Terminal velocity

Why Aren't Mosquitoes killed by Raindrops?
http://www.csmonitor.com/Science/2012/0604/How-military-might-benefit-from-study-of-hard-to-kill-mosquitoes

on average, raindrops have about the same diameter as their test subjects, wingtip to wingtip. But the raindrop weighs anywhere from 2 to 50 times that of the mosquitoes. By the time the drops approach the ground, they travel at between 13 and 20 miles an hour. Proportionally, that's like an encounter between a bus and a pedestrian at up to 20 miles an hour.  .. with an impact from a raindrop, a mosquito can handle up to 300 Gs, the team calculates.

In the end, a combination of a mosquito's external skeleton and its status as a featherweight kept it from falling victim to rainfall.
the mosquito has hydrophobic hairs on its body and sprawling legs that create drag. This lets it slip out from under the raindrop before meeting a wet end.
..Rapid acceleration also produces the greatest risk to mosquitoes: flying close to the ground. When hit by a raindrop, they would accelerate into the ground with great force and without sufficient time to slide out from underneath. 
http://blogs.scientificamerican.com/observations/2012/06/04/how-the-mosquito-survives-a-raindrop-collision/
See video at this site above.


Based on wind resistance, for example, the terminal velocity of a skydiver in a belly-to-earth (i.e.:face down) free-fall position is about 195 km/h (122 mph or 54 m/s).
http://en.wikipedia.org/wiki/Terminal_velocity

When the buoyancy effects are taken into account, an object falling through a fluid under its own weight can reach a terminal velocity (settling velocity) if the net force acting on the object becomes zero. When the terminal velocity is reached the weight of the object is exactly balanced by the upward buoyancy force and drag force.

http://en.wikipedia.org/wiki/Drag_(physics)

http://irl.cs.ucla.edu/papers/right-size.html

the resistance presented to movement by the air is proportional to the surface of the moving object. Divide an animal’s length, breadth, and height each by ten; its weight is reduced to a thousandth, but its surface only to a hundredth. So the resistance to falling in the case of the small animal is relatively ten times greater than the driving force.

An insect, therefore, is not afraid of gravity; it can fall without danger, and can cling to the ceiling with remarkably little trouble. It can go in for elegant and fantastic forms of support like that of the daddy-longlegs. But there is a force which is as formidable to an insect as gravitation to a mammal. This is surface tension. A man coming out of a bath carries with him a film of water of about one-fiftieth of an inch in thickness. This weighs roughly a pound. A wet mouse has to carry about its own weight of water. A wet fly has to lift many times its own weight and, as everyone knows, a fly once wetted by water or any other liquid is in a very serious position indeed. An insect going for a drink is in as great danger as a man leaning out over a precipice in search of food. If it once falls into the grip of the surface tension of the water—that is to say, gets wet—it is likely to remain so until it drowns. A few insects, such as water-beetles, contrive to be unwettable; the majority keep well away from their drink by means of a long proboscis.

Exactly the same difficulties attach to flying. It is an elementary principle of aeronautics that the minimum speed needed to keep an aeroplane of a given shape in the air varies as the square root of its length. If its linear dimensions are increased four times, it must fly twice as fast. Now the power needed for the minimum speed increases more rapidly than the weight of the machine. So the larger aeroplane, which weighs sixty-four times as much as the smaller, needs one hundred and twenty-eight times its horsepower to keep up. Applying the same principle to the birds, we find that the limit to their size is soon reached. An angel whose muscles developed no more power weight for weight than those of an eagle or a pigeon would require a breast projecting for about four feet to house the muscles engaged in working its wings, while to economize in weight, its legs would have to be reduced to mere stilts. Actually a large bird such as an eagle or kite does not keep in the air mainly by moving its wings. It is generally to be seen soaring, that is to say balanced on a rising column of air. And even soaring becomes more and more difficult with increasing size. Were this not the case eagles might be as large as tigers and as formidable to man as hostile aeroplanes.

Yet although Galileo demonstrated the contrary more than three hundred years ago, people still believe that if a flea were as large as a man it could jump a thousand feet into the air. As a matter of fact the height to which an animal can jump is more nearly independent of its size than proportional to it. A flea can jump about two feet, a man about five. To jump a given height, if we neglect the resistance of air, requires an expenditure of energy proportional to the jumper’s weight. But if the jumping muscles form a constant fraction of the animal’s body, the energy developed per ounce of muscle is independent of the size, provided it can be developed quickly enough in the small animal. As a matter of fact an insect’s muscles, although they can contract more quickly than our own, appear to be less efficient; as otherwise a flea or grasshopper could rise six feet into the air.

