Accident Studies (Part - 2) - Civil Engineering (CE) PDF Download

Accident data analysis

The purpose is to find the possible causes of accident related to driver, vehicle, and roadway. Accident analyses are made to develop information such as:

1. Driver and Pedestrian - Accident occurrence by age groups and relationships of accidents to physical capacities and to psychological test results.

2. Vehicle - Accident occurrence related to characteristic of vehicle, severity, location and extent of damage related to vehicles.

3. Roadway conditions - Relationships of accident occurrence and severity to characteristics of the roadway and roadway condition and relative values of changes related to roadways.

It is important to compute accident rate which reflect accident involvement by type of highway. These rates provide a means of comparing the relative safety of different highway and street system and traffic controls. Another is accident involvement by the type of drivers and vehicles associated with accidents.

1. Accident Rate per Kilometer : On this basis the total accident hazard is expressed as the number of accidents of all types per km of each highway and street classification.

where, R = total accident rate per km for one year, A = total number of accident occurring in one year, L = length of control section in kms

2. Accident involvement Rate : It is expressed as numbers of drivers of vehicles with certain characteristics who were involved in accidents per 100 million vehicle-kms of travel.

where,R = accident involvement per 100 million vehicle-kms of travel, N = total number of drivers of vehicles involved in accidents during the period of investigation and V = vehicle-kms of travel on road section during the period of investigation

3. Death rate based on population : The traffic hazard to life in a community is expressed as the number of traffic fatalities per 100,000 populations. This rate reflects the accident exposure for entire area.

where, R = death rate per 100,000 population, B = total number of traffic death in one year and P = population of area

4. Death rate based on registration : The traffic hazard to life in a community can also be expressed as the number of traffic fatalities per 10,000 vehicles registered. This rate reflects the accident exposure for entire area and is similar to death rate based on population.

where, R = death rate per 10,000 vehicles registered, B = total number of traffic death in one year and M = number of motor vehicles registered in the area

5. Accident Rate based on vehicle-kms of travel : The accident hazard is expressed as the number of accidents per 100 million vehicle km of travel. The true exposure to accident is nearly approximated by the miles of travel of the motor vehicle than the population or registration.

where, R = accident rate per 100 million vehicle kms of travel, C = number of total accidents in one year and V = vehicle kms of travel in one year

Numerical Example

The Motor vehicle consumption in a city is 5.082 million liters, there were 3114 motor vehicle fatalities, 355,799 motor vehicle injuries, 6,721,049 motor vehicle registrations and an estimated population of 18,190,238. Kilometer of travel per liter of fuel is 12.42 km/liter. Calculate registration death rate, population death rate and accident rate per vehicle km.

Solution Approximate vehicle kms of travel = Total consumption o fuel × kilometer of travel per liter of fuel =5.08 × 109 × 12.42 = 63.1 × 109 km. 1. Registration death rate can be obtained from the equation

Here, R is the death rate per 10,000 vehicles registered, B (Motor vehicle fatalities) is 3114, M (Motor vehicle registered) is 6.72 × 106 . Hence,

2. Population Death Rate can be obtained from the equation.

Here, R is the death rate per 100,000 population, B (Motor vehicle fatalities) is 3114, P (Estimated population) is= 18.2 × 10⁶ .

3. Accident rate per vehicle kms of travel can be obtained from the equation below as:

Here, R is the accident rate per 100 million vehicle kms of travel, C (total accident same as vehicle fatalities) is 3114, V (vehicle kms of travel) is 63.1 × 10⁹ .

Accident reconstruction

Accident reconstruction deals with representing the accidents occurred in schematic diagram to determine the pre-collision speed which helps in regulating or enforcing rules to control or check movement of vehicles on road at high speed. The following data are required to determine the pre-collision speed:

1. Mass of the vehicle

2. Velocities after collision

3. Path of each vehicle as it approaches collision point

Below in Figure 42:4 a schematic diagram of collision of two vehicles is shown that occur during turning movements. This diagram is also known as collision diagram. Each collision is represented by a set of arrows to show the direction of before and after movement. The collision diagram provides a powerful visual record of accident occurrence over a significant period of time. The collision may be of two types collinear impact or angular collision. Below each of them are described in detail. Collinear impact can be again divided into two types :

1. Rear end collision

2. Head-on collision.

It can be determined by two theories:

1. Poisson Impact Theory

2. Energy Theory

 Poisson impact theory

Poisson impact theory, divides the impact in two parts - compression and restitution. The Figure 42:5 shows two vehicles travelling at an initial speed of v₁ and v₂ collide and obtain a uniform speed say u at the compression stage. And after the compression stage is over the final speed is u1 and u2. The compression phase is cited by the deformation of the cars. From the Newtons law F = ma,

where, m₁ and m₂ are the masses of the cars and F is the contact force. We know that every reaction has equal and opposite action. So as the rear vehicle pushes the vehicle ahead with

force F. The vehicle ahead will also push the rear vehicle with same magnitude of force but has different direction. The action force is represented by F, whereas the reaction force is represented by −F as shown in Figure 42:6. In the compression phase cars are deformed. The compression phase terminates when the cars have equal velocity. Thus the cars obtain equal velocity which generates the following equation:

m₁(u − v₁) = −Pc m₂(u − v₂) = Pc                                          (42.7)

where, P_c ≡  dt which is the compression impulse and τc is the compression time. Thus, the velocity after collision is obtained as:

The compression impulse is given by:

In the restitution phase the elastic part of internal energy is released

where, P_r ≡  is the restitution impulse and τ_r is the restitution time. According to Poissons hypothesis restitution impulse is proportional to compression impulse

P_r = e P_c                                                                                       (42.12)

Restitution impulse e is given by:

                                                                           (42.13)

The total impulse is P = P_c + P_r

The post impact velocities are given by:

where ∆v = v₁ − v₂. But we are required to determine the pre-collision speed according to which the safety on the road can be designed. So we will determine v₁ and v₂ from the given value of u₁ and u₂ .