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Whiplash Information: Car Accidents and Whiplash Biomechanics
Whiplash is a serious public issue around the world. Experts estimate that there are 1,000,000 injures from rear end collisions in the US each year, with an annual cost of about $30 billion dollars.
Whiplash injuries are a modern phenomena. The term whiplash was first used 1928, and whiplash injuries started to become more common after World War II with the rise in popularity of the automobile.
Whiplash has been controversial since the 1950’s and remains so 50 years later. The greatest debate regarding whiplash today is the area of low speed collisions, especially injuries arising from accidents with little or no visible vehicle damage.
Most people are not aware that there have been literally hundreds of studies written on the problems of whiplash, and that since 1995 a number of respected scientist have from around the world have made some exciting new discoveries that uncover how the human body can be injured in low speed rear end collisions.
The goal of this video is to acquaint you with these discoveries, show you how low speed rear end collisions result in abnormal motion of the human spine, and describe some of the factors that can increase the rise of occupant injury in these collisions. This information can help us understand and treat whiplash pain, and can direct us to new ways to reduce the number of injuries in the future.
To understand the complexity of whiplash injuries, we first need to look at the basic physics of rear end collisions. These simple concepts of physics explain how the vehicles and occupants move during a crash. There are three concepts we need to understand: momentum, acceleration, and inertia.
MOMENTUM
- Momentum is simply the energy of a moving object, and is mathematically described as being equal to the mass or weight of an object multiplied by its velocity or speed. From this equation we can see that the heavier an object is or the faster it is moving the more momentum it will have.
M=mv
m=mass
v=velocity
For instance a 2,000 lb. car traveling 5 mph will have only 1/2 the momentum of the same car traveling 10 mph. Also a car that weighs 2,000 lb. traveling 10 mph will have 1/2 the momentum of a 4,000 lb. car traveling 10 mph.
Momentum also has another important property. According to the laws of physics, momentum in a collision is always conserved. That is when two objects collide the momentum that existed before the collision must be present after the collision.
As we see here the momentum of Vehicle 1 and Vehicle 2 before the collision must equal momentum of Vehicle 1 and Vehicle 2 After the collision.
m(1)v(1) + m(2)v(1) = m(1)v(2) + m(2)v(2)
Vehicle 1 Vehicle 2 Vehicle 1 Vehicle 2
Before Before After After
This is known as the law of conservation of momentum. Let’s see how this relates to automobile crashes:
- First we will start with a car stopped at a red light. This is known at the Target vehicle. It has a mass of 1,000 kg but it has a velocity of 0 and therefore has a momentum of 0 as well.
- Now the car behind, known as the Bullet vehicle also has a mass of 1,000 kg but is moving at 5 m/sec or 11 mph.
- Therefore before the collision we have a momentum of 0 for the target vehicle plus a momentum of 5,000 for the bullet vehicle for a total momentum before the collision of 5,000.
- According to the law of conservation of momentum, the momentum after the collision must be 5,000.
- Once the bullet vehicle strikes the target vehicle the speeds of the two cars are different.
- After the collision we find that the bullet vehicle has slowed from 5 m/sec to just 1 m/sec. Therefore the momentum of the bullet vehicle is 1 times 1,000 or 1,000.
- Since the Law of conservation of momentum requires the momentum must be 5,000 after the collision, that means that the target vehicle must have a momentum of 4,000 and thus a velocity of 4 meters per second.
- That means that the target vehicle accelerated from 0 m/sec to 4 m/sec.
Let’s look at a different example:
- The bullet Vehicle has the same velocity as before, 5 m/sec, but weighs twice the target vehicle or 2,000 kg. Instead of a momentum of 5,000, the bullet vehicle now has a momentum of 10,000.
- The target vehicle again is stopped and has a momentum of 0, so before the collision we have a momentum of 10,000.
- The bullet vehicle in this example slows down to 1 m/sec after the collision resulting in a final bullet momentum of 2,000.
- To equal the momentum of 10,000 prior to the collision, the target vehicle must have a final momentum of 10,000 minus 2,000 or 8,000.
- Since the mass of the target vehicle is 1.000 lb. the final velocity must be 8 m/sec.
Because the mass of the bullet vehicle was twice the target vehicle, even though the speed of the collision was the same as the first example, the velocity of the target vehicle doubles from 4 m/sec to 8 m/sec.
In other words, although the speed of the crash was the same the collision was twice as severe, because of the increased weight of the bullet vehicle.
These two examples are simpler than what really happens during a collision as we will see later. But it does graphically illustrate that when we are looking at rear end collisions we need to not only examine the speed of the collision, but we also need to take into consideration the weight of the two vehicles involved in the crash
ACCELERATION
- The second concept of physics is acceleration: it is described mathematically as Delta V divided by Delta T. Delta is simply the Greek symbol that means “Change in”. So acceleration is the change in velocity of the object divided by the amount of time in which the acceleration takes place.
a = Dv/Dt
D means ” change in”
In our earlier example describing momentum we saw that in one instance the target vehicle accelerated from 0 m/sec to 4 m/sec. In practically every study on low speed rear end collisions, the amount of time this acceleration takes place is about 100 milliseconds or .1 sec. If we put these numbers into the equation for acceleration we get a result of 40m/sec2.
a=Dv / Dt
From 0 to 4 m/sec
a= 4 m/sec / .1 sec
a= 40 m/sec2
In the second example describing momentum we saw that the target vehicle accelerated to 8m/sec in the same amount of time. Thus the acceleration in the 2nd example is 80m/sec2.
a=Dv / Dt
From 0 to 8 m/sec
a= 8 m/sec / .1 sec
a= 80 m/sec2
To simplify matters, engineers often use the term G Force as short hand to describe acceleration.
- G refers to the amount of acceleration that earth gravity exerts on objects.
- For instance, earth’s gravity is 1 G and the complete absence of gravity is 0 G or 0 gravity.
- Mathematically 1 G is equal to 9.8m/sec2 ( 1 G = 9.8m/sec2)
To calculate G forces we can simply divide the acceleration of the car which was 40m/sec2 in the first example divide by 9.8m/sec2 and we get a result of little over 4 Gs of acceleration.
G Forces
1 G = 9.8m/sec2
40m/sec2 / 9.8 m/sec2 = 4.1 Gs
Inertia
The Final concept of physics that we need to understand when dealing with low speed collisions is the idea of inertia.
Newton’s 2nd law states that
- “Every body continues in its state of rest or uniform motion in a straight line in so far as it may be compelled to change that state by the action of some outside force.”
In plain English this simply means that a stationary object will never move, unless something acts upon it to make it move. Likewise an object that is moving will continue to move until something makes it stops it moving.
We can look at our earlier car crash model and see inertia at work.
- The target vehicle is stopped at a red light and will stay stopped until something makes it move. In this example the bullet vehicle.
- Likewise the bullet vehicle will keep moving forward until something makes it slow down. In this case the car in front of it.
- Most importantly, inertia plays a critical role on how the human body moves during a crash, and is the primary reason why people get hurt in low speed impacts.
Review the basics of a rear end collision
Let’s now review the basics of a rear end collision:
- The target vehicle is stopped at a red light.
- The bullet vehicle has both mass and velocity and therefore it has momentum.
- The bullet vehicle strikes the target vehicle applying an external force to the target vehicle.
- The target vehicle is accelerated forward rapidly.
Now that we understand what happens to the cars during a rear end collision. We can now examine the motion of the occupant inside the vehicle.