# The predictive capacity of the MADYMO ellipsoid pedestrian model for pedestrian ground contact kinematics and injury evaluation

Shi Shang, Catherine Masson, Maxime Llari, Max Py, Quentin Ferrand, Pierre-Jean Arnoux, Ciaran Simms

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Shi Shang, Catherine Masson, Maxime Llari, Max Py, Quentin Ferrand, et al.. The predictive capacity of the MADYMO ellipsoid pedestrian model for pedestrian ground contact kinematics and injury evaluation. Accident Analysis & Prevention, 2021, 149, pp.105803. 10.1016/j.aap.2020.105803. hal-04082952

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
The predictive capacity of the MADYMO ellipsoid pedestrian model

for pedestrian ground contact injury evaluation

Shi Shang¹, Catherine Masson², Maxime Llari², Max Py², Quentin Ferrand², Pierre-Jean Arnoux ², Ciaran
Simms¹

¹Trinity Centre for Bioengineering, Trinity College Dublin, Ireland

² Laboratoire de Biomécanique Appliquée (IFSTTAR – Université de la Méditerranée), France

Email: (sshang@tcd.ie)

Abstract

Pedestrian injuries occur in both the primary vehicle contact and the subsequent ground contact.
Currently, no ground contact countermeasures have been implemented and no pedestrian model has
been validated for ground contact, though this is needed for developing future ground contact injury
countermeasures. In this paper, we assess the predictive capacity of the MADYMO pedestrian model
in reconstructing six recent pedestrian cadaver ground contact experiments. Whole-body kinematics
as well as vehicle and ground contact related *HIC* and *BrIC* scores were evaluated. Reasonable
results were generally achieved for the timings of the principal collision events, and for the overall
ground contact mechanisms. However, the resulting head injury predictions based on the ground
contact *HIC* and *BrIC* scores showed limited capacity of the model to replicate individual
experiments. Sensitivity studies showed substantial influences of the vehicle- pedestrian contact
characteristic and certain initial pedestrian joint angles on the subsequent ground contact injury
predictions. Further work is needed to improve the predictive capacity of the MADYMO pedestrian
model for ground contact injury predictions.

Keywords

Pedestrians, vehicle contact, ground contact, MADYMO model assessment
# 1. Introduction

The World Health Organization (WHO) estimates that more than 300,000 pedestrians have died in 2019 (WHO 2020), based on its Global Status Report on Road Safety 2018 (WHO 2018). Pedestrian collisions usually involve a primary contact with the vehicle, followed by a secondary contact with the ground (Han et al. 2018, Shang 2020). Accordingly, although most research has focused on vehicle contact (Kerrigan et al. 2007, Yao et al. 2008), the significance of the ground contact has also been emphasized (Simms and Wood 2006, Crocetta et al. 2015, Han et al. 2018, Shang et al. 2018, Shi et al. 2019, Shang et al. 2020b). A recent analysis based on German real-world crash data (GIDAS) showed that 43% of 1221 selected cases had injuries subjected to ground contact, demonstrating the importance of ground related pedestrian injuries and providing significant motivation for countermeasures to prevent or moderate pedestrian injuries from ground contact (Shang et al. 2018). (Shang et al. 2020b) recently conducted six cadaver tests which recorded the whole process from vehicle contact until after the end of the ground contact. They observed that peak linear accelerations in ground contact are generally higher than for the vehicle contact. They also observed a high predicted risk of rotationally induced brain injury from ground contact, even for very low vehicle collision speeds.

However, many open questions remain regarding the influence of vehicle front shape and the design of potential countermeasures to minimize pedestrian ground contact injuries, and a suitably validated computational model is a much more sustainable tool for addressing these than cadaver experiments.

The MADYMO 50th percentile male pedestrian model, developed by TNO Automotive, is the most commonly used multibody pedestrian models for vulnerable road user crash reconstruction (van Hoof et al. 2003, van Rooij et al. 2003, Simms and Wood 2006, Untaroiu et al. 2009, Elliott et al. 2012, Xu et al. 2016, Shang et al. 2018). The model was validated for both full model (Ishikawa et al. 1993) and model segments such as tibia and femur static 3-point bending tests, cadaver side impact tests for the pelvis, thorax and shoulder, cadaver leg impactor tests for bending moment and shear force of lower extremities (Kajzer et al. 1993). De Lange et al. (DeLange et al. 2006) verified the kinematics of the MADYMO pedestrian model with eighteen full vehicle-pedestrian impact tests. However, the validation was only for vehicle contact and not for ground contact, even though it has since been applied for analyzing the ground contact (Crocetta et al. 2015, Zou et al. 2019). (Crocetta et al. 2015) defined six different pedestrian ground impact mechanisms by simulating hundreds of
impact configurations with different vehicle shapes, pedestrian heights and vehicle speeds, with
partial validation by comparison to real-world videos (Barry and Simms 2016). The model has also
been applied in the use of potential braking related countermeasures (Zou et al. 2019). However, the
capacity of the MADYMO pedestrian model to replicate kinematics of individual pedestrian ground
contact collisions remains unknown.

