiates some amount of angular rotation, rather than dropping straight down and trying windmill arms to "flip" 90° or so to end up landing on their side or back.

 

[A.T.]

By "end over end" I mean flipping like a front or back flip as opposed to twisting which is what the cat does in the video. Angular inertia for twisting is much less than for flipping (end over end).

What you say is that: The cat's moment of inertia around it's long body axis is less then around it's lateral axis.

That is true, but misses the actual awesomeness of this cat stunt: The cat starts falling with zero angular momentum. So no matter how low the moment of inertia around it's long axis is, it cannot simply start rotating around it as a whole. To keep zero total angular momentum during the entire fall, the cat has to rotate it's halves around two angled axes, which themselves are counter rotating around a horizontal axis trough the COM.

I also think the term "twisting" is a bit misleading if it means "torsion". So just to clarify: The cat doesn't (have to) twist the body halves against each other (rotate them in opposite directions around the long axis). In the video they both rotate CCW (but with some delay, hence the torsion impression).