The Physics of Car Collisions

Introduction
Car collisions happen every day, all over Singapore. Some are not very serious, while others are fatal. In 2008, there were 221 deaths and 10,760 injuries sustained in Singapore from road accidents. Compared to the previous year with 214 deaths and 10,352 injuries, road accidents are a growing trend in recent years. Not just for Singapore, accidents are the third leading cause of death for males in the United States, with Motor Vehicle Accidents making up 37.5% of the cause of accidental deaths. So how exactly does a car collision affect your body?
There are a few different types of car crashes, mainly:

Head-on collision with another object:

This type of collision usually results in the biggest momentum forwards for passengers in the car, due to the sudden stop in forward momentum of the cars. The upper bodies of passenger(s) are jerked forward while the lower body is anchored to the seat, because of the lower end of the seat belt, which is usually more secure. The force with which the body is thrown forwards depends on two factors: the combined speed at impact and the hardness of the car body. The greater the speed of the car on impact, the greater the force acting on the car passengers and hence the more they jerk forward. Also, if the car body is made of very hard metal, then it would crumple less and hence the time taken for the whole car to come to a complete stop would be very short. Since time is decreased, then the rate of deceleration of the car would be very fast and hence a greater force acting on the passengers, jerking them forward, because: Force = Mass X Acceleration; or in this case, Opposite Force (of the car) = Mass X Deceleration ( of the car). The bodies of the passengers will jerk forward because, with the car’s initial cruising speed, both the car and the passengers are moving at a constant speed forward. During collision, the car’s speed is slowed down very quickly, leaving the passengers to continue in the forward direction, hence their jerking motion. All the forces present in a head-on car collision are generally linear, and hence the physics behind it isn’t too hard.

Rear-end collision resulting in chain of accidents:

This kind of accident usually happens during rush hour, when traffic jams result in long lines of waiting cars. Usually, the car at the end of the line rams into a stationary car, which ends up ramming the other car in front, and so on. Another cause of this kind of accident is when the car at the front suddenly stops cruising forward, leaving the next car to bash into it because of a lack of time to break, and this results in a pile up of accidents. In such cases, up to 10 cars or more may be involved and both the front and rear ends of cars in the middle of the accident are damaged. For the first cause, passengers in the car which caused the accident are jerked forward just like a head-on collision. Passengers in subsequent cars involved are first jerked backward into their seat by the suddenly forward momentum of the car, before being jerked forward because of the sudden cease of that forward momentum. For the second cause, passengers are first jerked forward by the sudden stop in forward momentum of their car, before being jerked back into their seats again by the impact of the car behind them, which results in a sudden forward momentum of the car the passengers are in. Forces in these scenarios are all linear, hence in these cases, the front air bags would be of most use.

Impact of another car from the side

In such a scenario, passengers in a stationary car are first thrown towards the side of the collided vehicle because of the sudden displacement of the car (i.e. side-ways momentum). After this, passengers are usually thrown into the opposite side of the car because of the decrease in initial side-ways momentum their car has experienced. The car which started the accident, i.e. the one which collided into the stationary car, would experience the same forces as a head-on collision. Side airbags would be of the most use for the initially-stationary car, while front airbags would be of most use for the other car.

Calculation of damage sustained by both passengers and car

The amount of force that causes an accident is largely dependent on Newton’s 2nd and 3rd laws, i.e. F=MA, and For every action, there is an equal and opposite reaction, respectively. Newton’s 1st law, Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it, explains why passengers in cars are thrown about in a collision, which usually results in a sudden acceleration or deceleration. Factors that affect the degree of damage to the car and injury to passengers are the hardness of the car body, the initial cruising speed of the car, angle of collision ( from where does the car impact on to), the design of the car, the weight of the car, and body mass and position of the passengers of the car.

1) The harder the car body, the greater the rate of acceleration or deceleration on the whole, for the car. A greater acceleration for the same mass results in greater force ( F=MA), which would mean passengers of the car would be subject to more violent jerking and might possible sustain more injury, even though the car would have less damage. Likewise, the softer the car body, the more damage the car would sustain. This would mean the car body would crumple up more and a slower rate of acceleration or deceleration on the whole for the car, resulting in less violent jerks of passengers, meaning less chance of injury. Of course, if the car were too soft, passengers would be crushed to death by the impact.

2) The faster the initial cruising speed of the car, the greater the impact felt. This is explained by 3rd law. If a car were to crash into a brick wall, the brick wall would exert an equal and opposite pressure on the car, which is what causes the car to crumple up and throw the passengers about. For a slower initial cruising speed, the less the force acting on the brick wall and since an equal and opposite reaction is acted on the car, the lesser the force crumpling up the car.

3) For head-on and 90 degrees car crashes, front and side airbags would offer the greatest protection and hence minimize injuries sustained by passengers.

However, for 45 degree crashes, meaning impact from the corners of the car, airbags tend to cover less of the areas in which passengers are thrown at, meaning passengers might bump into hard windows are metal frames of the cars and probably more severe injuries.

4) Design of the car is a complicated aspect.

Recent technological innovations like seatbelts, airbags, impact-absorbing side-panels, front-and-rear head restraints, impact-absorbing bumpers and interiors with no sharp edges have all contributed to less injury sustained by passengers during car collisions.

