HOW DOES A CAT ALWAYS LAND ON ITS FEET ?
When a cat falls down from a certain height, its four paws are always
the parts of its body that touch the ground first. If being tossed up and
twisted in the air, the cat always manages to land on its feet. What
principals of dynamics does the cat employ to perform this trick? What
body parts of the cat get involved in doing this acrobatic performance?
When I was a kid, I owned a cat, and these questions had popped up
before, yet I'd never actually had an answer for them. This was a chance
for me to really spent time to look for the answers. And it was the
reason that compels me to choose this topic for the web project although I
knew ahead of time that I would encounter difficulty in finding enough
information. Besides, the answers for the above questions would not be
simple because the cat body is not a rigid body, but it's very flexible,
and every point on that body moves differently at every instant. This made
the problem more challenging for me.
Let's consider a cat at the beginning of its fall, when it's up side
down. Its four paws are pointing upward and its back is falling toward
the ground. At this very instant the only external force acting on this
body is gravity, which is in the vertical direction. What the cat needs
is an external force in other direction or a torque to turn its body
around, so its paws would point toward the ground. However, these force
and torque do not exist.
The cat then creates an internal moment by twisting its body muscles.
And just like a skater pulling in her arms at a spin in order to increase
the angular velocity of her body, the cat simultaneously pulls in its
front paws as it twists its body. According to the equation:
Int(M_c)dt = dH_c = d(I_c*w)
The net moment is constant, but the angular inertia (I) is reduced;
therefore, the angular velocity (w) increases. In this case, the front
angular inertia (I_front) of the cat is reduced, but the rear angular
inertia (I_rear) is not. And because its body is flexible, the angular
velocity of the front of the cat is higher that of its rear. At this
instant, the rear paws of the cat are still pointing toward the sky while
his front paws are rolling downward.
Because of gravity, the cat is also falling closer to the ground.
Instinctively, he reaches out his front paws again, getting ready to land.
As he does so, he increases I_front, and consequently reduces his front
angular velocity. When he reaches out his front paws, he also pulls in
his rear paws. Conversely, his (I_rear) decreases, and his rear angular
velocity increases. Therefore, his rear paws catch up with his front
paws. Now all four feet of the cat are pointing downward, and the cat is
ready to land.
Of course, the cat may experience a more complicated, twisting fall than
being presented, but through thousands of generations of practicing, the
cat can easily gain its orientation in the air and controls how much and
how fast he should twist his body and pull or extend his legs to achieve
the right angular velocities for his body.
There is also a myth saying that the tail of the cat plays an
important role in helping the cat landing upright. However, this is not
necessarily true because tailless cats can perform this trick perfectly
well, too. To the best of my knowledge, the tail helps the cat keep its
balance when jumping, running, and chasing preys. It acts as a counter
weight when the cat makes a sharp turn at high speed. The tail may
influence the landing in some way but not the deciding factor of the cat's
ability to land on its feet.
So far, humans have not been able to copy this ability of the cat. It
would be wonderful if we can create the landing gears for air crafts to
land like cats, or the landing gears for space crafts to safely land on
other planets where runways are not available.
Even though our technology is very advanced, we still have a lot to
learn from animals and their abilities. As I worked on this project, I
found out that things around us are not yet perfect, and they still need
to be improved. With thinking and imagination we can step closer to be
able to do things that the cats, the fish, or the birds can.
Because of the scarcity of information about this topic, I couldn't find
any reference. Most of what I knew came from consulting with Dr. Lipkin,
and observation. The hypothesis above about how a cat lands may not be
entirely correct. If you do know or find out more about this topic, I
would gladly like to learn from you.
HUY D. NGUYEN