Researchers also developed other multibody or finite element pedestrian models for vehicle-pedestrian collisions. (Yang and Lovsund 1997) developed a 3D MB pedestrian model with emphasis on the head and lower extremities. The model consists of fifteen body segments with fourteen joints. The leg segments are breakable (Yang et al. 1993) and the knee joint formulation (Yang et al. 1995) facilitates biofidelic responses of the knees and leg fracture. The model was validated based on pedestrian substitutes' kinematics, the body segments' accelerations, contact forces, and failure descriptions compared with previously published cadaver impacts (Ishikawa et al. 1993). Finite element pedestrian models such as THUMS (Maeno and Hasegawa 2001, Iwamoto et al. 2003) and GHBMC (Untaroiu et al. 2016) pedestrian models are developed to simulate deformable vehicle-pedestrian impact scenarios. However, none of these models have been validated for ground contact.

In summary, a variety of pedestrian models (multibody and finite element) have been developed and applied to vulnerable road user crashes. These have been validated based on lower extremity bending and shear loadings, the head response including acceleration and force, head trajectories, whole-body kinematics etc. However, all models are validated for the vehicle impact only, and model validations for ground contact are so far lacking. The importance of pedestrian ground contact is growing and the risk of suffering serious head brain injury due to ground contact has been recently highlighted (Shang et al. 2018, Shang et al. 2020b). Given the high cost of cadaver tests, there is significant value in a pedestrian model which can simulate the ground impact and can be applied in large-sample parametric study such as virtual test system (Li et al. 2018). The recent staged cadaver impact tests (Shang et al. 2020b) provide a valuable experimental reference set, including pedestrian kinematics and injury criteria evaluations (skull fracture, *HIC* and *BrIC*) for multi-body model assessment.
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Accordingly, the aims of the current study are to:

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1) reconstruct the cadaver impact tests of (Shang *et al.* 2020b) to assess the capability of the MADYMO pedestrian model for use in ground contact scenarios, and assess the difference between the MADYMO multibody model and the cadaver in post-impact kinematics and head injury criteria predictions.

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2) Perform sensitivity studies to assess the influence of the vehicle pedestrian contact characteristics, the influence of initial pedestrian position on subsequent pedestrian ground contact and the effect of internal damping on overall body kinematics.

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If the pedestrian model can reasonably replicate kinematics and injury outcomes, it may be suitable for investigating the effect of vehicle front shape on the risk of pedestrian ground contact injuries over a broad range of collision configurations. Moreover, it could be used for developing active countermeasures to prevent pedestrian ground contact related injuries, such as controlled braking or airbag technologies (Khaykin and Larner 2016, Zou *et al.* 2019).

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## 2. Materials and methods

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The MADYMO ellipsoid multibody pedestrian model, as well as simplified vehicle models, were employed to assess their performance in ground contact, by comparison with the cadaver tests reported in (Shang *et al.* 2020b), see Figure 1.

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Given uncertainty in several input characteristics of the models, sensitivity studies were designed to assess the influence of the vehicle to pedestrian contact definition (loading and unloading functions, hysteresis), internal damping in the pedestrian models and the initial pedestrian joint angles.

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<figure><img src="image_2.png" /><figcaption>Figure 1: Steps followed in assessing the multibody models</figcaption></figure>

**2.1. Multibody vehicle models**

Simplified multibody vehicle models were built in MADYMO, with the geometry based on (The-Blueprints) to represent the vehicles tested in (Shang *et al.* 2020b). Each vehicle model consists of a lower bumper, bumper, bonnet leading edge, bonnet, windshield, wheels and roof, see Figure 2.

<figure><img src="image_3.png" /><figcaption>(a) Peugeot 307</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>(b) Citroen C4</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>(c) Renault Kangoo II</figcaption></figure>

<caption>Figure 2 The vehicle models with the simplified MADYMO models</caption>

**2.2. Pedestrian models**

The heights and weights of the pedestrian cadavers varied, as shown in Table 1 of (Shang *et al.* 2020b), replicated here as Appendix A and these were replicated by scaling the MADYMO 50th percentile pedestrian model using a customized Matlab code based on the pedestrian's height and weight. This global scaling does not address relative differences in body segment proportions. The scaled multibody models, as well as the corresponding pedestrian cadavers are shown in Figure 3. The initial postures (joint angles) of the models were adjusted based on the measurements of cadaver poses from the side and the front views which were captured pre-impact. Due to the joint limitation of the pedestrian model and the segment dimension differences, some differences between cadaver
and the simulation postures exist, see for example the left forearm in Figure 3 (a). For Test 05 in Figure 3 (e), the posture is the result of difficulties with initial placement of the cadaver which had very low mass (38kg) and unusually stiff joints (the cause of this is unknown as full medical histories were not available).

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<figure><img src="image_6.png" /><figcaption>(a) Test 01</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>(b) Test 02</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>(c) Test 03</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>(d) Test 04</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>(e) Test 05</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>(f) Test 06</figcaption></figure>

<caption>Figure 3 The initial postures of PMHS pedestrians and the corresponding scaled multi-body models</caption>

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## 2.3. Movement input of the multibody vehicle models

The planar time-displacement curves in the X (horizontal) direction and the Z (vertical) direction, and the time-rotation curve of the vehicle, were extracted every 20ms (overall impact duration was approximately one second) using a customized Matlab script and used to prescribe the vehicle

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motion in the models. The general steps for selecting the tracking points are as shown in Appendix B.

