Crumple zones are designed to absorb the energy from the impact during a traffic collision by controlled deformation through Crumpling. This energy is much greater than is commonly realized. A 2,000 kg (4,409 lb) car travelling at 60 km/h (37 mph) (16.7 m/s), before crashing into a thick concrete wall, is subject to the same impact force as a front-down drop from a height of 14.2 m (47 ft) crashing on to a solid concrete surface. Increasing that speed by 50% to 90 km/h (56 mph) (25 m/s) compares to a fall from 32 m (105 ft) - an increase of 125%.  This is because the stored kinetic energy (E) is given by E = (1/2) mass × speed squared. It increases by the square of the impact velocity.
Typically, crumple zones are located in the front part of the vehicle, in order to absorb the impact of a head-on collision, though they may be found on other parts of the vehicle as well. According to a British Motor Insurance Repair Research Centre study of where on the vehicle impact damage occurs: 65% were front impacts, 25% rear impacts, 5% left side, and 5% right side. Some racing cars use aluminium, composite/carbon fibre honeycomb, or energy absorbing foam to form an impact attenuator that dissipates crash energy using a much smaller volume and lower weight than road car crumple zones. Impact attenuators have also been introduced on highway maintenance vehicles in some countries.
On September 10, 2009, the ABC News programs Good Morning America and World News showed a U.S. Insurance Institute for Highway Safety crash test of a 2009 Chevrolet Malibu in an offset head-on collision with a 1959 Chevrolet Bel Air sedan. It dramatically demonstrated the effectiveness of modern car safety design over 1950s design, particularly of rigid passenger safety cells and crumple zones. 
Early Development History
The crumple zone concept was invented and patented by the Austrian Mercedes-Benz engineer Béla Barényi originally in 1937 before he worked for Mercedes-Benz and in a more developed form in 1952. The 1953 Mercedes-Benz "Ponton" was a partial implementation of his ideas by having a strong deep platform to form a partial safety cell - patented in 1941. The Mercedes-Benz patent number 854157, granted in 1952, describes the decisive feature of passive safety. Barényi questioned the opinion prevailing until then, that a safe car had to be rigid. He divided the car body into three sections: the rigid non-deforming passenger compartment and the crumple zones in the front and the rear. They are designed to absorb the energy of an impact (kinetic energy) by deformation during collision. The first Mercedes-Benz carbody developed using this patent was the 1959 Mercedes W111 “Tail Fin” Saloon. The safety cell and crumple zones were achieved primarily by the design of the longitudinal members: these were straight in the centre of the vehicle and formed a rigid safety cage with the body panels, the front and rear supports were curved so they deformed in the event of an accident, absorbing part of the collision energy and preventing the full force of the impact from reaching the occupants.
A more recent development was for these curved longitudinal members is to be weakened by vertical and lateral ribs to form telescoping 'crash can' crush structures.
Crumple zones work by managing crash energy, absorbing it within the outer parts of the vehicle, rather than being directly transferred to the occupants, while also preventing intrusion into or deformation of the passenger cabin. This better protects car occupants against injury. This is achieved by controlled weakening of sacrificial outer parts of the car, while strengthening and increasing the rigidity of the inner part of the body of the car, making the passenger cabin into a 'safety cell', by using more reinforcing beams and higher strength steels. Impact energy that does reach the 'safety cell' is spread over as wide an area as possible to reduce its deformation. Volvo introduced the side crumple zone with the introduction of the SIPS (Side Impact Protection System) in the early 1990s.
When a vehicle and all its contents, including passengers and luggage are travelling at speed, they have inertia / momentum, which means that they will continue forward with that direction and speed (Newton's first law of motion). In the event of a sudden deceleration of a rigid framed vehicle due to impact, unrestrained vehicle contents will continue forwards at their previous speed due to inertia, and impact the vehicle interior, with a force equivalent to many times their normal weight due to gravity. The purpose of crumple zones is to slow down the collision and to absorb energy to reduce the difference in speeds between the vehicle and its occupants.
