As the winter Olympics begin in Salt Lake City, bobsled drivers have been honing their skills on an electromechanical simulator based on the laws of physics.
Bobsledding is notoriously expensive – it typically costs $15-30m to create a world-class track and over $25 000 to design and test a competitive sled. Moreover, bobsled teams in the US and Asia can run up large travel bills since all but four of the tracks certified by the International Bobsledding and Tobogganing Federation (FIBT) for world-cup competition are in Europe.
These financial incentives have motivated the use of simulators, similar to those in commercial aviation, to teach the intricacies of bobsled driving. At the University of California at Davis, our group has developed such a simulator and installed two of them permanently at the US Bobsled Federation facilities in Lake Placid and Salt Lake City. The simulators allow athletes to train all year round for the world-cup circuit and the Olympic games (see A Kelly and M Hubbard 2000 Sports Engineering 3 13).
Although existing one-dimensional studies of bobsled dynamics and sled performance are useful, to design a simulator we need to fully characterize the surface of the track and the motion of the sled in three dimensions. We base our mathematical models of various bobsled-track surfaces on measurements of the permanent concrete or stone foundations, which are covered with several centimetres of ice. Indeed, the surface in our models is accurate to about 4 mm and is more precisely known than the surface of the ice itself.
The track surface is then incorporated into three differential equations that describe the motion of a body that slides along the track with one rotational and two translational degrees of freedom. These equations also contain various vehicle parameters, such as the mass of the sled, its moments of inertia, aerodynamic drag and lift coefficients, and the coefficients of friction for the steel runners on the ice. We also need to know exactly how the driver steers the sled in his or her attempt to control the vehicle.
Steering to victory
Bobsled events are frequently finely contested. At the 1998 winter Olympics in Japan, for example, Great Britain and France tied for the bronze medal having taken exactly the same time to complete four runs, while the US team came in fourth just 0.02 seconds behind.
The driver’s job is to manoeuvre the sled to minimize the time it takes to complete the course. But controlling the sled is an extremely delicate task because only the front runners are steerable. Moreover, the drag coefficient of friction for the runners on the ice is small (~0.015), which means that the lateral steering force is small.
Typically the driver turns the runners less than 5° to produce a lateral force on the front runners and an angular acceleration. He or she has the difficult job of controlling both the position of the sled and the angular acceleration with a single steering movement – a task that is more challenging than simultaneously steering and balancing a bicycle. This difficulty is compounded by the lack of control due to the small coefficient of friction.
At the start of a run, the team pushes the bobsled to generate as high an initial speed as possible. The driver controls the vehicle only after the push is completed. Thus an accurate model of the push process is required to provide the simulation with realistic initial conditions. The sled eventually approaches its terminal forward velocity, which is determined by the balance between the forward component of gravity, aerodynamic drag and ice friction. Since the local mechanical energy of the sled (i.e. the sum of its potential and kinetic energy) is roughly conserved in a turn, the driver must steer into the turn to maximize the kinetic energy, and thus the speed, while minimizing the distance travelled. These gains must be traded off against losses in speed due to additional steering-induced friction in order to preserve speed for the remainder of the run.
At every stage in the development of the model, it is important to incorporate actual data. The vehicle-simulation parameters we use come from wind-tunnel tests, studies of ice friction, mass and inertia measurements of the bobsled, and measurements of track shapes. Comparing the simulation results with measurements can validate the model and identify areas for improvement. Without constant testing against experiment the model can rapidly lose touch with reality.
Mimicking the motion
Our bobsled simulator is an electromechanical system that has been designed and constructed to closely mimic the real experience. The driver steers and the simulator calculates how the sled would react. The simulator also provides the driver with sensations similar to those experienced in the actual event. Indeed, it is important to involve as many of the driver’s senses as possible to heighten the feeling of realism. Our bobsled simulator therefore addresses the visual, tactile and auditory senses, as well as the driver’s sense of balance, using both hardware and software.
The heart of the simulator is a high-speed computer that calculates the differential equations that model the dynamics. The driver’s steering is measured with an optical encoder and fed directly to the computer to affect the equations of motion. These equations are solved in real time at 100 Hz. Meanwhile, a continuously changing visual image is generated showing what would be seen by the driver from his or her position on the track.
Although visual feedback accounts for some 70% of the perceived motion, the angular motion of the organs in the inner ear is also important. Sleds experience angular accelerations in all three directions, but the roll component around the forward axis is by far the largest and most violent, with angular accelerations frequently exceeding 60 rad s-2. A DC motor controls the roll of the simulator cockpit to mimic this motion.
Another important factor for drivers is the “feel” of the steering. Our simulator calculates the forces on the runners and those that are transmitted through the steering linkage to the drivers’ hands. We then reproduce these forces using an active DC-motor control system in the steering mechanism to produce realistic tactile sensations. Since the track surfaces are rarely smooth, the interaction between the runners and surface irregularities on the ice produces extremely severe vibrations and auditory noise. A final touch of realism in the simulator is provided by recorded acoustic noise from actual track runs.
Although every effort is made to have accurate and realistic sensory feedback, the simulator does have its limits. For example, bobsledding involves extremely high specific forces, with the team experiencing forces equivalent to five times the acceleration due to gravity for up to 2 seconds at a time. But it is impossible to simulate such accelerations in a cockpit based in the lab, which limits the specific forces to 1g.
Because everything is computed in real time, virtually all the variables of interest can be displayed to the driver after the run to learn what went right and wrong. This is one of the great advantages the simulator has over a real bobsled – it is very expensive and takes immense effort to measure the same variables during real runs. Immediate quantitative feedback to the driver is extremely important to help improve his or her driving technique.
Another great benefit of the simulator is that the driver can practise the runs many times. On a real track, drivers are lucky to make four runs lasting one minute due to competition from other teams wanting to use the same track. Another obvious advantage of the simulator is safety: teams can experiment with driving strategies that would be too risky and dangerous to try in practice.
Improved performance
So has the simulator led to faster times in competitions and more medals? Unfortunately, it is nearly impossible to test the effectiveness of the simulator experimentally. The reason is that the performance of the driver is just one – and perhaps not even the most important – of the three major factors that determine the finish time. The other two – push effectiveness (i.e. the velocity and time at the end of the push) and the aerodynamic and frictional efficiency of the sled – are unrelated to driving skill.
That said, the simulator allows us to completely control factors that are uncontrollable in real races. Differences in the finishing time in the simulator are solely down to driving technique, since all the other conditions are held constant. By measuring these times over long periods, it is clear that the simulator does lead to a gradual improvement in driver performance.
Even though the simulated experience can never completely replace actual sledding, drivers praise its realism, its ability to capture the essential features of driving, and its effectiveness in increasing their familiarity with particular track layouts. So far, our simulator has proved an effective tool in tuning the skills of world-class drivers. And at the other end of the spectrum, the simulator can help to train novice drivers rapidly and safely.