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## 2.4. Contact characteristic applied on the MB vehicle model

Three sources of vehicle contact characteristic were available: the published force-deformation characteristics derived from impactor tests (Martinez et al. 2007), recent test on the actual vehicle types performed by the European New Car Assessment Programme (EURO-NCAP) (Euro-NCAP) and another older force deformation characteristics from impactor tests (Mizuno and Kajzer 2000) and (Liu et al. 2002). The windshield and bonnet stiffness from (Mizuno and Kajzer 2000) were obtained by impactor tests and the stiffness of bonnet leading edge and bumper were obtained from leg form tests by (Liu et al. 2002). This combination of vehicle contact characteristic has previously been used by (Li et al. 2016) for a virtual test system. Euro NCAP assesses the pedestrian safety performance of new cars with a rating (up to 5-star) based on sub-system impactor tests (Hobbs and McDonough 1998, Euro-NCAP 2010). (Martinez et al. 2007) summarized 425 Euro NCAP tests and then estimated a series of simplified average stiffness curves. The force-deformation curves of each tested vehicle from the Euro NCAP tests as well as the force-deformation curves from (Martinez et al. 2007) and (Mizuno and Kajzer 2000) are shown in Figure 4. The detailed process of obtaining the vehicle front stiffness by using subsystem impactors can be found in (Martinez et al. 2007).

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<figure><img src="image_12.png" /><figcaption>(a) windshield</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>(b) bonnet</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>(c) bonnet leading edge</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>(d) bumper</figcaption></figure>

<caption>Figure 4 Force-deformation contact characteristics of vehicle front components from different sources</caption>

## 2.5. Ground contact stiffness

Considering the individual differences of the tested cadavers and also the different locations on the head (some of the head contacts occurred to the face while others occurred to the posterior of the head), the ground contact stiffness was set individually in MADYMO for each reconstruction. To estimate the contact stiffness, a multibody sphere with inertia properties matching the head and initial linear and angular velocities matching the experimental head kinematics just prior to head ground contact was used to simulate the head impacts with the ground, see Table 1. The method used to estimate the contact stiffness of the ground was based on the assumption that a quarter wave of simple harmonic motion (Triana and Fajardo 2013) reasonably models head acceleration until the peak is reached in the head ground impact, see Equation 1. From this, stiffness is calculated based on the peak acceleration and speed change.

<table><caption>Table 1 The input parameter of the multibody sphere (simplified head model)</caption><thead><tr><td>Parameter</td><td>Input</td></tr></thead><tbody><tr><td>Head Mass</td><td>4.5kg</td></tr><tr><td>Inertia</td><td>(2.08e-02 2.37e-02 1.53e-02 0 0 0) kg·m<sup>2</sup><br>(directly from MADYMO 50<sup>th</sup> percentile pedestrian model)</td></tr><tr><td>Linear speed</td><td>From (Shang et al. 2020b)</td></tr><tr><td>Angular speed</td><td>From (Shang et al. 2020b)</td></tr><tr><td>Initial position</td><td>0.02m high from the ground in vertical direction</td></tr></tbody></table>
$$ 
\begin{aligned}
\sqrt{\frac{m}{K}} &= \omega = \frac{1}{\Delta T} = \frac{1}{\left(\frac{\Delta V}{Acc_{peak}}\right)} = \frac{Acc_{peak}}{\Delta V} \\
K &= m \times \left(\frac{\Delta V}{Acc_{peak}}\right)^2
\end{aligned}
$$

Equation 1

where *m* is the mass of the head, *ω* is the natural frequency, *ΔT* is the time duration of the impact, *ΔV* is the speed change during impact and *Acc<sub>peak</sub>* is the peak acceleration. The stiffness (*K*) calculated for each test and the anterior/posterior head contact location are shown in Figure 5. The head ground contact characteristics for Test 06 is not listed as the acceleration measurement was corrupted during ground contact. As the input of Test 06 was similar to Test 05 and the pedestrian ground contact mechanisms of the two tests were same, the stiffness of the ground for Test 06 was set as same as that of Test 05. The comparison of the accelerations obtained from the simplified head model with each corresponding cadaver tests are illustrated in Figure 6, and the average values were applied for posterior and anterior head contacts. The average value of *K* from Test 01, Test 02 and Test 05 was used to define *K<sub>p</sub>* (posterior), as shown in Table 2, for the 30 kph tests, which have a relatively high ground stiffness due to the posterior head impact. In contrast, in Test 03 and Test 04, the front softer part of the head, such as the nose and face impacted the ground first, namely the anterior head impact, and the ground contact stiffness in these two tests was set as *K<sub>a</sub>* (anterior) as shown in Table 2, using the average value of *K* from the corresponding tests. *K<sub>p</sub>* and *K<sub>a</sub>* were then chosen as head ground contact characteristic depending on which area of the head impacts the ground first, as determined in a pre-simulation.

<figure><img src="image_16.png" /><figcaption>Figure 5 Ground stiffness for each test calculated</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>(a) Test 01</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>(b) Test 02</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>(c) Test 03</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>(d) Test 04</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>(e) Test 05</figcaption></figure>

Figure 6 Comparison of the accelerations obtained from simplified head model test by using K and $K_a$ or $K_p$ (the comparison of Test 06 was not given because the experimental head acceleration was corrupted)
<table><caption>Table 2 Stiffness of ground applied in MADYMO simulations</caption><thead><tr><td></td><td>Value</td><td>Test used for reconstruction</td></tr></thead><tbody><tr><td>k<sub>p</sub></td><td>1400 kN/m</td><td>Test 01, Test 02, Test 05 and Test 06</td></tr><tr><td>k<sub>a</sub></td><td>97 kN/m</td><td>Test 03 and Test 04</td></tr></tbody></table>

## 2.6 Injury Assessments

Assessments of head injury caused by translational accelerations were approximated using the *HIC* criterion, whereas injuries caused by rotational angular velocities were approximated using the *BrIC* criterion. It is noted this is not the actual *HIC* as it was not possible to fix the accelerometer to head CG in the cadaver tests for practical reasons, while the accelerometers can be fixed in the mouth, it is possible to apply the *HIC* computation to the head accelerometer data with an approximate 10% difference (Shang *et al.* 2020b). Evaluation of *UBrIC* (Gabler *et al.* 2018) instead of *BrIC* (Takhounts *et al.* 2013) would be preferable but was not possible due experimental limitations in the cadaver tests of (Shang *et al.* 2020b).

