The Georgia Police Academy

1. The Georgia Police Academy Traffic Accident Reconstruction Level V

2. Background and Purpose The National Highway Traffic Safety Administration (NHTSA), requires that automobiles sold in this country meet crash worthiness standards. Each automobile manufacturer must provide new automobiles for the purpose of crash testing so NHTSA can verify that the standards are being met. When crash tests are done all the data is collected and maintained. Since the tests are done in a controlled environment the vehicle’s speed and resulting crush damage are known.

3. This testing has allowed engineers to develop a mathematical model that can be used to measure a vehicle’s speed based on the amount of crush damage it receives in a collision. Although its application is limited, this information does provide traffic accident investigators with another tool that may be used to calculate speed. Traffic Accident Reconstruction Level V, introduces students to the proper techniques for making accurate speed estimates from crush damage.

4. Critical issues such as work, energy, the conservation of energy, equation application and the energy equation derivation are addressed. Students who successfully complete this course should have the knowledge and confidence to accurately estimate speed from vehicle crush in some instances.

5. Terminal Performance Objective Given a simulated traffic accident, students will evaluate vehicle crush data to accurately calculate vehicle impact speeds.

6. Enabling Objectives • Demonstrate the ability to use work, force and distance to calculate energy. • Demonstrate one method for calculating elastic potential energy when force constant and distance are known. • Define the Law of Conservation of Energy. • Demonstrate one method for calculating energy of a vehicle that skids over numerous surfaces, when weight, drag factor and distance are known.

7. Enabling Objectives (con’t) • Demonstrate two methods for calculating vehicle speed when the amount of crush and after impact vehicle dynamics are known. • Define the terms dynamic collapse and restitution as they apply to vehicle damage.

8. Work Technically, work is done when a force acts on an object through a distance. Work is also a measure of the effect force has on changing an object. The amount of change or work done is reflected in changes in the object's velocity, position, size, and shape.

9. Work can be described mathematically as the product of the force (F) and the distance (d) through which it acts, provided the force and distance covered are in the same direction. This may be written in equation form: W = Fd

10. Remember from past courses that the unit for force is pounds (lb) and the unit for distance is feet (ft). W = Fd F = force (lb) d = distance (ft) W = work (ft-lb)

11. Example Assume a force of 300 lbs is required to push a box 20 feet. Calculate the amount of work done.

12. W = Fd W = (300 lbs) (20 ft) W = 6000 ft-lbs

13. If the force and distance are not in the same direction, then the equation is rewritten. W = Fd Cos 1

14. Example Assume the force is equal to 300 lbs, the angle is 45 degrees, and the distance is 20 feet. Calculate the amount of work done.

15. W = Fd Cos 1 W = (300) (20) (Cos 45E) W = 4242 ft-lbs

16. Work is the product of the magnitudes of force and distance. Therefore, work is a scalar quantity. Being a scalar quantity, work has only magnitude and sign (positive or negative), but has no direction associated with it. Work is positive if 1 is greater than or equal to 0 degrees but less than 90 degrees. Work is negative if 1 is greater than 90 degrees but less than or equal to 180 degrees.

18. Example Assume the force acting on the vehicle in the previous slide is 1000 lbs, the distance the force acts through is 100 ft, and the angle is 0 degrees. Calculate the amount of work done.

19. W = Fd Cos 1 W = (1000) (100) (Cos OE) W = 100,000 ft-lbs

21. W = Fd Cos 1 W = (2000) (50) (Cos 180E) W = -100,000 ft-lbs

22. Energy When work is done, energy is transferred between different objects. The amount of energy possessed by an object is an indication of its ability to do work. Work and energy are proportional. The more energy an object has, the more work it can perform.

23. Equations can be derived to calculate the amount of energy transferred between objects when work is done under a variety of conditions. These derivations use the positive sign if the object's energy is increased and negative if it is decreased when work is done. This agrees with the previous examples given of the accelerating and decelerating vehicles. The accelerating vehicle is gaining energy and increasing its ability to do work. The decelerating vehicle is losing energy and decreasing its ability to do work.

