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The Georgia Police Academy
Traffic Accident Reconstruction Level II
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Background and Purpose
In some instances, vehicles may leave the ground at some point during the accident sequence. When this occurs, the vehicle’s speed may be determined provided the accident investigator collects several pieces of crucial information from the accident scene.
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Traffic Accident Reconstruction Level II, introduces students to the proper techniques for collecting and evaluating evidence associated with accident vehicles that fall, flip, or vault. Students who successfully complete this course learn the procedures necessary to accurately estimate the speed of accident vehicles involved in this type of accident.
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Terminal Performance Objective
Given a simulated traffic accident, students will accurately evaluate falls, flips and vaults for the purpose of estimating the speed of objects that travel through the air.
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Enabling Objectives Define and describe falls, flips and vaults
List three kinds of information needed to calculate the speed of objects that fall, flip or vault Demonstrate an ability to estimate speed from falls, flips and vaults Define and describe uniform projectile motion
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Definitions Many traffic accidents occur in which a vehicle will travel through the air. This motion can usually be considered as a fall, flip, or vault. As accident investigators we are called upon to estimate takeoff speeds. If certain information is gathered at the scene, such as the point where the vehicle left the ground and the point where it first came back into contact with the ground, you might be able to determine the speed of the vehicle when it first left the ground.
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The definition of a fall, flip, or vault must be understood by the accident investigator.
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Fall - A fall occurs when a vehicle is traveling forward and is no longer supported by the surface it is moving over. At the beginning of the fall the vehicle can be going uphill, downhill, or on a level surface. A side slipping vehicle could experience a fall also. In fall situations the vehicle will generally land lower than the takeoff point. In some situations the landing point could be higher than the takeoff point.
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Flip - Flips occur when vehicles are moving sideways and the resistance at the tires is sufficient to cause the vehicle to rise and move through the air. This can be caused by the wheels hitting a curb or furrowing in loose material. Vehicles "tripped" in this manner generally travel through the air horizontally for a considerable distance.
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In these situations it is difficult to determine the takeoff angle
In these situations it is difficult to determine the takeoff angle. Consequently, a takeoff angle that will give a minimum speed is assumed. A rollover is sometimes used to describe a flip. However, rollovers may occur without the wheels striking a curb or furrowing in loose material. Therefore a rollover and a flip are not the same.
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Vaults - Vaults are similar to flips, except they are "end-over-end" flips. A vehicle which vaults must be moving forward instead of sideways. The term vault is often interchanged with the term fall. They are not the same.
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The most accurate estimates of speed in accident reconstruction are those made from reliable observations and measurements in a situation where the vehicle left the ground and fell through the air before landing. In fall situations the vehicle nearly always lands right side up, although it may roll or flip after it lands.
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A car which is moving through the air and is no longer supported by the ground, tends to keep moving in a straight line in the direction it was headed when it left the ground. The weight of the car (force of gravity) makes it fall toward the ground with increasing vertical velocity until it lands (what goes up, must come down). If grade is present at the takeoff point (either up or down) the car will have a vertical component of velocity.
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Principles In the vertical direction, gravity is the only force acting on the car. It causes the car to be accelerated downward at a rate of 32.2 fps². The car's horizontal component of velocity will remain essentially the same at landing as it was at takeoff. The only force acting on the car as it travels through the air is air resistance. Since the distances traveled by cars through the air is relatively short, the effect of air resistance is negligible and does not have to be considered.
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If we can develop equations to determine the time it takes a car to travel both the vertical and horizontal distances in a fall, then we can also calculate the velocity of the car at the beginning of the fall.
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Information Needed To make speed calculations from vehicles which have traveled through the air, the following information is needed:
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The horizontal distance traveled by the vehicle's center mass from where it left the ground to where it landed The vertical distance traveled by the vehicle's center mass from where it left the ground to where it landed The angle of takeoff of the path the vehicle was traveling before it left the ground
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Information Needed Normally, a vehicle does not come to rest where it strikes the ground. It rolls or slides on the surface until it stops. Measurements must be made from the point where the vehicle left the ground to its position when it first landed. The investigator must be certain that he measures to the first point of ground contact. The takeoff angle must be measured along the path the vehicle actually traveled before it left the ground. This path is often shown by tire marks of one kind or another.
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Measuring and calculating the takeoff angle (G = V/H Inv. Tan)
Example: vertical measurement = 3 inches; horizontal measurement = 48 inches G = V/H G = 3/48 G = .0625 1 = Inv Tan of G 1 = Inv Tan = 3.57 degrees
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Measuring the distance a vehicle falls when it takes off into the air may be quite simple or a bit complicated. The spot where the vehicle took off is located by coordinates or triangulation. Measuring the vertical fall is more difficult when the vehicle goes off the top of a bank into a deep ditch.
