Case Study: Simulating Motorcycle Motion in PC-Crash Version 13

Introduction

Recently, PC-Crash simulation software [1] incorporated a single-track vehicle driver model for simulating motorcycle motion. In the past, a two-wheeled vehicle in PC-Crash would simply fall over - it had no stability. With the single-track vehicle driver model, the model will generate the necessary steering inputs and lean for the motorcycle to follow a curved path while remaining upright and stable. A later post will explore how this model functions at the friction limits (i.e., can it be used to successfully simulate a motorcycle experiencing a low-side or high-side fall). This current case study simply illustrates the use of the model for reconstructing a real-world crash where non-limit cornering preceded a collision. This crash involved a motorcyclist operating a KTM adventure motorcycle traversing a series of curves on a winding mountain road before coming upon a vehicle stopped in the road preparing to turn left. The motorcycle operator attempted to avoid the truck by swerving left but contacted the left rear of the truck. The animation below shows the PC-Crash simulation that was generated as a part of this reconstruction and the aerial image below the animations shows the curvature of the roadway in the area of the crash. The collision depicted in the animation was simulated using the ellipsoidal impact model in PC-Crash (another topic for a future post). This animation was rendered from the vantage point of another rider traveling behind the involved motorcyclist. Not depicted in this animation is a rider ahead of the KTM, who successfully avoided the truck.

To use the single-track driver model within PC-Crash, a path is established for the motorcycle to follow. In attempting to follow this path, the driver model utilizes user-defined inputs that are entered in the “driver model” tab of the “vehicle data” dialogue box. Inputs for the driver model include the maximum steering angle, the maximum steering velocity, and the look ahead duration [2]. The look ahead duration defines how far along the user-defined path the model looks. The path looks this duration ahead on the path to determine what steering angle should be used. The steering input is limited by the maximum steering angle and steering velocity. When a single track vehicle is selected in the “vehicle data” the single track driver model is automatically activated (as long as a path has been created), and the user can vary the parameters of the model to simulate the desired vehicle motion.

Analysis

In this case, we used a Faro laser scanner, a DJI Mavic 2 Pro drone, Aeropoints, and PIX4D Mapper software to generate an accurate three-dimensional representation of the curves where this collision occurred. This mapping data was used to generate a three-dimensional terrain for the motorcycles to drive on. The vegetation surrounding the curves had been documented in several scene photographs taken immediately after the crash and in a video that had been taken approximately 2 weeks after the crash. We used techniques of photogrammetry to reconstruct the size and location of specific plants that would have been present at the time of the crash, and those were accurately represented in PC-Crash. The motorcyclists had offered testimony related to how they were positioned on the roadway and the speed they were traveling. According to this testimony, the KTM motorcycle was positioned in the right wheel track track traveling 35 mph. The rider behind the KTM was in the left wheel track also traveling 35 mph. Paths were established in PC-Crash for each of these motorcycles and the inputs into the driver model were optimized to generate motion for the motorcycles that followed the curvature of the roadway. PC-Crash automatically calculated the lean angles of the motorcycles that were required to follow these paths.

The lean angle required for a motorcycle to traverse a curved path is the angle that brings the overturning moment generated by the tire frictional forces into balance with the opposing moment generated by the tire forces perpendicular to the road surface. The required lean angle increases with increasing speed and decreasing path radius. Fricke [3] and Cossalter [4] report that the lean angle of a motorcycle for a given path and speed can be calculated with the following equation (Equation 1):

In this equation, the variables have the following meaning:

This equation assumes that: (1) the motorcycle is traveling a steady speed high enough that the rider would have used countersteering to initiate the lean; (2) that the rider is leaning at the same angle as the motorcycle; and (3) that the part of the tire contacting the road does not change as the motorcycle leans. For a real motorcycle tire, as the motorcycle leans, the portion of the tire contacting the road will change. Cossalter showed that the additional lean angle required due to the tire width could be calculated with the following equation (Equation 2):

In this equation, t is the tire width and h is the combined motorcycle and rider center of gravity height. References 5, 6, 7 examine and validate these equations.

The graph below compares the lean angles calculated by PC-Crash in the simulation to the lean angles calculated for the same path with Equations (1) and (2). As this graph shows, the PC-Crash calculated lean angles closely followed those generated with Equation (1). This means that, in calculating the lean angles, PC-Crash is using the standard, basic lean angle equation and is not adjusting the lean angles for tire width. In most instances, this will be more than adequate, but it’s something the analyst should be aware of in instances where a motorcyclist leaned far enough for components of the motorcycle to contact the road surface. PC-Crash will likely underestimate the peak lean angles used by a rider for a specific path.

Here are two additional views of the simulation. These animations were generated entirely within PC-Crash.

References

1. Rose, N. and Carter, N., “An Analytical Review and Extension of Two Decades of Research Related to PC-Crash Simulation Software,” SAE Technical Paper 2018-01-0523, 2018, https://doi.org/10.4271/2018-01-0523.

2. “PC-CRASH: A Simulation Program for Vehicle Accidents,” Operating and Technical Manual, Version 12.1, April 4, 2020.

3. Fricke, L.B., Traffic Crash Reconstruction, 2nd Edition, Northwestern University Center for Public Safety, Evanston, Illinois, 2010, ISBN 0-912642-03-3.

4. Cossalter, V., Motorcycle Dynamics, Second Edition, self-published, 2006, ISBN 978-1-4303-0861-4.

5. Rose, N.A., Carter, N., Pentecost, D., “Analysis of Motorcycle and Rider Limits on a Curve,” Collision: The International Compendium for Crash Research, 9(1): 28-36, ISSN 1934-8681.

6. Carter, N., Rose, N.A., Pentecost, D., “Validation of Equations for Motorcycle and Rider Lean on a Curve,” SAE Int. J. Trans. Safety 3(2):2015, doi:10.4271/2015-01-1422.

7. Rose, N.A., Carter, N., and Smith, C., “Further Validation of Equations for Motorcycle Lean on a Curve,” SAE Technical Paper 2018-01-0529, 2018, doi:10.4271/2018-01-0529.

Contributors

Connor Smith, a managing accident reconstructionist at Explico, and Michael Erickson, a senior forensic animator at Explico, contributed to the work presented in this post.