## 3. Simulation results

The six staged tests (Shang *et al.* 2020b) were reconstructed and simulated using the MADYMO platform. Each test was simulated using the three different vehicle contact characteristics (Euro-NCAP), (Mizuno and Kajzer 2000, Liu *et al.* 2002) and (Martinez *et al.* 2007), see Figure 4. Pedestrian kinematics and head injury predictions (HIC and BrIC) from vehicle contact and ground contact were compared between the simulation and the corresponding experiment, see Figure 7 and Figure 8.

### 3.1. Pedestrian kinematics

The key event timings of the vehicle-pedestrian impact from the staged tests and simulations as well as the ground contact mechanisms are compared, see Table 3. The ground contact mechanisms are summarized by assessing the whole-body rotation angles and the posture before landing, with reference to the definition of (Crocetta *et al.* 2015). Overlaying the video still shots from the experiments with the simulations was not practical due to camera projection issues. In Test 01 and Test 02, pedestrian vehicle separation times are generally earlier in the simulations than in the
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cadaver tests. However, the head ground contacts occurred more than 100ms earlier for the simulation in Test 01 but late in Test 02.

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<table><caption>Table 3-1 Comparison of key events (s) of Test 01</caption><thead><tr><th>Contact characteristic source</th><th>t<sub>head-vehicle contact (s)</sub></th><th>t<sub>separation (s)</sub></th><th>t<sub>head-ground contact (s)</sub></th><th>Ground contact mechanism, from (Crocetta et al. 2015)</th></tr></thead><tbody><tr><td>Staged test</td><td>0.145</td><td>0.770</td><td>0.995</td><td>M1</td></tr><tr><td>Mizuno and Liu<sup>1</sup></td><td>0.140</td><td>0.595</td><td>0.845</td><td>M3</td></tr><tr><td>Martinez</td><td>0.140</td><td>0.615</td><td>0.875</td><td>M3</td></tr><tr><td>EU NCAP</td><td>0.145</td><td>0.610</td><td>0.865</td><td>M3</td></tr></tbody></table>

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<table><caption>Table 3-2 Comparison of key events (s) of Test 02</caption><thead><tr><th>Contact characteristic source</th><th>t<sub>head-vehicle contact (s)</sub></th><th>t<sub>separation (s)</sub></th><th>t<sub>head-ground contact (s)</sub></th><th>Ground contact mechanism, from (Crocetta et al. 2015)</th></tr></thead><tbody><tr><td>Staged test</td><td>0.153</td><td>0.710</td><td>0.986</td><td>M3</td></tr><tr><td>Mizuno and Liu</td><td>0.150</td><td>0.625</td><td>1.045</td><td>M3</td></tr><tr><td>Martinez</td><td>0.150</td><td>0.615</td><td>1.020</td><td>M3</td></tr><tr><td>EU NCAP</td><td>0.150</td><td>0.655</td><td>1.070</td><td>M3</td></tr></tbody></table>

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<table><caption>Table 3-3 Comparison of key events (s) of Test 03</caption><thead><tr><th>Contact characteristic source</th><th>t<sub>head-vehicle contact (s)</sub></th><th>t<sub>separation (s)</sub></th><th>t<sub>head-ground contact (s)</sub></th><th>Ground contact mechanism, from (Crocetta et al. 2015)</th></tr></thead><tbody><tr><td>Staged test</td><td>No show</td><td>0.834</td><td>1.180</td><td>M2</td></tr><tr><td>Mizuno and Liu</td><td>0.170</td><td>0.845</td><td>1.1170</td><td>M2</td></tr><tr><td>Martinez</td><td>0.170</td><td>0.805</td><td>1.1095</td><td>M2</td></tr><tr><td>EU NCAP</td><td>0.160</td><td>0.800</td><td>1.1130</td><td>M2</td></tr></tbody></table>

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<table><caption>Table 3-4 Comparison of key events (s) of Test 04</caption><thead><tr><th>Contact characteristic source</th><th>t<sub>head-vehicle contact (s)</sub></th><th>t<sub>separation (s)</sub></th><th>t<sub>head-ground contact (s)</sub></th><th>Ground contact mechanism, from (Crocetta et al. 2015)</th></tr></thead><tbody><tr><td>Staged test</td><td>0.169</td><td>0.740</td><td>0.970</td><td>M2</td></tr><tr><td>Mizuno and Liu</td><td>0.185</td><td>0.745</td><td>1.030</td><td>M2</td></tr><tr><td>Martinez</td><td>0.185</td><td>0.745</td><td>1.255</td><td>M2</td></tr><tr><td>EU NCAP</td><td>0.185</td><td>0.705</td><td>1.190</td><td>M2</td></tr></tbody></table>