Seatbelts restrain the passengers so they don't fly through the windshield, and are in the correct position for the airbag and also spread the loading of impact on the body. Seat belts also absorb passenger inertial energy by being designed to stretch during an impact, again to reduce the speed differential between the passenger's body and their vehicle interior. In short: a passenger whose body is decelerated more slowly due to the crumple zone (and other devices) over a longer time survives much more often than a passenger whose body indirectly impacts a hard, undamaged metal car body which has come to a halt nearly instantaneously. It is like the difference between slamming someone into a wall headfirst (fracturing their skull) and shoulder-first (bruising their flesh slightly) is that the arm, being softer, has tens of times longer to slow its speed, yielding a little at a time, than the hard skull, which isn't in contact with the wall until it has to deal with extremely high pressures. The stretching of seatbelts while restraining occupants during an impact, means that it is necessary to replace them if a vehicle is repaired and put back on the road after a collision. They should also be replaced if their condition has deteriorated e.g. through fraying or mechanical or belt mounting faults. In New Zealand it is officially mandatory to replace worn inertia reel type seatbelts only with 'webbing grabber' type belts that have less play and are more effective on older cars. Newer cars have electronically fired pre-tension seatbelts that are timed to work with the airbag firing. Buying used seatbelts is not a good idea even in countries where it is legal to do so, because they may have already been stretched in an impact event and may not protect their new users as they should.
The final impact after a passenger's body hits the car interior, airbag or seat belts is that of the internal organs hitting the ribcage or skull due to their inertia. The force of this impact is the way by which many car crashes cause disabling or life-threatening injury. Other ways are skeletal damage and blood loss, because of torn blood vessels, or damage caused by sharp fractured bone to organs and/or blood vessels. The sequence of energy-dissipating and speed-reducing technologies—crumple zone — seat belt — airbags — padded interior—are designed to work together as a system to reduce the force of the impact on the outside of the passenger(s)'s body and the final impact of organs inside the body. In a collision, slowing down the deceleration of the human body by even a few tenths of a second drastically reduces the force involved. Force is a simple equation: Force = mass X acceleration. Cutting the deceleration in half also cuts the force in half. Therefore, changing the deceleration time from .2 seconds to .8 seconds will result in a 75 percent reduction in total force.
A misconception about crumple zones sometimes voiced is that they reduce safety for the occupants of the vehicle by allowing the body to collapse, therefore risking crushing the occupants. In fact, crumple zones are typically located in front of and behind the main body of the car (which forms a rigid 'safety cell'), compacting within the space of the engine compartment or boot/trunk. Modern vehicles using what are commonly termed 'crumple zones' provide far superior protection for their occupants in severe tests against other vehicles with crumple zones and solid static objects than older models or SUVs that use a separate chassis frame and have no crumple zones.
They do tend to come off worse when involved in accidents with SUVs without crumple zones because most of the energy of the impact is absorbed by the vehicle with the crumple zone — however, even for the occupants of the 'worse off' car, this will still often be an improvement — as the result of two vehicles without crumple zones colliding will usually be more hazardous to both vehicle's occupants than a collision that is at least partly buffered.
Another problem is 'impact incompatibility' where the 'hard points' of the ends of chassis rails of SUVs are higher than the 'hard points' of cars, causing the SUV to 'override' the engine compartment of the car. In order to tackle this problem, more recent SUV/off-roaders incorporate structures below the front bumper designed to engage lower-height car crumple zones.
Computer modelled crash simulation
In the early 1980s, using technology developed for the aerospace and nuclear industries, German car makers started complex computer crash simulation studies, using finite element methods simulating the crash behaviour of individual car body components, component assemblies, and quarter and half cars at the body in white(BIW) stage. These experiments culminated in a joint project by the Forschungsgemeinschaft Automobil-Technik (FAT), a conglomeration of all seven German car makers (Audi, BMW, Ford, Mercedes-Benz, Opel (GM), Porsche, and Volkswagen), which tested the applicability of two emerging commercial crash simulation codes. These simulation codes recreated a frontal impact of a full passenger car structure (Haug 1986) and they ran to completion on a computer overnight. Now that turn-around time between two consecutive job-submissions (computer runs) did not exceed one day, engineers were able to make efficient and progressive improvements of the crash behaviour of the analyzed car body structure. The drive for improved crash worthiness in Europe has accelerated from the 1990s onwards, with the 1997 advent of Euro NCAP, with the involvement of Formula One motor racing safety expertise.
'Sleds' inside safety cells
The 2004 Pininfarina Nido Experimental Safety Vehicle locates crumple zones inside the survival cell. Those interior crumple zones decelerate a sled-mounted survival cell. Volvo has also been developing this idea for use in small cars. Their driver's seat is mounted to what is basically a 'sled' on a rail, with shock absorbers in front of it. In an impact, the whole "sled" of driving seat and belted in driver, slides forward up to 8 inches, and the shock absorbers dissipate the peak shock energy of the impact, lengthening the deceleration time for the driver. Simultaneously, the steering wheel and the driver's side dashboard slide forward to make room for the driver, as he is thrown forwards stretching the seatbelt. Combined with a front crumple zone and airbag, this system could greatly reduce the forces acting on the driver in a frontal impact.
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