Recently, we were asked by a designer of thrill rides if we could help them define a design tool that would allow them to push the envelope in rider experience, while considering engineering constraints and, of course, rider safety. As a proof-of-concept, the specific issues that needed to be considered were:

The Rider Model

Developing the rider model was pretty straightforward: essentially this was done using a vertical beam to represent the torso, with a compliant revolute joint to represent the hip joint, connected to the car. The neck and head were modeled similarly at the top of the torso. Not needed for the proof-of-concept, but we thought it would be fun to try, the arms were modeled as double pendulums with compliant joints at the shoulders and elbows.

Figure 1: Rider Model

Figure 2: Restraints Model showing Custom Components

The most challenging aspect of this project was the contact model we needed to use to simulate the seat back and seat belt that would be used to restrain the rider. To achieve this, we developed a custom component that implemented a modified Hertzian contact model that applied a large torque to a joint that turned beyond a threshold. For more information on this approach, see http://en.wikipedia.org/wiki/Hertzian_contact_stress

For the seat back, we apply a contact force at 0.2 radians (~11°) from the resting position, and the seat belt is modeled with a contact force at 0.4 radians (~23°) in the opposite direction.

Figure 3: Contact model in Maple

On simulation, the plotted results also show the rider’s torso being pushed into the seat back as the car is accelerated. As the torso contacts the seat back, the head continues to move and cause the neck to rotate. Obviously, the neck angle and rotational acceleration are very important considerations for rider safety, and the results from this simulation would give cause for concern!

Figure 4: Results from Simulation

Furthermore, with a few simple graphical elements we were able to produce a realistic animation of the rider responding to the car being pushed by a force and then released.

The Ride Model

The rider model was then integrated into the full model of the ride, complete with drive train, motor-speed control, and calculation of the tangential forces on the car and rider. The track is specified using a spreadsheet to define the heights of the track over the track distance.

Figure 5: Simple Ride Model

Figure 6: Track height definition

This data is then read into the model using data interpolation blocks. The data between the defined points is interpolated using a cubic spline fit, from which the tangential forces are computed.

On simulation, we were able to show how the rider would be affected by the tangential forces, with and without restraints. We’ll leave you with the resulting animations.

For confidentiality reasons, we can’t discuss the specific results from the project, but you can get a sense of the ease with which we were able to deliver this proof of concept, not to mention the fun we had doing it!