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You will usually have little difficulty determining where the takeoff was. Landing is not so simple. It is usually marked by scars in the bank or ground or tire marks on hard surfaces. Remember the distance traveled by the vehicle's center mass must be calculated.
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Match the marks at the landing point to the object on the vehicle which made the marks and adjust for distance traveled by center mass.
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Some special equipment may be needed to measure accurately a large or long vertical drop. A surveyor, who has special equipment, may have to help in some cases. However, the simplest equipment such as string and line level, measuring tapes, and a carpenter's level will work for most situations.
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When the vehicle falls a considerable distance the investigator may have to measure the fall using the "step" method or another method which involves using trigonometry.
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Example (Trig) From takeoff to first landing distance is 100 feet (hypotenuse). The angle of the tape measure pulled directly from takeoff to landing is V = 10 inches, H = 48 inches. G = V/H G = 10/48 G = .208 Inv Tan = degrees, Sin =.203, Cos = .978
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Multiply the distance (100 feet) times the sine to get (h) the vertical distance, and the distance times the cosine to get (d) the horizontal distance. .203 (100) = 20.3 feet; .978 (100) = 97.8 feet
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Equation The equation to calculate the speed of a vehicle at the point of takeoff is: S = 2.73 d/%d Sin 1 Cos 1 - h Cos² 1 S = Speed at takeoff d = Distance traveled horizontally by the vehicle's center of mass from takeoff to landing.
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h = Distance traveled vertically by the vehicle's center of mass from takeoff to landing. The value of h is positive if the landing point is above the takeoff point, and negative if the landing point is below the takeoff point.
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1 = The angle of takeoff as measured relative to a horizontal plane
1 = The angle of takeoff as measured relative to a horizontal plane. If the takeoff angle is uphill the sine and cosine value of that angle will be calculated. If the takeoff angle is downhill the angle will be subtracted from 360 and the sine and cosine value calculated.
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Examples: Distance = 50 feet Height = 3 feet (vehicle lands lower than takeoff) Takeoff Angle = 10 degrees uphill
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S = 2.73 d/%d Sin 1 Cos 1 - h Cos² 1 S = 2.73 (50)/%50 (.173) (.984) - (-3) (.984)² S = 136.5/% (-3) ( ) S = 136.5/% ( )
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S = 136.5/% S = 136.5/% S = 136.5/ S = mph (
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Distance = 40 feet Height = 1 foot (vehicle lands lower than takeoff) Takeoff Angle = 5 degrees uphill
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S = 2.73*40//40*.087*.996-(-1*.992) S = 109.2//3.466-(-.992) S = 109.2// S = 109.2//4.458 S = 109.2/2.11 S = mph (
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Distance = 60 feet Height = 5 feet (vehicle lands lower than takeoff) Takeoff Angle = 4 degrees uphill
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S = 2.73*60//60*.069*.997-(-5*.995) S = 163.8//4.127-(-4.975) S = 163.8// S = 163.8//9.102 S = 163.8/3.01 S = mph (
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Distance = 45 feet Height = 2 feet (vehicle lands higher than takeoff) Takeoff Angle = 11 degrees uphill
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S = 2.73*45//45*.190*.981-(2*.963) S = // S = //6.461 S = /2.54 S = mph (
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Distance = 26 feet Height = 4 feet (vehicle lands higher than takeoff) Takeoff Angle = 12 degrees uphill
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S = 2.73*26//26*.207*.978-(4*.956) S = 70.98// S = 70.98//1.439 S = 70.98/1.19 S = mph (
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Distance = 44 feet Height = 6 feet (vehicle lands lower than takeoff) Takeoff Angle = 5 degrees downhill
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S = 2.73 *44/%44 (-.087) (.996) - (-6*.992) S = /% (-5.952) S = /% S = /% S = / S = mph (
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Distance = 49 feet Height = 10 feet (vehicle lands lower than takeoff) Takeoff Angle = 8 degrees downhill
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S = 2.73*49//49*-.139*.990-(-10*.980) S = // (-9.8) S = // S = //3.058 S = /1.74 S = mph (
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Distance = 35 feet Height = 2.5 feet (vehicle lands lower than takeoff) Takeoff Angle = Level
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S = 2.73*35/%35*0*1-(-2.5*1) S = 95.55/%0+2.5 S = 95.55/ S = mph (
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You can say the speed calculated is how fast a vehicle would have had to be going to takeoff on the slope where it left the ground and traveled the distance horizontally while dropping the vertical distance to its landing spot. This is neither a maximum nor a minimum speed. If the measurements are accurate, you could not say that the vehicle would have had to be going faster or slower than the speed calculated. Therefore, the calculated speed is a very good estimate.
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Finding the vehicle's position when it first landed can be a difficult process, especially if the landing place is a steep slope, a water surface, or is covered with rocks or trees. Establishing the landing position may involve considering three circumstances:
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Dimensions of the vehicle, to determine the location of its center of mass;
Scars on the ground showing where the vehicle first landed; Damage to the vehicle showing which part of it struck the ground first.
