Sunday, 10 May 2015

How Cats Always Land on their Feet

My boyfriend recently showed me a gif that he saw on Reddit that startled me initially, as it involved a cat falling from a high building. You'd think the cat would die, but it didn't. It turned itself feet first onto the ground, and scurried away.

You can see the gif here: https://imgur.com/gallery/iRJmCUt (Scary, isn't it?)

This blog post will detail the findings my boyfriend and I uncovered whilst researching about how cats always land feet first, and how cats can survive falls from high buildings. Resources that helped aid in this post's information is linked or mentioned throughout this post.

Why don't cats go SPLAT when they fall from a really high building?

Everyone who took physics knows that the reason why we all fall and come back down to earth is because of gravity. That is,

F = mg

The only force trying to resist this force on earth would be air resistance,

where,  
Cd  = coefficient of drag (around 0.2)
  ρ  = density of air
  A  = area of object
  v  = velocity of object

Now, you probably know that terminal velocity is basically the maximum velocity a body experiences after X seconds of free falling. This terminal velocity remains the same, or to put it in another way, is constant after X seconds due to the air resistance force and the gravitational force cancelling each other out so that the net F = 0.



During free fall, a cat is usually splaying its body out like a flying squirrel.


When calculating the terminal velocity of the cat, we see that because the cat is splaying its body out, the "projected area" is bigger, so the overall terminal velocity of the cat is smaller. When you actually do experiments, you discover that the terminal velocity of an average cat is calculated to be around 60 mph. Compare that to 120 mph of an average skydiver.

Because of this, cats will generally not die from the force that occurs when landing on the ground. They will not fall to death like a human likely would.

How does a cat always land feet first? (An Explanation of the 'Cat Righting Reflex')

First I would like to explain what angular momentum is, as this is what we need to explain first. Angular momentum is how much an object is rotating, but it depends on the moment of inertia and the angular velocity of the body. It defined in the picture below:


I is the moment of inertia (you can simplify it as the quantity of area away from the axis of rotation), and w is the angular velocity. This picture also shows that angular momentum is the reason why when a ballerina's arms go in, she twirls faster - because angular momentum is preserved. In case (a), I is big because the area around her is big, since her arms are spread out. In the second case, because I is smaller now and L should be constant, w must increase, so she spins faster.

So, now, we should start explaining how a cat actually falls on their feet.

Before photography came into existence (so we could capture frame by frame of how exactly a cat's body orientates itself feet-first to the ground), we thought that a cat flipping feet first was some kind of paradox. This is because it seemed to violate the law of conservation of angular momentum.

This is described in the following youtube video: https://www.youtube.com/watch?t=50&v=1wfcnEBMRqk

A screenshot is below:


As the above screenshot of the video described, it seems that every cat in the world is violating the law of conservation of angular momentum, as angular momentum is always conserved unless an outside force acts upon it.

The only two forces that act on the cat are gravity and air resistance.

Gravity cannot really add or remove angular momentum of the cat, as gravity acts on the center of mass on the cat, which is "in line" with the cat's axis of rotation, so therefore, gravity cannot affect the conservation of the cat's angular momentum. The only other force would be air resistance, but this isn't the correct answer either.

After photographing carefully what cats do when freefalling, we get realize that cats do in fact not violate this law, and do not use air resistance to help conserve angular momentum. But how do they conserve angular momentum, you may ask?

Please click the following gif, as it will explain to you how angular momentum is preserved when a cat is rotating to land feet-first: http://upload.wikimedia.org/wikipedia/commons/7/78/Cat_fall_150x300_6fps.gif

A screen shot is here:


After looking at the gif, you can see now how angular momentum is actually conserved! Cats have a very flexible back, so they are able to do these weird rotations of their bodies to orientate themselves upright!

Other fun facts about how cats have 9 lives

How can the cat from the first link I shared in this post survive such a tall height? Read the following from Emily Russell's presentation on "The Physics of Cats" (2007)
A study was released in the Journal of the American Veterinary Medical Association in 1987 of 132 cats which had fallen from high-rise windows in New York. The average fall height was 5.5 stories. 90% of the cats survived. Above a fall height of 7 stories (around 70 feet), the number of injuries the cat sustained actually decreasedThis is because once it has turned over and reach terminal velocity, the cat relaxes its muscles, so that its landing is softer.
Neat, eh? TIL (Today I learned) how cats fall safely to the ground!

