Extraction of Pedestrian Crossing Speeds From Collision Evidence

In fatal pedestrian to vehicle collisions, accident investigators must attempt to reconstruct events that led up to the collision to determine liability in a court of law. In the absence of suitable video footage, the vehicle speed is calculated using particle based throw distance calculators such as the Searle method. Until recently, no methods concentrated on the velocity of the crossing pedestrian, vital for determining responsibility. A new approach, the Pedestrian Crossing Speed Calculator (PCSC), which uses evidence left on the bonnet and windscreen along with pedestrian anthropometry to calculate a pedestrian crossing speed, has been proposed in a previous research, and validated against three real accidents where the pedestrian approach was orthogonal to the vehicle. The range of application of the PCSC theory is investigated in this paper. This study has considered 48 Finite Element simulations to further validate the PCSC against a saloon type and SUV vehicles. In the case of the saloon type, the PCSC theory for a pedestrian crossing approach angle <10°, i.e. a pedestrian crossing trajectory no longer perpendicular to the vehicle trajectory, has been fully vindicated. The study has also confirmed the PCSC hypothesis stating that for saloon vehicles the relationship between and increase in bonnet dent width was caused by an increase in pedestrian gait angle. The study also concluded that the PCSC theory was less conclusive in the case of SUV collisions. This paper confirms that PCSC is unique and can have an important role in the field of accident reconstruction and for law enforcement; with the potential to determine vehicle speeds from a known pedestrian crossing speed, which will allow the calculation of the vehicle velocity in the absence of physical evidence left on the road surface. Nomenclature Extraction of Pedestrian Crossing Speeds From Collision Evidence C Bastien H Davies, B Rubrecht, R Wellings and B Burnett 1 Transport Safety and Simulations Group, Institute for Future Transport and Cities (IFTC), Coventry University, Coventry, UK 2 University Hospital of Coventry and Warwickshire, Clifford Bridge Road, Coventry, UK * Corresponding Author : Christophe Bastien, Department of Future Transport and Cities, UK. Introduction 1.1 The Pedestrian Crossing Speed Calculator (PCSC) Theory Pedestrian collisions are often tragic and sometimes even fatal events that happen all around the world. These events are caused by the pedestrian, careless driving or a combination of the two. The Police authorities are then responsible for gathering all the evidence leading to the fatal collision. Evidence can be found in multiple ways, like video footage (either CCTV or dashcam), data from the vehicle ECU, witness statements and physical evidence left on the road, such as skid marks. Pedestrian throw distance calculators such as Searle’s method can then be used with physical evidence to estimate the velocity corridor the vehicle was expected to be travelling in, although using this method, the crossing speed of the pedestrian cannot be ascertained. The Pedestrian Crossing Speed Calculator (PCSC) [1] is a new particle based method of accident reconstruction that uses physical evidence left on the Page 26 ‘Impact’ : Spring 2021 ECU Electronic Control Unit. A generic term for any embedded system that controls one or more of the electrical systems or subsystems in a motor vehicle H Lateral distance between vehicle dent and windscreen damage W Longitudinal distance between vehicle dent and windscreen damage  Angle of the actual pedestrian head centre of gravity between the location at initial strike to its location on the windscreen along the vehicle travelling direction  Theoretical angle between the pedestrian velocity and the vehicle velocity  Head offset to the bumper impact location. It compensates offset by half a pedestrian stride length θ Pedestrian gait angle  Pedestrian crossing angle relative to the vehicle direction Vped Pedestrian crossing velocity UKPF UK Police Force CoG Centre of Gravity CI Confidence Interval front end of the vehicle to calculate the crossing speed of the pedestrian. Not only this, but if the pedestrian crossing speed is known, then it can be applied in reverse to find the velocity of the vehicle. When a pedestrian impacts a vehicle, the first point of contact is between the bumper and knee [2][3]. After initial contact, the pedestrian rotates about the bonnet leading edge and hits the windscreen, the impact of which is offset laterally and longitudinally from first contact [4]. This head contact location is heavily influenced by two factors; the front-end geometry of the vehicle and the height of the pedestrian. A bonnet with a lower height leading edge carries the pedestrian further onto the vehicle [5] and a tall pedestrian is 17% more likely to hit the windscreen [6]. Figure 1 shows an example of the pedestrian kinematics with different