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Terminal Velocity

The following you may find a little "heavy!" I've tried to make it a little "lighter," I hope my explanation makes things clear. Anyway, read on, then you can get to the interesting part about the terminal velocity of a cat.

An object (or person or animal) that has nothing to support it when it is being attracted by gravity is in "free fall." The force of gravity exerted by the Planet Earth is termed as one gravity, 1G. This is 9.78 metres per second squared (but this is only really achieved in a vacuum - read on). You can also call this 9.78 metres per second per second.

That means that after two seconds in free fall an absent minded person jumping from a plane without a parachute will be falling at twice 9.78 metres per second. After three seconds he'll be falling at three times 9.78 metres per second. And so on, till he achieves strawberry jam status on returning to Earth's surface.

But fortunately for us, we live in an atmosphere. Apart from giving us something to breathe, this also limits the speed at which an object will fall (though not enough to save our absent minded skydiver). Without an atmosphere, drop a feather and a ten kilogramme block of lead and they'll fall at the same rate. With an atmosphere, air resistance wins out against the feather

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and it floats down slowly. But the block of lead wins out against gravity and falls at a rate much closer to the theoretical acceleration (9.78 m/s/s) of 1G would suggest. You can demonstrate this effect by carrying out the following experiment. *

(1) Remove your right shoe and sock.
(2) Drop a feather repeatedly till it falls on your foot (feathers tend to go off - course, so it'll take a few attempts to hit the target). Note that the speed at which the feather hits your foot causes no pain and no damage. From this, you can ascertain that (i) the weight of the feather is very small (ii) air resistance is causing it to fall very slowly.
(3) Now repeat the process, but substituting a 10kg block of lead. As long as you can overcome the subconscious impetus to not drop a 10kg block of lead on your foot, you will note that air resistance does not affect it's fall anywhere near as much. It will travel directly and rapidly to the surface of your foot.

The subsequent pain, broken bones and visit to Casualty (I believe that's ER for my American audience) illustrates that our atmosphere has a lot less effect on the fall of a 10kg block of lead.

The highest speed a falling object reaches is termed "Terminal Velocity." After a certain time and distance falling in free fall (in an atmosphere), the speed of an object reaches a maximum and will not increase any higher. This is decided by such factors as shape, weight and surface area. It is the point at which the pull of gravity is equalled by the drag of air resistance, preventing any further acceleration.

A sheet of paper has a large surface area compared to its weight, so it'll act like a sail as it falls. Air resistance will slow it down. But drop a box of five reams of paper on your foot, and the effect is very different, even though the surface area exposed to the passing air is the same. The result of this experiment would be closer to that of the earlier one with the block of lead.

So for living things, terminal velocity really can be "terminal" velocity. For humans, over much of a distance, it usually is. For cats, it usually is not.

A person in free fall reaches terminal velocity after about 3 seconds, at a speed of around 120 - 140 mph, in a distance of only around 200 feet (30 metres per second, 60 metres). That means whether we fall out of a 15 story building or an airliner at 30,000 feet, it makes no difference, we still hit the ground at about the same speed. Adopting a diving profile will increase that speed, to about 200 mph. Fully spreading arms and legs will reduce it a little.

The terminal velocity of a cat is about 60 mph, reached after about 70 feet or five stories. A cat travelling at terminal velocity landing on its feet has an excellent chance of survival, though possibly with all four legs broken. In fact, the posture adopted by a falling cat actually reduces its speed after it reaches terminal velocity. The very act of presenting all four legs to land on presents the most surface area, slowing the fall. A human falling feet first will present less surface area, increasing the speed of fall.

Statistics have shown that cats falling 15 stories have a higher survival rate (95%) than those falling 4 stories (90%). This is probably because a cats natural abilities allows it to prepare on the longer fall by positioning itself feet first. On the shorter fall, the cat is more likely to come down head first.

* The author accepts no liability for injury caused to any person foolish enough to attempt this experiment.

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© Peter Smith 2008

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