IT IS NOT THE FALL THAT KILLS. IT IS THE MOMENTUM.

Falling, it turns out, is perfectly harmless, for according to GR, you will momentarily be free from the local effects of gravity, moving effortlessly through a geodesic in space-time. You would not be falling at all. If you are unfamiliar with GR, then according to the Newtonian laws, no harm will come unto you if you are to jump off of a tall building or step out of an aeroplane midway in flight. But Sir Newton would warn you not to come to a sudden stop. Plummeting down a great height can be an exhilarating experience. Who would not want to feel the effect of weightlessness, and that too, for free? All is well, provided you do not land on solid ground, a tree, a car or on the stretched arms of a passerby who is oblivious to your perilous experiments. 

After writing so much on free fall, it is rather hard to stop myself from jumping out of the window. The only reason I have not yet dived is that I am well aware of my outcome. If I hit a tree, I will be badly impaled through a very wrong place. If not, I will probably land on the solid concrete ground, ending up like a fresh batch of tomato puree sprinkled with a few crunchy bones. Do excuse the silly description. 

When a person jumps off a tall building or from a vertical height (suppose, close to the edge of space), he is essentially in free fall. We have seen that while falling through a resistive medium, in this case, air, the person will acquire a terminal velocity, which will also be his maximum velocity of fall. Using appropriate formulas and certain approximations, we can calculate the terminal velocity of an average human weighing 70 kg to be around 50-55 m/s, depending on whether he is falling in a belly-to-earth or head-down position. This speed is the typical estimate for skydivers with their parachutes closed. Using this value, we see that our person falls through a vertical height of 348 m in about 10 seconds, acquiring 94% of the projected velocity. In 12 seconds, he falls through 455 m, gaining 97% of the said terminal velocity. However, this 55 m/s terminal velocity is not a rigid number. Skydivers can fall with much greater terminal velocity, thereby setting new records. Since the late 1990s, Speed Skydiving has become a new sport. As the name suggests, the sole objective of the sport is to achieve and maintain the highest possible terminal velocity. The current world record for the highest terminal velocity attained by a male skydiver stands at 530 km/h or 147 m/s, and for a female, the record stands at 478 km/h or 133 m/s approximately. 

Contrary to what most people might think, high speeds are absolutely not fatal for human bodies. Theoretically, we can even travel at the speed of light, zapping through space at the rate of 300,000 km/s and be perfectly safe. Velocity is safe. Velocity is good. During reentry, the Apollo 10 crew had to withstand a speed of 40,000 km/h or 11,000 m/s with respect to the Earth. Since Newton's laws are Galilean invariant, we can effectively travel at 300,000 km/s and step out of our spacecraft ''happy and merry''. But the problem with light-speed travel lies somewhere else. Approaching high speeds demands rapid acceleration. Assuming that we have solved all the technological limitations that liquidate our dreams of light-speed travel, even then, our essentially human bodies are not suitable for ''over-the-cloud'' accelerations. The following Scientific American article tells us why it is impossible for humans to accelerate to light speed. An average person can not survive any more than 9 g's of acceleration and that too for a short while. At 9 g's, his body will feel a gravity force 9 times greater than what he experiences on Earth. Such a force will be enough to collapse his heart. Plus, there is a time bar. The article says, ''We can withstand 5 g's for two minutes, 3 g's for only an hour''. None of us would survive 9 g's for not more than a few seconds. As a concluding remark to this paragraph, let me add one more piece of information. Suppose someone wants to accelerate to light speed under 10 seconds, then roughly speaking, he would have to survive 30 million g's! 

If truth be told, when a person falls from a great height, neither his terminal velocity nor the Earth's gravity will be responsible for his death. He may die from a lack of oxygen with the water in his body boiling off due to low-atmospheric pressure if he has decided to jump from the edge of space. There is also a chance that he may collide with satellite debris. But we can not say that he died in free fall. Nor can we blame gravity. Even when a person falls from a tall building, he stays perfectly safe until he hits the road, a car or falls into a tree. If velocity or acceleration is not responsible for his poor outcome, then there has to be something much stronger. 

