Effect of the tail of the cat in the falling cat problem

To explain why a falling cat can turn by 180 degree without external torque and without violation of the conservation of angular momentum, one usually models the cat as two cylinders as in

http://en.wikipedia.org/wiki/Falling_cat_problem

This may explain the turn. However I often heard contrary to this that she can rotate her body simply because she rotates her tail very fast into the opposite direction (and essentially keeps the rest of the body rigid).

So, what effect does the tail have in reality? Is there any detailed model, which takes the tail rotation into account and calculates how large its effect is?

• Actually I know experimentally that a cat can do this quite effectively without her tail. Our littler cat taunts our bigger one by sneaking up on him (often when he's relieving himself), whacking him on the rump and then making a swift getaway by springing up and backwards very strongly and doing the flipover in air manouevre whilst she does so, so that she lands a few metres away, right way up but headed in the opposite direction, whereupon she sprints off. When she was two years old, she got hit by a car and ended up needing her tail removed. After she got better, she took up taunting .... Jun 20, 2014 at 6:57
• ... our bigger cat again, doing exactly the same trick and manouevre but without her tail. Her lack of tail does not noticeably hinder her ability to flip over and make her quick getaway! Moreover, she did this within a matter of days after recovering - i.e. she did not seem to need to train herself to compensate for her lack of tail. It kind of makes sense: although the tail has a high moment, it is very, very light. I suspect most of the relevant moment of inertia is in the powerful muscles of the hinder legs, well beneath the spine: these are quite amazingly big in our littler cat. Jun 20, 2014 at 7:00
• Dear Julia: here is another relevant video: theatlantic.com/technology/archive/2011/09/… Thomas Kane, one of the early researchers was actually trying to teach astronauts to do the same thing, and they seem to be almost as good at it as cats with a bit of practice! Also of relevance (at an elegant, but more difficult level) is people.ucsc.edu/~rmont/papers/cat.PDF . "Das Umdrehen der Fallenden Katze in der Luft" by Rademaker and ter Braak (1935) is an early experimental study: unfortunately I don't have a copy anymore. Jun 23, 2014 at 7:22