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A scale diagram profiling the vehicle at its takeoff point and landing point should be made to establish the horizontal and vertical distances traveled.
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Speeds from falls, flips, and vaults can not be combined with any speed after the fall, flip, or vault.
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Unknown Takeoff Angles (Flips)
Previously we have dealt with examples of falls. The equation to determine the speed of vehicles which flip is the same as that for vehicles which fall. Flips are quite different in that the determination of the takeoff angle can be very difficult.
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A flip will occur when the vehicle strikes an object that stops forward movement of part of the vehicle at or near the ground. The rest of the vehicle tends to keep going in the direction the vehicle was initially heading. It can only do this by pivoting on the part that is stopped, usually a wheel.
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This pivoting requires that the vehicle's center of mass rise or lift
This pivoting requires that the vehicle's center of mass rise or lift. While in the air the vehicle can rotate rapidly causing it to land upside down. The vehicle will rarely stop where it first lands but will continue to roll until it comes to rest.
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Speed estimates from flips require the same information as those from falls. The investigator must document the horizontal distance the vehicle's center mass moved through the air from takeoff to landing. The vertical distance traveled by the vehicle's center mass between takeoff and landing must also be measured as well as the takeoff angle.
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As previously mentioned, determining the takeoff angle for vehicles that flip is difficult and can rarely be determined accurately. An equation can be used to calculate the angle which will give a minimum speed. The result will be an angle of approximately 45 degrees which will give the greatest distance for the lowest speed.
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The equation for the angle, 1, that allows the minimum speed estimate to be calculated is:
1 = Inv Cos [-h/%(d² + h²)]
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Inv Cos = Inverse cosine of everything in the brackets
1 = Angle which will give the minimum speed h = Height of fall (+h is the vehicle lands higher than takeoff and -h if it lands lower) d = Horizontal distance 2 = Constant
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Example Assume an accident vehicle flips and travels 28 feet horizontally landing 6 inches higher than takeoff. The takeoff angle can not be determined from evidence at the accident scene.
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1 = Inv Cos [-h/%(d² + h²) 2 1 = Inv Cos [-(+.5)/%(28² + .5²)]
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1 = Inv Cos [-.5/%( )] 2 1 = Inv Cos [-.5/%784.25]
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1 = Inv Cos [-.5/28] 2 1 = Inv Cos[-.017] 1 = 91.02 1 = 45.51
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S = 2.73 d/%d Sin 1 Cos 1 - h Cos² 1 S = 2.73 (28)/%28 (.713) (.700) - (+.5) (.700)² S = 76.44/% (+.5) (.490)
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S = 76.44/% S = 76.44/% S = 76.44/3.70 S = mph (minimum speed)
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Examples: Distance = 39 feet Height = 1.5 feet (vehicle lands lower than takeoff) Takeoff Angle = Unknown
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1 = Inv Cos [-(-1.5)//(39²+ -1.5²)]
2 1 = Inv Cos[-(-1.5)//( )]
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1 = Inv Cos [-(-1.5)// ] 2 1 = Inv Cos [1.5/39.02]
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1 = Inv Cos [.038] 2 1 = 87.82/2 1 = degrees
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S = 2.73*39//39*.693*.720-(-1.5*.519) S = //19.45-(-.778) S = // S = //20.22 S = /4.497 S = mph (
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Distance = 52 feet Height = 2 feet (vehicle lands lower than takeoff) Takeoff Angle = Unknown S = mph
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Distance = 41 feet Height = 2.25 feet (vehicle lands higher than takeoff) Takeoff Angle = Unknown S = mph
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Speeds from flips calculated in this manner are subject to the usual, generally minor errors reflecting inaccuracies of original measurements. Using any angle larger or smaller than the angle given by the equation will result in a higher speed. The calculation assumes that the angle of takeoff is that at which the vehicle would go farthest for its speed.
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Additional speed is lost in tearing up the ground or possibly damaging wheels (for example, when curbs are struck). Therefore, it can be said that the speed of the vehicle was actually greater than that estimated, possibly much greater, so the calculated speed is a minimum.
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Derivation The fall, flip, and vault speed equation is based on a concept in physics called uniform projectile motion. This concept says that motion in the horizontal direction and motion in the vertical direction are independent of one another.
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The Fall equation is based on a concept in physics called Uniform Projectile Motion. This concept means that motion in the horizontal direction and motion in the vertical direction are independent of one another. The time it takes a vehicle to move through the air vertically is the same time it would take it to move through the air horizontally.
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Project 5 Answers 1. 35.94 mph 9. 52.19 mph 2. 65.22 mph 10. 22.44 mph
miles mph mph mph degrees , .029, .999 mph , .999, 1.43 deg mph
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