5) The greater the weight, or mass, of the car, the greater the forces dealt.

This is because of F=MA, meaning if the car crashing into a stationary car were very heavy as compared to the stationary car, the stationary car could be sent flying. However if the roles were reversed and the car crashing into the stationary car were much lighter than the stationary car, the stationary car would not sustain much damage.

6) If the passenger of the car were very light, he or she would have a higher chance of being thrown out of his seat than if he or she were a heavier person, as can be explained by F=MA. For the same force applied on the person, if he or she were heavier, meaning greater mass, the acceleration would be less, based on F=MA. Likewise if he or she were lighter, for the same force applied, the acceleration would be greater. The center of gravity of the person would also affect how much he or she is jerked about during collision, the relationship being that a person with low center of gravity would be more stable in his or her seat, while a person with higher center of gravity would be less stable in his or her seat. Center of gravity is related to height above the ground, and mass, meaning to say, in layman terms, a tall person would sway about more than a short person, and a heavier person would bounce around less than a light person.

I bring out a hypothetical situation to illustrate the calculations.

A car (A) of 1000 kg travelling at a constant speed of 100km/h collides with another car (B) also of 1000kg and travelling at a constant speed of 100km/h in the opposite direction of the first car. There is 1 passenger in both the cars and they both weigh 60kg each. After the collision, both cars were displaced 10 meters from the point of collision in 2 seconds

Given this, because of F=MA, the force that each car crashed with is [1060 (10/2) ] N, which is 5300N. The passenger of each car, would in return experience 5300N of forward momentum before being jerked back by the seatbelt. 5300N of force on any person is not a small amount, hence both persons might sustain brain hemorrhage on account of the sudden movement of the head. The head would move the most because it is furthest from the fulcrum which is the lower body strapped to the seat by the seatbelt. The airbag would probably cushion the head and slow its sudden acceleration forward and backward by some amount, but 5300N would probably still lead to, at least a broken nose from impact into the airbag. The ensuing snap back into the seat might be hard enough to injure the spinal chord of the passenger, and all this is assuming there are no sharp exposed metal pieces from the crumpled and twisted car metal to cause abrasions, lacerations and internal injury.

Injuries usually sustained in car collisions
A study from 1st January to 31st December in 1994 by the Jawaharlal Institute of Postgraduate Medical Education and Research (JIPMER) showed that:
- Limbs and face were the most common areas of the body which sustained external injuries in car collisions.
- Abrasion usually occurred around the limbs and face.
- Lacerations occurred on the face, head, and limbs.
- Multiple superficial injuries were found most common in the lower limbs and face.
- Injuries to the chest, pelvis and upper limb were seen in equal proportions of victims,
- Other sites of injuries were the back, spine, and neck.

Most of these injuries are a result of not wearing a seatbelt, lack of airbags and presence of sharp objects on the car during or after collision. Internal injuries could also be sustained, if sharp objects pierce organs inside the person’s body or if organs are thrown about too violently, especially for pregnant women.

Case study:

On January 4th 2010, Seattle, a baby was thrown out of the car, still strapped into her car seat, in a violent crash in the Central District. This case is a rather extreme, but true example of the forces applied on passengers of a car during a collision. In this case, the car the baby was in was hit twice, first by a van which spun it into the path of another minivan. The physics of such a case are as follows: The first van hit the car off center, resulting in a greater force towards one side of the car such that it spun from the unbalanced force applied instead of merely stopping or moving in the opposite direction. After this, it was hit again by an oncoming minivan.

While spinning, the car displayed another force, called Centrifugal Force, which is essentially force that is formed with spinning objects; a tendency to move away from the center with which an object spins. It was either this centrifugal force or the the impact on the second minivan which brought about the ejection of the baby and her car seat, from the car. The first collision with the first van probably loosened the straps holding the car seat down.

Reflections
My own insight into car collisions is that they can be prevented. Current technology has enabled many new safety features into cars such as airbags, seatbelts, shock absorbers, and many more. Also, with stricter traffic rules and regulations combined with less drink driving and constant eye-checks for drivers above the age of 50 ( to ensure that they can still see the road while driving), the number of accidents can be improved dramatically, maybe even prevented altogether.
The physics of car collisions may seem complicated at first, but really, they are quite simple and basic knowledge of Newton’s three laws is quite sufficient to understand them.

Sources:
- http://www.singstat.gov.sg/pubn/reference/yos09/statsT-transport.pdf
- http://csep10.phys.utk.edu/astr161/lect/history/newton3laws.html
- http://www.benbest.com/lifeext/causes.html
- http://answers.yahoo.com/question/index?qid=20090426180108AAdIFN8
- http://caraccidentattorney-losangeles.com/car-accident-claims-los-angeles/what-is-the-physics-behind-car-crashes/
- http://www.icm.tn.gov.in/idsp7.htm
- http://en.wikipedia.org/wiki/Traffic_collision
- http://physics.about.com/od/energyworkpower/f/energyforcediff.htm

- http://www.king5.com/news/local/Child-ejected-from-vehicle-in-Seattle-crash-80639202.html