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A man named Alan Magee survived a 20,000-foot fall from a plane during World War II and somehow survived. He landed on a glass roof of a railroad station, which broke his fall. Humans can survive falls from insane distances with no parachute or falling aid, but it requires a lot of luck or some clever planning.
How to survive a big fall
If you are stuck on a cliff with no other options but to fall, there are a few things you can do to put luck in your favor.
One of the best things you can do is to be as lightweight as possible. While this is a little bit outside of your control in the heat of the moment, if you do want to be prepared to survive a fall from a great distance, you'll want to start shedding the weight.
Smaller people fall slower, which ultimately reduces the forces on impact as much as possible.
If you brush an ant off your arm, it experiences a fall equivalent to a skydive in human scale, but it has no problem surviving. That's because it has a lot of wind resistance and a tiny relative mass. Which brings us to the second thing you'll want to do – increase your air resistance.
Gravity is what pulls you down during a fall, and the only way to fight that is through wind resistance. Parachutes leverage a large surface area to maximize wind resistance during a fall, but chances are you won't have a parachute if you're unexpectedly falling. However, you might be wearing a multitude of items of clothing.
During the fall, you'll want to spread out your jacket or shirt like a parachute to ensure that you have as much resistance as possible. Between this and not weighing a lot, your odds start to go up.
Now, you might be thinking that larger people have a larger surface area, which, in return, will slow them down through air resistance. While they do have a larger surface area, it's not enough to overcome the increased force from the added mass.
The landing zone
Rather expectedly, you'll want to try and land on something soft. The basic science behind this is that soft things will increase the amount of time you are slowing down, meaning a less rapid deceleration. When falling, it's the deceleration that kills you. Going from 60 mph to 0 in 1 second will probably kill you, but going from 60 to 0 in 2 seconds is just a ride in a car with really good brakes.
The amount of time you are slowing down makes a major difference in survivability.
All that said, your definition of soft might need to change. Chances are while you're falling, the softest thing you'll be able to land on will be a tree, generally not considered being "soft." Trees do break rather easily. The branches of which can essentially act as crumple zones helping to slow you down safely.
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Water is also good, as long as you enter the water in the right position. You'll want to impact water like a pencil. If you belly flop, you're probably not going to make it.
Water isn't always the best option, though. Even if you don't break every bone in your body on entry, landing in water tends to knock people out. On account of water usually not being filled with breathable oxygen and unconscious people not being able to swim, this isn't a great situation to be in. Surviving a fall is only good if you can breathe when you land.
If you're around buildings, rooftops, power-lines, and snowbanks have helped people survive in the past. These objects might be your best bet in surviving a large fall.
How should you land?
Experts aren't really sure what the best position of landing is, but they are certain that there is a wrong way to land: don't land head first.
Our heads tend to be important parts of our bodies, so using them as crumple zones for our oh-so-valuable feet is not advised.
The best position you can likely land in is on your back, face-up, and with your arms protecting your head. However, other tests have concluded that feet first is your best shot at survival. Basically, try to position yourself to have your head impact last.
Other ways to survive falling
There is one other way with a very high fall-survival rate that you can utilize. Just try not falling at all. It works most of the time. Pretty clever, huh?