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<table><caption>Table 3-5 Comparison of key events (s) of Test 05</caption><thead><tr><th>Contact characteristic</th><th>t<sub>head-vehicle contact (s)</sub></th><th>t<sub>separation (s)</sub></th><th>t<sub>head-ground contact (s)</sub></th><th>Ground contact mechanism, from (Crocetta et al. 2015)</th></tr></thead></table>

<footnote n="1">¹ The contact characteristics used in the simulations are from these authors correspondingly.</footnote>
<table><caption>Table 3-6 Comparison of key events (s) of Test 06</caption><thead><tr><th>source</th><th colspan="4">(Crocetta et al. 2015)</th></tr></thead><tbody><tr><td>Staged test</td><td>0.098</td><td>0.647</td><td>0.860</td><td>M1</td></tr><tr><td>Mizuno and Liu</td><td>0.120</td><td>0.735</td><td>1.790</td><td>M1/M2</td></tr><tr><td>Martinez</td><td>0.120</td><td>0.735</td><td>0.990</td><td>M1/M2</td></tr><tr><td>EU NCAP</td><td>0.115</td><td>0.735</td><td>1.040</td><td>M1/M2</td></tr></tbody></table>

<table><thead><tr><th>Contact characteristic source</th><th>t<sub>head-vehicle contact (s)</sub></th><th>t<sub>separation (s)</sub></th><th>t<sub>head-ground contact (s)</sub></th><th>Ground contact mechanism, from (Crocetta et al. 2015)</th></tr></thead><tbody><tr><td>Staged test</td><td>0.110</td><td>0.727</td><td>0.936</td><td>M1</td></tr><tr><td>Mizuno and Liu</td><td>0.135</td><td>0.725</td><td>0.945</td><td>M1/M2</td></tr><tr><td>Martinez</td><td>0.135</td><td>0.690</td><td>0.895</td><td>M1/M2</td></tr><tr><td>EU NCAP</td><td>0.130</td><td>0.680</td><td>0.925</td><td>M1/M2</td></tr></tbody></table>

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<figure><img src="image_22.png" /><figcaption>Figure 7-1 Test 01: Sequences of vehicle-pedestrian impact experiment compared with MB simulations. Contact characteristic of vehicle front applied from (Green model: EU NCAP; Blue model: Martinez; Red model: Mizuno)</figcaption></figure>
<figure><img src="image_23.png" /><figcaption>Figure 7-2 Test 02: Sequences of vehicle-pedestrian impact experiment compared with MB simulations. Contact characteristic of vehicle front applied from (Green model: EU NCAP; Blue model: Martinez; Red model: Mizuno)</figcaption></figure>
<figure><img src="image_24.png" /><figcaption>Figure 7-3 Test 03: Sequences of vehicle-pedestrian impact experiment compared with MB simulations. Contact characteristic of vehicle front applied from (Green model: EU NCAP; Blue model: Martinez; Red model: Mizuno)</figcaption></figure>
<figure><img src="image_25.png" /><figcaption>Figure 7-4 Test 04: Sequences of vehicle-pedestrian impact experiment compared with MB simulations. Contact characteristic of vehicle front applied from (Green model: EU NCAP; Blue model: Martinez; Red model: Mizuno)</figcaption></figure>
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<figure><img src="image_32.png" /></figure>

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Figure 7-5 Test 05: Sequences of vehicle-pedestrian impact experiment compared with MB simulations. Contact characteristic of vehicle front applied from (Green model: EU NCAP; Blue model: Martinez; Red model: Mizuno)
<figure><img src="image_40.png" /><figcaption>Figure 7-6 Test 06: Sequences of vehicle-pedestrian impact experiment compared with simulations. Contact characteristic of vehicle front applied from (Green model: EU NCAP; Blue model: Martinez; Red model: Mizuno)</figcaption></figure>
**3.2. Pedestrian planar head trajectories**

Pedestrian planar head trajectories (tracked based on the marker on pedestrian forehead) in both the X (horizontal, positive direction of vehicle travel) and Z (vertically upwards) directions from staged tests and the simulations are compared, see Figure 8. Appendix Figure B1 shows the definition of the coordinate system after (Shang et al. 2020b). For Test 01 and Test 02, the horizontal head motion in the simulations is greater than was observed in the experiments.

<figure><img src="image_41.png" /><figcaption>(a) Head marker-x T1</figcaption></figure>

<figure><img src="image_42.png" /><figcaption>(b) Head marker -z T1</figcaption></figure>

<figure><img src="image_43.png" /><figcaption>(c) Head marker-x T2</figcaption></figure>

<figure><img src="image_44.png" /><figcaption>(d) Head marker -z T2</figcaption></figure>

<figure><img src="image_45.png" /><figcaption>(e) Head marker-x T3</figcaption></figure>

<figure><img src="image_46.png" /><figcaption>(f) Head marker -z T3</figcaption></figure>
<figure><img src="image_47.png" /><figcaption>(g) Head marker-x T4</figcaption></figure>

<figure><img src="image_48.png" /><figcaption>(i) Head marker-x T5</figcaption></figure>

<figure><img src="image_49.png" /><figcaption>(k) Head marker-x T6</figcaption></figure>

<figure><img src="image_50.png" /><figcaption>(h) Head marker-z T4</figcaption></figure>