Paragliders can spend a long time in the air by altering their terminal velocity and can do other tricks utilizing various aerodynamic techniques. 
Image Credits: Creative Commons License

The cardinal element is momentum. Coming to this length, I must admit that the title does not reveal the truth in its entirety. Instead, I should say, ''It is the abrupt change of momentum, the sudden and almost instantaneous drop of terminal velocity to a complete zero upon striking the solid ground that kills''. The actual ''medical'' death happens because of extreme physical trauma, severe blood loss, ruptured arteries and shattered bones. I am not going into further medical details, for it is not my subject of expertise. 

Force, as we all know, is the rate of change of momentum, while momentum, all by itself, gives us the quantity of motion, equaling mass times velocity. Suppose a man weighing 70 kg is falling with a terminal speed of 56 m/s, which is the standard estimate. His net momentum will be 3920 (almost 4000) kg m/s. Now, as he hits the concrete ground (say), within some fraction of a second, his terminal velocity will drop from 56 m/s to 0 m/s. If we assume that this velocity drop takes place in an interval of 0.1 seconds, then he will be experiencing a force of 39,200 N rebounding throughout his body. The time factor is of paramount importance. If the velocity drop or the momentum change happens over a short time, the corresponding force will be enormous. If the same happens over a longer duration, the impact force would have reduced significantly. For example, say the man lands on some shock-absorbing material, wherein it takes about 10 seconds for his terminal velocity to drop to zero. In this case, he will experience a force of 392 N or less, and he will have great odds of survival. If he lands on a hard and rigid surface, there is a chance that his velocity will drop to zero in about 0.01 seconds or less. This time he will experience a force of 392,000 N. The g-force for such a type of collision will be of the order of 7000 times the usual. No human being can survive such forces. Our bones are tougher than we may think. In some instances, they even surpass the strength of steel. To give a rough idea, it takes about 4000 N force to break a typical femur. 

Concrete is known for its mechanical strength, especially compressive strength, i.e., it resists breaking. Depending on the nature of the concrete and its associated specifications, it will take millions of kg-force to crush a concrete slab. For reinforced concrete, we will require a seemingly immense force. However, concrete has one disadvantage, which is tensile strength. Concrete can not resist high tensile forces. The event of a man falling on a concrete floor can be treated as a perfectly inelastic collision between two rigid bodies, where the larger body (i.e., the floor) does not move. The man strikes with ''full momentum'' so to speak, and since the floor does not yield nor dissipate the impact force, the man feels this momentum rebounding throughout his body. Within a very short interval, the person's terminal velocity drops to zero. Before coming to a complete stop, his body severely deforms, and bones break apart. In fact, due to the unyielding nature of concrete, even stumbling on a cemented floor can turn fatal. 

On the contrary, if the person lands on a soft surface made up of a material that compresses and crumples upon impact, he will have great odds of surviving. This is why it is never advisable to catch a falling person, specifically if he is falling, say from 10 or more stories. Firstly it is near impossible for any of us to arrest the momentum of an adult individual. Chances are that both may die in the event. Moreover, if the falling person lands on someone else, then the catcher may be able to lessen the impact on the falling person by cushioning the fall, but he will feel the momentum of the falling person. The catcher will surely die. I am not going into the details since it is already there on the internet, but it is possible to save/catch a falling person using specific techniques.  

Thus we see that the longer it takes for the momentum to drop to zero, the lesser will be the resulting impact force and the greater the chances of survival. In summary, the longer it takes to decelerate the better.  

A good way to finish this article will be to quote J.B.S Haldane from his 1926 essay, ''On Being the Right Size'', in which he explains it all in minimal words. He writes, ''You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, a horse splashes. For 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 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''. 

References: 

1. https://www.fai.org/commission/isc
2. https://www.bbc.com/future/article/20150809-how-fast-could-humans-travel-safely-through-space
3. https://www.forbes.com/sites/startswithabang/2020/04/11/ask-ethan-how-do-we-feel-acceleration-in-space/?sh=2af892c4365f
4. https://www.abc.net.au/science/articles/2005/09/13/1459026.htm#:~:text=The%20aorta%20(the%20huge%20main,have%20also%20instantaneously%20torn%20loose.
5. https://www.nationalgeographic.com/science/article/who-are-you-calling-weak-human-jaws-are-surprisingly-strong-and-efficient
6. https://www.askamathematician.com/2012/07/q-why-is-hitting-water-from-a-great-height-like-hitting-concrete/
7. https://www.bbc.com/news/magazine-14150524