Imagine an absolutely nightmare scenario: you are locked in the elevator car, which rises on several floors, and then you hear an unpleasant crack, the damaged cable breaks, and the elevator falls with you. Can you escape by jumping up at the right moment?
In this predicament, the key point to be realized is that you are moving along with the elevator, and when it stops, reaching the bottom of the elevator shaft, you too will make a sudden and extremely unpleasant stop.
If you jump, will it help to avoid injury? Let’s install a camera in the lift shaft so that it falls with you, and watch the decisive last moment of slow motion.
You jump at the right time and rise up when the elevator touches the floor. At this point, you (from the point of view of our camera) are moving upwards at a speed, which we will later refer to as the speed of the jump. At the decisive moment before the collision with the foundation, the elevator falls at a speed that we will denote as the speed of the elevator.
Because of the jump, you fall more slowly than the elevator. The speed with which you hit the floor of a suddenly stopped elevator is the difference between the speed of the elevator and the speed of the jump.
For further calculations, we need two more quantities. Firstly, it is important to know from what height the elevator is falling, and secondly – how high you jumped.
Let’s be optimistic and assume that from fear you jumped vertically upward by 70 centimeters, like a basketball player from the NBA. Now we will look at several scenarios, saving you from detailed calculations.
Fall from a height of one floor (3 meters): jumping in time, you hit the bottom of the cabin as if dropped from a height of only 80 centimeters. Do not worry, everything will be okay. The only problem is that you will have only 0.8 seconds to prepare for the jump, so be vigilant!
Fall from the height of the third floor (9 meters): in this case, the blow will be as if you fell from a height of 4.7 meters. A timely jump can change the outcome from “possibly deadly” to “serious injury”. Most likely, one or both legs will be broken, but you will survive.
Some clever men offer to lie down on the bottom of the elevator, because in this position the impact force will be distributed throughout the body. This is actually a terrible idea. Spare your brain. When the body falls, it can partially take the blow, but the main cause of death when falling from a height is a head injury. So it will be better if the kick will take over your feet, although they are also sorry, of course.
Fall from the height of the fifth floor (15 meters): the impact on the bottom of the elevator will be the same as when falling from a height of 9 meters. In this case, a timely jump can actually increase the likelihood of survival very significantly. Perhaps it is he who will determine the final outcome. You will have 1.7 seconds to prepare and jump. Good luck!
The fall from the height of the seventh floor (21 meters): the impact force will be equivalent to a drop from the 14-meter height. Alas, in this case you will have only about 2 seconds to prepare for the meeting with the creator.
It’s unlikely that you will be frightened by anything else, but we can not but say that for simplicity of explanation we made several assumptions. So, the calculation was based on the fact that the jump will take place at the ideal moment, despite the fact that it is practically impossible to predict it. It is necessary to delay one single moment, and you already hit the floor, and in jumping a second ahead of time, you can hit your head at the ceiling and lose the speed of the jump.
Another assumption is that you will generally be able to push off the floor when jumping, which is unlikely, since gravity carries the floor of the elevator car from you. If you suddenly find yourself in a state of free fall, you will have to grab the handrail to keep in touch with the floor needed for the jump.
We also suggested that you hit hard floor at the bottom of the cabin, but some people survived in the falling elevator because of the cable that curled under the cabin and softened the blow. However, others were crushed by the weight of that part of the cable that remained on top and fell, breaking the roof of the cabin.
The air resistance can be completely ignored – the falling lift reaches a speed of about 200 kilometers per hour, before any noticeable slowdown in traffic begins.
However, the air can save you in a different way. Compressed air in the shaft under the elevator can provide additional cushioning. Suppose we again drop the elevator from a height of 7 floors. If the shaft was completely sealed, the elevator, like a piston, dropped just 50 centimeters until the additional pressure of the compressed air balanced its weight.
However, usually there is a gap between the walls of the shaft and the elevator car, which reduces the effect of depreciation. If everything happens faster than the elevator will increase the air pressure, or if this excess pressure opens the doors at the bottom of the shaft, you will still fall pretty quickly.
An approximate calculation suggests that for sufficient air compression it is necessary that the clearance between the walls of the elevator and the shaft is less than 30 centimeters.
In conclusion, some comforting news. There are no special reasons for concern. Modern elevators have a number of protective systems, such as spare cables and electromagnetic brakes. But if the worst happened, take advantage of your chance: jump!