front-end geometries, using Madymo a pedestrian multi-body computer model [1]. The Searle method is currently used in UK court proceedings, which is a particle-based mathematical model which uses evidence markers such as skin marks and pedestrian throw distance to calculate a vehicle velocity [8]. It has been shown to compare well to a collection of accident data, predicting vehicle velocities close to the known values [9]. Several deficiencies exist however with this method. A constant friction coefficient of 0.7 is used, which is not representative of a change in road condition, i.e. dry (0.73), wet (0.67), icy (0.30) [10]. Differences in velocities between the pedestrian and vehicle at the moment of impact also require the use of a projection efficiency, which is dependent on vehicle front end geometry. The Pedestrian Crossing Speed Calculator (PCSC) is a new forensic investigation tool that can be used to calculate the crossing speed of a pedestrian. It assumes the pedestrian to be a particle, and uses vector algebra to determine a directional vector post-impact. The basic theory of the PCSC is based on the ratio between two angles [1]: Equation 1 – Basic theory of PCSC The first angle, λ, is the absolute angle of the pedestrian-vehicle velocity vector, which can be seen in Figure 2. This vector is measured using two impact locations, the dent left on the leading edge of the bonnet by the pedestrian’s leg, and the dent left at the top of the bonnet or windscreen by the pedestrian’s head. Equation 2 shows how λ is calculated. Equation 2 Absolute angle of the pedestrianvehicle compound velocity vector. The angle β, on the other hand, is the pedestrian head approach angle between impacts of the leg on the bumper and the head on the windscreen. The lateral distance between these points is W, and the longitudinal distance between them is H, as observed in Figure 3. It is assumed in Equation 2 that the pedestrian is travelling on a path perpendicular to the vehicle’s ‘Impact’ : Spring 2021 Page 27 Figure 1 Difference in pedestrian kinematics when stuck by vehicles with different front-end geometries [7]. Figure 2 Resultant velocity vector generated by the pedestrian and vehicle velocities. direction of travel. This may not always be the case and so a non-zero approach angle between the pedestrian and vehicle can be observed. This change of angle is included in Equation 3, where  is the approach angle of the pedestrian. Equation 3 reverts to Equation 2 when the approach angle  is zero. The correction value is added to the vehicle velocity if the pedestrian is travelling towards or away from the car. Equation 3Absolute angle of the pedestrian-vehicle compound velocity vector with pedestrian approach angle included. It should also be noted that there are infinite ratios of vehicle-pedestrian velocities which can fulfil λ. The velocity ratio can be calculated from the impact evidence observable on the vehicle. The angle β, on the other hand, is a function of W and H and needs to include the pedestrian’s head offset from the leg impact location. This offset is captured in the term generic, and as such β can be calculated as per Equation 4. Equation 4 Head approach angle of the pedestrian between bumper and windscreen impact points.  can be a positive or negative value If the pedestrian’s head is forward of the bonnet impact point, the head approach angle β will be smaller than λ. If the pedestrian’s head is trailing the bonnet impact point, then β will be greater than λ. Considering  being the angle between the crossing pedestrian and the vehicle, Equation 5 gives an expression for the distance generic, which depends on the pedestrian’s condition pre-impact, i.e. width of pedestrian gait, anthropometrics etc. Equation 5 Head offset from impact point. The distance generic, expressed in Equation 5, is illustrated in Figure 5, where L is the pedestrian leg Page 28 ‘Impact’ : Spring 2021 Figure 3 Pedestrian impact locations. Figure 4 Effect of head position relative to the leg impact location. length, F is the height of bumper impact and θ is the pedestrian gait width. Equating λgeneric (Equation 3) and βgeneric (Equation 4) produces Equation 6, which is the final Pedestrian Crossing Speed Calculator (PCSC) equation: Equation 6 Full PCSC equation. The head position relative to the leg impact location will be determined by anthropometric factors, such as leg length and the condition of the pedestrian pre -impact. This condition is based on the hip gait angle of the pedestrian, θ. The distance between the bonnet impact location and the pedestrian’s head will be larger for a wider pedestrian stance and near zero for a standing stance. Table 1 summarises the maximum hip gait angles for a given stance. It must be noted that this does not divulge the crossing speed. For example, a pedestrian crossing at running speed can have a running gait, as well as a standing or walking gait depending where in their stride they are at impact. Table 1 Pedestrian con