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There are cats on record that have fallen 20 stories or more without ill effects. As long as the cat doesn't land on something pointy, it's likely to walk away.

You're thinking: no freaking way. But believers trot out a 1987 study from the Journal of the American Veterinary Medical Association. Two vets examined 132 cases of cats that had fallen out of high-rise windows and were brought to the Animal Medical Center, a New York veterinary hospital, for treatment. On average the cats fell 5.5 stories, yet 90 percent survived. (Many did suffer serious injuries.)

We know cats have exceptional coordination and balance, so maybe that contributed to the high survival rate. One cat, for example, is known to have survived a 46-story fall. (It apparently bounced off a canopy and into a planter.)

http://www.straightdope.com/columns/read/1143/do-cats-always-land-unharmed-on-their-feet-no-matter-how-far-they-fall

At terminal speed, air resistance balances weight, so

CDAv2=mg

The "killability" of a fall relates to the total kinetic energy per unit mass of the body absorbing the kinetic energy. This is simply proportional to v^2. But from above formula, v^2 is proportional to weight over area. Since weight is proportional to length^3, and area to length^2, v^2 is proportional to length. An ant is one thousandth the linear size of a man, so its fall from a height sufficient to achieve terminal velocity (which BTW is only a few inches; Empire State Building not needed) has only 1/1000 the killing power of a fall of a person from ESB.


http://www.physicsforums.com/showthread.php?t=68025

Is terminal velocity Terminal

We estimate the terminal velocity for a man falling in air. For air we have

We approximate the man to have cross sectional area 0.2 m and mass m=70 kg. The corresponding terminal velocity is

(ps: I miscalculated this on the blackboard) This will typically be a lethal fall. We can estimate the distance required to reach the terminal velocity to be

This estimate neglected drag just asking after what distance a free fall reaches the terminal velocity.
Lets consider how this result scales with the typical linear dimensions of the falling object, L. We have  and  so finally

Thus if we consider a bug with typical dimensions L=0.005 m ie. 100 times smaller tha a human, its terminal velocity will be  times smaller than for a human ie. 14 mph. Hitting the earth at that velocity probably is harmless. Thus we now understand why a bug can fall from arbitrary heights without serious bodily injury. Its mass to area ratio is so small that the terminal velocity is not "terminal".


http://www.pha.jhu.edu/~broholm/l10/node5.html

Human Free Fall:

In addition to Vesna Vulovic's 33,330-foot free fall, there are many other instances where airplane pilots or crew have plunged thousands of feet without a functioning parachute and survived.

Vulović fell approximately 10,160 metres (33,330 ft). She suffered a fractured skull, three broken vertebrae (one crushed completely) that left her temporarily paralyzed from the waist down and two broken legs. She was in a coma for 27 days. In an interview, she commented that according to the man who found her, "...I was in the middle part of the plane. I was found with my head down and my colleague on top of me. One part of my body with my leg was in the plane and my head was out of the plane. A catering trolley was pinned against my spine and kept me in the plane. The man who found me, says I was very lucky. He was in the German Army as a medic during World War II. He knew how to treat me at the site of the accident

Russian Lieutenant I. M. Chisov, piloting an Ilyushin-4 bomber, was attacked by 12 German Messerschmitts in January 1942. He bailed out at an altitude of about 22,000 feet. He chose not to open his parachute to avoid being killed by the fighter pilots, planning to open his chute at 1000 feet. However, he lost consciousness during free fall and landed on a steep ravine with 3 feet of snow.
Chisov awoke 20 minutes later. He only had a concussion of his spine and a fractured pelvis, returning to duty as a flight instructor three and a half months later.

Nick Alkemade of the RAF, tail gunner in an AVRO Lancaster bomber, was trapped in his burning gun turret after the bomber was attacked by a German Ju-88 bomber. His parachute was in the cabin area, but he couldn't get it, so he jumped out of the plane, preferring a quick death to being burned alive.
Alkemade fell from 18,000 feet, all the while thinking of his impending death, falling in a position with his head down. Suddenly, he was on the ground, looking up at the stars through some pine trees. He couldn't believe he was okay, but moving both arms and legs he soon realized he was not even hurt badly and smoked a cigarette before getting up.
Pine trees had slowed his descent and he fell to soft snow. His most serious injury was a sprained leg.
Alkemade was captured by the Germans. The Gestapo did not believe his story until they inspected the parachute harness and found his burnedparachute at the crash site.

http://everything2.com/title/chuteless+high-altitude+free+fall