24. Energy can be grouped into three general categories: • Rest energy • Kinetic energy • Potential energy

25. 1. Rest energy is energy an object possesses due to its mass. This form of energy is related to Einstein's theory of relativity and will not be discussed.

26. 2. Kinetic energy (KE) is energy an object possesses due to its motion. A vehicle in motion has more energy than a vehicle at rest. When a vehicle accelerates, it gains velocity and also increases its energy. The energy of a moving body is equal to:

27. KE = ½mv² • KE = Kinetic energy (ft-lbs) • M = Mass (weight divided by the acceleration of gravity) • v = Velocity (fps)

28. The amount of work required to accelerate the vehicle from rest to a given velocity can be calculated using this equation. The energy calculated is the energy gained by the vehicle and it is kinetic energy. In the equation mass and weight are related by the acceleration due to gravity. Considering this relationship the equation could also be written as follows:

29. KE = wv²/2g KE = Kinetic energy(ft-lbs) w = Weight (lbs) v = Velocity (fps) g = Gravity (32.2 ft/sec²)

30. Example Assume a 3,000 lb vehicle is accelerated from rest to a velocity of 40 fps. Calculate the amount of work done and energy gained.

31. KE = wv²/2g KE = (3000) (40)²/(2)(32.2) KE = 4,800,000/64.4 KE = 74,534 ft-lbs

32. The same amount of work would be required to bring the vehicle to rest. The same amount of energy that was originally gained, would have to be dissipated. Energy is dissipated when it is converted into thermal (heat) energy. This happens as a result of the friction between the tires and road surface, tires and brake system, or through rolling resistance in coasting to a stop.

33. In the derivation of the speed from skid mark equation we learned that the following equation can be used to calculate the amount of kinetic energy that must be converted to another form in order to bring a vehicle to a stop:

34. W = wfd W = Work (ft-lbs) w = weight (lbs) f = drag factor d = distance (ft)

35. Example Assume a 3000 lb vehicle from the previous example skidded to a stop with a drag factor of .71 from 40 fps, it would slide approximately 35 ft. Calculate the amount of work done.

36. W = wfd W = (3000)(.71)(35) W = 74,550 ft-lbs

37. The following two equations can be used to calculate speed estimates from skid marks. • W = wfd • KE = wv²/2g

38. The first equation is used to find the amount of kinetic energy the vehicle dissipated while skidding. The second equation, rearranged to solve for velocity, uses the energy calculated to find the velocity of the vehicle.

39. KE = wv²/2g • Multiply both sides by 2g • 2g * KE = wv²/2g * 2g/1

40. Cancel leaving: • 2g * Ke = wv² • Divide weight from both sides: • 2g * KE/w = wv²/w

41. Cancel leaving • v² = 2g * KE/w • Take the square root of both sides leaving • v = %(2g)(KE)/w

42. Since the quantity of one form of energy is the same as the quantity of any other form of energy, the equation can be written: v = %(2g)(E)/w

43. Example From the previous example, the amount of kinetic energy that was dissipated while skidding was approximately 74,534 ft-lbs and the vehicle weighed 3000 lbs. Calculate the velocity.

44. v = %(2g)(E)/w v = %(2)(32.2)(74,534)/3000 v = %4,800,000/3000 v = %1600 v = 40 fps

45. Kinetic energy is a scalar quantity. The kinetic energy of a given mass depends on the magnitude of its velocity and not on the direction of travel. Any change in kinetic energy depends on the sign of the work done. A positive sign indicates the kinetic energy is increased. A negative sign indicates the kinetic energy is decreased.

46. Acceleration rate is not a factor in kinetic energy. The mass and velocity of a body govern the amount of kinetic energy the body has. The rate at which the body reaches that velocity does not affect the kinetic energy.

47. 3. Potential energy (PE) is energy an object possesses due to its position. Two forms of potential energy will be covered in this course. • Gravitational potential energy (PEh) • Elastic potential energy (PEk)

48. Gravitational potential energy is the energy an object possesses due to its position above some reference plane, usually the surface of the earth.

50. The boxes in the overhead have a downward gravitational force which is their weight (w). The distance moved is the height (h) of the center of mass above its original position. These variables can be substituted into the equation for work: