In the age of computer simulations, do we still need to physically test cars? We investigate if it is possible to predict the 400 m acceleration time of an Audi RS4 Avant.
STANDING on the pit straight at the Aldo Scribante racing circuit is an Audi RS4 Avant about to set a 400 m acceleration time as part of this year’s Shootout (see page 58). Traction control mid-setting, dynamic mode selected, left foot on the brake and right foot flat on the accelerator. The engine revs shoot up and hover in the mid-range to indicate that launch control is pending. As tense as a fully stretched elastic band, the RS4 awaits the last action – release brake. A slight chirp from all four wheels announce that launch control is engaged as the 331 kW delivered by the howling 4,2-litre V8 catapults the Audi to the horizon. The 400 m marker is reached in 12,83 seconds at 177 km/h. Impressive indeed, but was all this mechanical punishment really necessary? Could we not have predicted the time and speed by elementary simulation calculations?
The simulation required a basic vehicle model and knowledge of the test conditions (see adjacent table) before the theoretical acceleration run could take place. Although most of the information is factual, a number of assumptions had to be made to simplify the calculations and is indicated by an asterisk.
Newton’s second law states: the sum of the forces (F) on an object is equal to the mass (m) of that object multiplied by the acceleration (a) of the object: F = ma. In other words, the acceleration of the RS4 is directly proportional to the nett force acting on it and inversely proportional to its mass. As the mass is known, we needed to calculate the nett force acting on the Audi for the entire 400 m of the theoretical test strip.
The tractive force acting on the vehicle is generated at the contact patches of the tyres on the road as a result of the engine torque delivered. If the engine speed is known, the maximum torque figure (in N.m) at the flywheel is known from the RS4’s torque curve. This torque figure is then multiplied by the transmission ratio and final drive ratio to get the torque figure on the wheels (see technical feature Why your car needs gears in CAR May ’14). By then dividing this figure by the radius of the wheels, the tractive force in Newton is known. As we assume there is no tyre slip (feasible with all-wheel-drive on dry tar), we do not have to deal with weight transfer or torque split between the axles. This tractive force figure is then lowered by 20% to account for all the drivetrain losses.
There are a number of forces opposing the forward motion of the RS4 as it sprints down the test strip. These forces have to be deducted from the tractive force to calculate the nett force acting in the vehicle. These forces include:
• Aerodynamic drag force;
• Rolling resistance force of the tyres;
• Inertial force of accelerating all the rotational components.
As we assume the test strip is level, there is no gravitational gradient force acting on the vehicle. By employing basic engineering formulas, we calculated the opposing forces as the Audi accelerated down the theoretical drag strip. Aerodynamic drag becomes the dominant opposing force as the speed rises and top speed is reached when the opposing forces equal the tractive force (ignoring gearing or speed limitations).
The simulation used a technique known as numerical integration to run all the calculations at a short time interval (0,1 seconds in this case). For each time interval, the acceleration of the Audi was calculated by dividing the nett force by the mass of the vehicle (a = F/m). The new vehicle speed at the start of the next time interval (0,1 seconds later) could now be calculated. This vehicle speed was then used to determine the new engine speed, engine torque, wheel torque, tractive force and the opposing forces acting on the vehicle with the new vehicle acceleration known (this calculation loop is repeated). Numerical integration gets more accurate if the time interval for the calculations is reduced.
As the torque figure during the initial clutch engagement from standstill was unknown, 400 N.m was assumed with launch control active. The simulation also needed to keep track of the maximum engine speed limitation (8 300 r/min) to use the next gear ratio in the following time interval calculations – denoting a gearshift. The distance covered during each time increment was calculated and added until the 400 m marker was reached.
It is clear from the vehicle speed vs. distance graph below that there is an excellent correlation between the actual data measured at Aldo Scribante and the predicted values of the simulation. This is confirmed by looking at the acceleration times in the table below. There is a minor diversion at the higher speed ranges where the actual vehicle is a little faster than the theoretical vehicle. This can easily be corrected in the simulation by slightly tweaking the frontal area to lower aerodynamic drag at speed.
The simulation managed to predict the acceleration results (time and speed) to a close degree. This proves that it is indeed possible to predict a vehicle’s straight-line performance without a litre of fuel being burned. The advantage of such a simulation is that the vehicle does not even have to exist before it can be benchmarked against competitor vehicles. This is exactly what automakers do in the concept phase when planning a new performance vehicle. It does not, however, negate actual vehicle testing (see Why physical testing is still needed) as nobody drives a vehicle in a computer simulation but rather on actual roads. There is obviously also an enjoyment factor in experiencing the real deal – one of the main reasons performance vehicles exist in the first place!