<figure><img src="image_51.png" /><figcaption>(j) Head marker-x T5</figcaption></figure>

<figure><img src="image_52.png" /><figcaption>(l) Head marker-x T6</figcaption></figure>

<caption>Figure 8 Comparison of pedestrian forehead trajectories between cadaver experiments and simulations</caption>

### 3.3. Pedestrian head injury criteria assessments

The *HIC* and *BrIC* scores were calculated for both vehicle and ground contact for all six cases and compared with the staged PMHS test results, as shown in Figure 9. The average errors for the injury indices for both vehicle and ground contact over all six tests obtained from simulations using vehicle contact characteristics from Mizuno and Liu, Martinez and EU NCAP compared with the cadaver tests are 51.3%, 62.0%, 73.3%, respectively.
<figure><img src="image_53.png" /><figcaption>(a) *HIC* from vehicle contact</figcaption></figure>

<figure><img src="image_54.png" /><figcaption>(b) *HIC* from ground contact</figcaption></figure>

<figure><img src="image_55.png" /><figcaption>(c) *BrIC* from vehicle contact</figcaption></figure>
<figure><img src="image_56.png" /><figcaption>Figure 9 Comparison of head injury indices from vehicle and ground contact
(d) BrIC from ground contact</figcaption></figure>

267 **4. Sensitivity study**
268 The vehicle contact characteristics do not obviously affect the kinematics during the vehicle contact.
269 However, Section 3.3 shows they do have a large influence on the secondary ground contact and the
270 resulting injury predictions. The influence of the pedestrian initial joint angles and internal damping
271 of the MADYMO pedestrian model are also of interest. In these sensitivity studies, the Mizuno and
272 Liu's stiffness was used as the baseline for comparisons as this stiffness gave the smallest overall
273 error, see Figure 9.
274

275 **4.1. Sensitivity study of hysteresis and unloading curve**
276 Apart from the loading function, the hysteresis slope and unloading curve definitions in MADYMO
277 further influence the contact modelling. The effects were tested based on the simplified head model
278 impact simulations. The hysteresis slope over 5 magnitudes (9e4, 9e5, 9e6, 9e7 and 9e8) and the
279 unloading curves in 3 different ratios (0%, 5% and 10%) of loading curve were tested, see Figure 10.
280 Results showed that lower hysteresis slopes produced relatively higher acceleration peaks and wider
281 waves which can greatly impact *HIC* scores. Altering the unloading curve showed a negligible effect
282 on the peak and impact time duration.
283
<figure><img src="image_57.png" /><figcaption>Figure 10 Testing of hysteresis slope and unloading curve effect on the contact using a simplified sphere model</figcaption></figure>
## 4.2. Sensitivity study of pedestrian initial joint angle

The initial joint postures of the MADYMO pedestrian model were set based on the measurement of the joint angles of captured images in different views of the cadavers just before testing (Shang et al. 2020b). The effect of the joint angles was studied to assess the influence of joint angle on the resulting kinematics. Considering Test 01, the initial hip angle, knee angle and ankle angle of the struck leg were changed ± 5 degrees in YZ plane (see Table 4) to check the influence on the ground related head injury indices. Only one parameter was changed each time and the other two were kept constant (baseline) for this sensitivity study. The results are shown in Figure 11. The injury indices obtained from the baseline model and the pedestrian with initial joint angle 2 (as illustrated in Table 4) are close while for the pedestrian with initial hip joint angle 2 and knee joint angle 2, the injuries showed noticeable differences when compared with the baseline results, as did the ground contact mechanisms, see Figure 12.

<table><caption>Table 4 Initial angles of joint sensitivity study</caption><thead><tr><th>Joint</th><th>Angle 1 (-5°)</th><th>Baseline angle (°)</th><th>Angle 2 (+5°)</th></tr></thead><tbody><tr><td>Ankle</td><td>2</td><td>7</td><td>12</td></tr><tr><td>Knee</td><td>21</td><td>26</td><td>31</td></tr><tr><td>Hip</td><td>-5</td><td>0</td><td>5</td></tr></tbody></table>

<figure><img src="image_58.png" /></figure>

<figure><img src="image_59.png" /></figure>

<figure><img src="image_60.png" /></figure>

<figure><img src="image_61.png" /></figure>

<figure><img src="image_62.png" /></figure>

<figure><img src="image_63.png" /></figure>

<figure><img src="image_64.png" /></figure>

<figure><img src="image_65.png" /></figure>

<figure><img src="image_66.png" /></figure>
<figure><img src="image_67.png" /><figcaption>(a) Ankle sensitivity for *HIC*</figcaption></figure>

<figure><img src="image_68.png" /><figcaption>(c) Knee sensitivity for *HIC*</figcaption></figure>

<figure><img src="image_69.png" /><figcaption>(e) Hip sensitivity for *HIC*</figcaption></figure>

<figure><img src="image_70.png" /><figcaption>(b) Ankle sensitivity for *BrIC*</figcaption></figure>

<figure><img src="image_71.png" /><figcaption>(d) Knee sensitivity for *BrIC*</figcaption></figure>

<figure><img src="image_72.png" /><figcaption>(f) Hip sensitivity for *BrIC*</figcaption></figure>

<figure><img src="image_73.png" /><figcaption>Figure 12 Pedestrian ground contact mechanisms in Test 01 from different initial hip angle from Table</figcaption></figure>
4.3. Sensitivity study of bending of pedestrian model

As seen in Test 01 and Test 02 shown in Figure 7, the pedestrian model bounced off the vehicle after the head windscreen impact, but this did not occur in the cadaver tests. A potential reason for the excessive bouncing could be insufficient internal damping in the pedestrian models. A sensitivity study of human model bending was therefore performed, with a modified damping coefficient of 100 N·s/m used to reconstruct Test 01 and compared with the baseline simulation (almost no damping), see Figure 13. The damping added to the model did not significantly reduce the rebound but did significantly change the post-impact kinematics and the mechanism of ground contact.