Friday, 8 May 2015

My Recent Discoveries and Ramblings on Tetraethyllead Gas & Alexander Gettler's Forewarnings

I personally am an avid fan of documentaries, watching them since I could understand English when I first immigrated to Canada. Recently though, I feel like it's getting harder and harder to find the specific kinds of documentaries that I like. I would say a lot of the documentaries I encounter are just interviews of people about various political and cultural events. However, many of the people are ordinary average joes, that give their biased opinions on such matters. I like the type of documentaries that tell me facts, like science or history documentaries, where they give me a story about how a man discovered vaccination, or how the D-Day was planned.

This brings me to talk about a delightful documentary I recently watched, that I was initially going to skip: "The Poisoner's Handbook: The Standards for the Rest of America". It chronicles the lives of two influential scientists, Alexander Gettler and Charles Norris, and their constant fight to legitimize forensic science, even when no one believed them or when people had a conflict of interests in a couple of murders they were trying to solve using facts, not stupidity. Gettler was a genius in chemistry, and Norris studied medicine at Columbia. They both worked in New York as the first "forensic science" office, if you could call it that. Basically, back in those times (early 1900s), many people were not familiar with the legitimacy of forensic science, so Gettler and Norris had a lot of opposition, while all they were trying to do was to make science a significant voice in the argument over whether a person was innocent or guilty of a certain crime.

Some of the bodies they had to investigate had evidence of serious chronic lead poisoning. These people had worked in a factory for "ethyl gas", the car companies (e.g. GM) called it. In actuality, however, this was a very euphemistic name, since this gas had lead in it - a kind of lead that the human body can absorb easily and can make a person succumb to death by lead poisoning. The full name of this gas should properly be called tetraethyllead gas.

3D Ball and Stick Model of TEL Compound

So, while the car companies wanted to use this new "ethyl gas" as it was very profitable (tetraethyllead was an anti-knock additive), and while they were telling the public that it was "safe", after Gettler (the toxicologist) found out that all of the factory workers who died had lead poisoning, he publicly denounced ethyl gas and wanted it to be banned. 

The documentary then proceeds to talk about how through a bit of corruption, the car companies managed to hire "industry scientists" that deemed ethyl gas was safe as long as factory workers had gloves and other safety equipment on, and that the gas itself will not harm the public as millions of cars emit this gas, "ethyl gas" went unbanned. By the end of the documentary, I was still a bit confused, as the documentary did not explain what happened to "ethyl gas". I mean, was it banned? Did lots of people get poisoned from inhaling car smoke all the time after some decades? What really happened?

Well, I did a quick Google search, and found a very startling result: tetraethyllead gas was only banned in most industrialized countries in 2000. It wasn't even banned before I was born! That honestly really startles me. I mean, lead has been well known as a lethal poison, for thousands of years! How did car companies get away with this?

Although I haven't read more into the following yet, I am particularly interested and concerned about just how much lead (exactly) has accumulated in the environment since the 1920s (when ethyl gas was first widely used).

I then came across the name Derek Bryce-Smith. After reading about him, I noticed many striking similarities between his attempts to righteously ban ethyl gas, just like Gettler back in the early 1900s. Bryce-Smith also was ostracized and criticized. Car companies didn't like what he had to say about the dangers of their gas. Both he and Gettler understood social responsibilities however, and confronted the "dogma and financial interests" of the big car companies.

Here's a quote I'd like to share, from the Telegraph's article about Bryce-Smith:

As a result [of tetraethyllead gas], countless millions of children suffered damage to their brains. By the time leaded fuel was phased out in Britain, at least one child in 20 – by the government’s own figures – had been exposed at levels known to diminish intelligence: in India, the proportion was one in two. No one will ever know what potential was lost worldwide in consequence, or how many children developed severe learning difficulties. But raised lead levels have also been associated with ADHD, accelerated ageing, and even a greater tendency to criminal behaviour.
This is frightening. I never even knew all of this happened. I'm also disappointed that the general public had no idea about this either. I hope more people know about the story of Alexander Gettler (and his work to make forensic science legitimate in criminal cases), and of course, Derek Bryce-Smith, who campaigned against lead gas more than half a century ago, and died in 2011. Fortunately by the time of his death, only a few countries still used this lead-laden gas.

----------------

Resources:
http://en.wikipedia.org/wiki/Tetraethyllead#Phaseout_and_ban (where I found out TEL wasn't banned until 2000 in most industrialized countries, and discovered the social good that Derek Bryce-Smith set out, where he tried to ban ethyl gas.)

http://www.theguardian.com/theguardian/2011/jul/19/derek-bryce-smith-obituary (The Guardian's obituary of Derek Bryce-Smith)

http://www.telegraph.co.uk/news/earth/environment/8671336/Pollution-triumph-of-the-inconvenient-truth.html (Another article about Derek Bryce-Smith. Has a lot more detail than the Guardian's.)