Forensic Accident Investigations, Inc. Fundamentals of Traffic Accident Reconstruction Robert C. McElroy, Ph.D.
Traffic Accident Investigations: Why and How? Traffic Accident Reconstruction Mathematics - Newton’s Laws - Energy - Example - Momentum - Example Animation and Simulation Introduction
Many accidents have serious consequences. Economic - Repairs to vehicles, structures. - Denial of resources personally or commercially. Physical - Serious Injury - Permanent Disability - Death In most accidents at least two people are involved, each of whom will blame each other. Why perform Accident Investigations? Determining what happened is important.
Accident Investigation Process Collect data from many sources Inspect and photograph - Accident site - Vehicles Review official reports - Police Traffic Crash Report - Traffic Homicide Report (if any) - Fire / Rescue Reports - Hospital / Coroner Reports Statements - Drivers - Witnesses Any Other Documents - Dispatch Records - Tow Truck Operator Statements - US DOT and NHTSA Publications - Applicable Laws or Statutes
Traffic Accident Reconstruction Analyze collected data to generate a timeline of events. Human Factors Environmental Factors Physical Factors - Newton’s Laws - Energy - Momentum
Newton’s First Law “ An object at rest will remain at rest and an object in motion will continue to move at a constant speed in a straight line unless, in either case, the body is acted upon by an outside force.” The Law of Inertia
Newton’s Second Law “ The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass.” Force = mass x acceleration F = m a acceleration = Force / mass a = F / m mass = Weight / force of gravity m = W / g
Newton’s Third Law “ Whenever one body exerts a force upon a second body, the second body exerts an equal and opposite force on the first body.” Force 1 on 2 = Force 2 on 1 The Law of Reciprocity Action = Reaction Examples - Billiard Balls - Punching Someone (hurts their jaw and your hand) - Yelling at your Spouse (gets you yelled at in return)
Conservation of Energy “ Energy is neither created nor destroyed, it only changes form.” Some Types of Energy - Chemical (gasoline) - Potential (gravity) P e = m g h - Kinetic (motion) K e = 1/2 m v 2 - Work (force) W e = F d
Slide to Stop 1. Work done to stop a vehicle = Kinetic energy prior to skid a) W e = F d b) K e = 1/2 m v 2 2. Recall Newton’s Second Law: F = m a 3. Substitute c) m = W / g and d) a = g f F = (W / g) g f -> F = W f 4. Substitute into a) W e = W f d 5. Substitute c) into b) K e = 1/2 (W / g) v 2 6. Set 4. Equal to 5. W f d = 1/2 (W / g) v 2 7. Simplify to 2 g f d = v 2 [or] v = 2 g f d g = 32.2 ft / s2 8. Finally v = 64.4 f d (ft/s) [or] s = 30 f d (mph) Typical Accident Reconstruction Equation Derivation of basic principles for a common situation
Measured skid distance is 45 feet and deceleration factor for the vehicle & road surface combination is .7 G . Slide to Stop Example Use derived formula for a typical case The vehicle is calculated to have been going 30.7 mph when the brakes were applied.
Eq Group Eq # Problem Description Speed 1 Speed from Distance & Drag 2 Constant Speed from Distance & Time 3 Speed from Drag & Time 4 Final Speed from Start Speed, Drag & Time 5 Final Speed from Start Speed, Drag & Distance 6 Start Speed from Final Speed, Drag & Time 7 Start Speed from Final Speed, Drag & Distance Time 10 Time from Constant Speed & Distance 11 Time from Speed & Drag 12 Time from both Speeds & Drag 13 Time from Distance & Drag Distance 20 Distance from Speed & Drag 21 Distance from Constant Speed & Time 22 Distance from Two Speeds & Drag 23 Distance from Initial Speed, Drag & Time Acceleration 30 Drag from Speed & Distance Factor 31 Drag from Speed & Time 32 Drag from both Speeds & Time 33 Drag from both Speeds & Distance 34 Drag from Distance & Time 35 Drag from Initial Speed, Distance & Time 36 Drag from Road Friction, Brake Efficiency & Grade 37 Drag from Horizontal Force & Weight Linear 40 General Two-Dimensional Momentum Momentum 41 Inline - V1 from V2, V3, and V4 42 Inline - Coefficient of Restitution 43 Inline - Plastic, V3 = V4 44 Inline -Elastic Special 45 Tangent Offset 46 Radius from Chord and Mid-Ordinate 47 Critical Curve Speed 48 Combined Speed from Drag Surfaces 49 Combined Speeds Airborne 50 Horizontal Launch and Fall Speed 51 Small Angle Speed at Launch Equation 52 General Projectile Speed Equation Energy 60 Speed from Linear Kinetic Energy 61 Kinetic Energy from Speed and Weight 62 Force from Kinetic Energy and Distance 63 Distance from Kinetic Energy and Force Motorcycle 70 Lateral Acceleration Factor from Speed and Radius 71 M/C Lean angle from Speed and Radius 72 Turning Radius From Speed and lateral acc Animation 80 Final Speed from Start Speed, Drag and Time Assist 81 Distance from Start Distance, Speed, Drag and Time Reaction 90 Total D from P/R time, Speeds & Drag f Times 91 Total D from Start Speed, Times & f 92 P/R Time from Speeds, Total D & f 93 P/R Time from Start Speed, Total D, f & Time 94 Start Speed from Total D, Times & Drag 95 Start Speed from Total D, Final Speed, P/R Time & f 96 Drag from Speeds, P/R Time & Total D 97 Drag from Start Speed, Total D & Times 98 Total Time from P/R Time, Speeds & f 99 Total Time from P/R Time, Brake D & Drag General Equations Commercial Software Packages Aid in Calculations
Derivation of Momentum Equation Recall Newton’s Second Law … 1. Force = mass x acceleration F = m a 2. acceleration = velocity / time a = v / t 3. Substitute 2. into 1. F = (m v) / t 4. More algebra Impulse-> F t = m v 5. Define mass m = W / g 6. Substitute 5. into 4. F t = (W v) / g 7. Yet more algebra (F t g) = W v Assume at point of collision, no external forces act on vehicles. Recall Newton’s Third Law (Force 1 on 2 = Force 2 on 1 ). Time and gravity constant for both vehicles. W 1 V 1 = W 2 V 2 [or] W 1 V 1 + W 2 V 2 = W 1 V 3 + W 2 V 4 At collision Pre-collision Post-collision
Momentum Example Smith v. Jones Recall Momentum Equation: W 1 V 1 + W 2 V 2 = W 1 V 3 + W 2 V 4 Solve for V 3 + V 4 using skid to stop. Solve Equation in x and y for V1 and V2. Solve for original speeds using eqn #5. Smith = Ford Escort 2000 lbs 45 ft post crash skid 30 ft pre crash skid entry angle = 270 departure angle = 318 f = .7 Jones = Ford F-350 3500 lbs 25 ft post crash skid 15 ft pre crash skid entry angle = 0 departure angle = 300 f = .7
Momentum Programs Commercial Software Packages Aid in Calculations