<figure><img src="image_74.png" /><figcaption>Figure 13 Sequence of baseline pedestrian model (orange) and the model with added damping kinematics (purple) in vehicle crash for Test 01</figcaption></figure>

5. Discussion

This paper presents the first kinematics assessment of a multibody pedestrian impact model for the phases following vehicle impact up to and including the ground contact, using cadaver test data for comparison.

A computational model for assessing pedestrian ground contact injuries, and for possible use in the development of ground contact injury prevention countermeasures, has a number of hierarchical requirements. In terms of whole-body kinematics, there is the need for replicating the main body segment trajectories following the initial vehicle contact, followed by the pre-impact pose and
velocity for the ground contact, especially the head. Subsequently, replicating the 6 DOF motion of the head and other body segments during ground contact is needed for injury criteria evaluation. For finite element models, tissue level stress/strain responses can be assessed, but this is beyond the scope of the current paper which focuses on the evaluation of the multibody MADYMO ellipsoid pedestrian model.

Table 3 shows that the timings of the head to vehicle contact are well reproduced for Test 01 and Test 02 of Shang et al 2020, where the collision speed is 30 kph and the normalized bonnet leading-edge height is 0.7. However, for the 20kph cases (Tests 03 and 04) and the two high bonnet cases at 30 kph (Tests 05 and 06), there are substantial differences (of the order of 20 ms) in the head to vehicle contact times. For Tests 01 and 02 the models separate from the vehicle too early, showing evidence of insufficient energy absorption. However neither varying the contact characteristics nor introducing additional damping was successful in addressing this. The timing of the subsequent ground contact is poor in some cases (maximum error is 0.9s in Test 05, see Table 3-5, the arm of the pedestrian model prevented the head impacting the ground) but the correspondence to the pedestrian ground contact mechanisms identified by (Crocetta et al. 2015) is reasonable (correct mechanism identified in three cases, incorrect in one case, and partially correct in two cases. However, Figure 7 shows some substantial differences in the flight trajectory and ground contact sequences. In consequence it is not surprising that the resulting injury criteria assessments in Figure 9 show cases where very substantial differences between the model and the corresponding experiment are evident. Thus the current MADYMO pedestrian models cannot reliably distinguish the influence of the various factors varying between the different tests (vehicle shape and speed, body size and pose, vehicle contact characteristic).

The sensitivity studies show that the choice of vehicle contact characteristic makes a significant difference to pedestrian ground contact kinematics and injury evaluations, as do the hysteresis slope and the initial knee and hip angles. Somewhat surprisingly, the contact characteristic using the older data from impactor tests by Mizuno and Liu generally yielded the lowest errors for *HIC* in the vehicle contact (Figure 9a), but the reliability of the resulting ground contact *HIC* is poor (Figure
347

9b). Similarly, the predictions of the *BrIC* in both the vehicle and ground contacts are a poor match to the experimental data.

348

349

Increasing the internal damping in the pedestrian model does affect the kinematics but did not improve the comparison with the experimental data. A further round of simulations was conducted with the goal of improving the match between the predicted and test ground impact mechanisms by changing the vehicle contact stiffness. The results are not presented here, but the outcome was that while this approach was successful in improving the ground contact kinematics, the resulting vehicle contact injury predictions were very different to the experiments.

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352

353

354

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356

Accordingly, future work must focus on amendments to the MADYMO pedestrian model to improve its predictive capacity and ground contact, and on assessing the predictive capacity of other multibody and finite element model formulations (Maeno and Hasegawa 2001, Iwamoto et al. 2003, Untaroiu et al. 2016). This is needed before the model can be confidently applied to assess ground contact injury countermeasures (for example about technology or vehicle front shape changes). Similarly, it is clear that the MADYMO pedestrian model currently has limited potential for application to individual collision reconstruction purposes, though there have been substantial applications of this in the literature (Shen and Jin 2008).

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364

365

## 6. Limitations

366

There are several limitations to this study. Firstly, the experimental data is based on cadaver testing and it is understood that a living human response would be different, especially for the two 20kph tests where voluntary motion is likely to play a significant role. Only one pedestrian model formulation was assessed, and it is possible that a different multibody or a finite element model would perform better. The models were globally scaled based on height and mass, not as an individual body segment level. The experimental measurements of the pre-impact joint angles of the cadavers were not precisely known.

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374

## 7. Conclusions

375

We have presented the first assessment of a computational model (here the MADYMO ellipsoid

376
multibody pedestrian model) for predicting pedestrian flight and ground contact following a vehicle collision. A comparison with six cadaver tests performed over the speed range 20-30kph and with three different vehicle types and pedestrian sizes showed good capacity to predict vehicle contact times, but differences between the models and experiments manifested prior to vehicle pedestrian separation, and resulted in considerable differences in the ground contact kinematics. The resulting head injury predictions based on the ground contact *HIC* and *BrIC* scores showed limited capacity of the model to replicate individual experiments. Sensitivity studies showed substantial influences of the vehicle- pedestrian contact characteristic and some of the initial pedestrian joint angles on the subsequent ground contact injury predictions. Further work is needed to improve the predictive capacity of the MADYMO pedestrian model for ground contact injury predictions.

387

## Acknowledgement

The authors would like to thank EURONCAP for generous provision of the impactor data. The support of the China Scholarship Council (CSC) is highly appreciated.

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Appendix A: Information of vehicle and pedestrian cadavers tested in (Shang et al. 2020a)

<table><caption>Table A1 Summary of tests performed in (Shang *et al.* 2020a)</caption><thead><tr><th>Test number</th><th>Vehicle model</th><th>Vehicle speed (km/h)</th><th>Pedestrian age (y/o)</th><th>Pedestrian sex</th><th>Pedestrian height (m)</th><th>Pedestrian mass (kg)</th><th>NBLEH</th></tr></thead><tbody><tr><td>Test 01</td><td>Peugeot 307</td><td>30.5</td><td>88</td><td>Male</td><td>1.74</td><td>66</td><td>0.7</td></tr><tr><td>Test 02</td><td>Peugeot 307</td><td>30.4</td><td>83</td><td>Male</td><td>1.72</td><td>69</td><td>0.7</td></tr><tr><td>Test 03</td><td>Citroen C4</td><td>20.4</td><td>94</td><td>Male</td><td>1.67</td><td>64</td><td>0.9</td></tr><tr><td>Test 04</td><td>Citroen C4</td><td>21.0</td><td>83</td><td>Male</td><td>1.67</td><td>55</td><td>0.9</td></tr><tr><td>Test 05</td><td>Renault Kangoo II</td><td>30.1</td><td>94</td><td>Female</td><td>1.58</td><td>38</td><td>1.2</td></tr><tr><td>Test 06</td><td>Renault Kangoo II</td><td>30.4</td><td>86</td><td>Male</td><td>1.62</td><td>69</td><td>1.1</td></tr></tbody></table>

489
Appendix B: Steps of defining and validating the movement input of the MB vehicle models

(1) According to the width of the vehicle and the markers on the lab ground, using ginput function in Matlab to pick 2 pairs of points (a1 and a2, a3 and a4) which define 1 m in y=0 and y=0.75, then the scale (the length of b1b2, the coordinates of b1 and b2 are in line with the coordinates of the reference points picked from the side of the vehicle) can be calculated based on the mathematical relation, see Figure B1 (a). The scale in Y direction depends on the coordinates of the points P1 and P2 in Figure B1 (b).

(2) P1 is a reference point which can be used to find the tracking point P0 based on their relative positional relationship. Pick two points P1 and P2 in a line on the side of the vehicle, then the angular change of the vehicle can be calculated.

<figure><img src="image_75.png" /><figcaption>Figure B1: The steps of choosing the tracking point</figcaption></figure>

After the X and Z motion of the tracking point and the angle of the vehicle were calculated, the polynomial fittings (third-degree polynomial for X motion, ninth-degree polynomial for Z motion, fourth-degree polynomial for vehicle angle. Different orders were used for respective best matching of the fitting curve) were applied to fit the time history curves to ensure a smooth MB vehicle movement. Take Test 01 for instance, the motion of the tracking points corresponding the fitting curves are shown in Figure B2 (a), (c) and (e). It should be noted since the changes in the Z direction and theta (vehicle angle) are very small, a minor difference can result in relatively big errors when tracking the points P1 and P2. To reduce the error, the movements were tracked three times and
512 averaged for each test, see Figure B2 (b), (d) and (f).

513

<figure><img src="image_76.png" /><figcaption>(a) Vehicle X motion</figcaption></figure>

<figure><img src="image_77.png" /><figcaption>(b) 3 fitting curves of P0 X motion as well as the average curve</figcaption></figure>

<figure><img src="image_78.png" /><figcaption>(c) Vehicle Z motion</figcaption></figure>

<figure><img src="image_79.png" /><figcaption>(d) 3 fitting curves of P0 Z motion as well as the average curve</figcaption></figure>

<figure><img src="image_80.png" /><figcaption>(e) Vehicle angle</figcaption></figure>

<figure><img src="image_81.png" /><figcaption>(f) 3 fitting curves of vehicle angle as well as the average curve</figcaption></figure>

<caption>Figure B2: The fitting curves of the motion of the tracking point</caption>

514

515 The input and output motions of the tracking point P0, as well as two other checking points Q1 and

516 Q2 [as demonstrated in Figure B3(a)], were compared to check whether the MB vehicle model
moves as well as the input motions. Figure B3 (b) and (c) show that the movement of the tracking point P0 and the input is identical. For the two other reference points, the horizontal motion obtained from the video of the test and motion obtained from the MADYMO simulation output is closely related. The differences in vertical direction were small (up to 3 cm) and may be due to the vehicle's rotation angle, which can be ignored. The checking point results indicate the feasibility of using the tracking system to capture the vehicle movement.

523

<figure><img src="image_82.png" /><figcaption>(a) The locations of two checking points</figcaption></figure>

<figure><img src="image_83.png" /><figcaption>(b) X motion</figcaption></figure>

<figure><img src="image_84.png" /><figcaption>(c) Z motion</figcaption></figure>

<caption>Figure B3 The comparison of input and output motions of checking points</caption>

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