Features - Technical
NOVEMBER 9, 1999
BY PETER WRIGHT
Absolute performance counts for nothing in Formula1, only relative performance matters. It is of no consequence how fast or slow you are, as long as you are faster than your competitors on a particular circuit, at a particular time on a particular day.
Competitors' lap times are easy to obtain but they can be misleading if they decide to create a lap that does not start at the Start/Finish line, or only drive individual fast sections and add them up later. Section times can be measured, as can local speeds, but every sector needs timing beams and a crew to operate them - they can only ever be coarse measurements. What is really sought after is data for the car's speed at all points on the track. It is possible to analyse this basic information and derive useful power, aerodynamic and handling figures for a competitor's car. The process is the reverse of lap simulation, in which a team will input all the performance parameters for their car, and output a speed plot and lap time for the circuit. If they have the speed plot for a competitor, and the tyres are the same, the weight is on the minimum, and the driver uses a similar line and effort, it is possible to make good estimates of power, drag and downforce and to gain some indication of the balance of the car.
Apart from placing a "mole" in each of one's competitors' teams, who then passes out data files on lap speeds and other information, there are few methods of obtaining another car's speed plots. It could be possible using a helicopter hovering above the circuit, and digitising a video of the cars lapping the track, but this approach would be very expensive and time consuming.
A more viable alternative would be to adapt a technique developed by P.Azzoni and D. Moro (University of Bologna, Italy), and G.Rizzoni (Ohio State University, Columbus, USA), presented to the 1998 SAE Motorsports Engineering Conference as a paper titled "Reconstruction of Formula1 Engine Instantaneous Speed by Acoustic Emission Data". Strangely, the authors did not put forward the speed profile of a competitor's car as one of the variables that could be analysed by using the technique. From the proximity of Bologna to Maranello, it is possible to surmise that Ferrari funded the work, and that they did not publish this application as that is exactly what Ferrari uses it for!
The principle employed in the technique, is the derivation of engine RPM from the frequency analysis of the sound emitted by an engine. A V-10, 4-stroke engine fires 5 times per revolution. As each cylinder fires and the exhaust valves open, it produces a pressure wave down the exhaust, which, when combined with other cylinders and sound reflections within the exhaust system, generates a sound which is predominately made up of frequencies that are a function of the firing frequency. That fundamental frequency for a Formula1 V-10 is: 5 x RPM/60 Hz (Hz = cycles per second). Thus, with suitable analysis of the sound of an engine, it is possible to determine the engine RPM.
All that is needed to sense the sound is a good quality microphone. If the microphone is stationary with respect to a moving car, the motion of the car - the well-known Doppler effect - will affect the frequency picked up. When a vehicle, such as a train or a car, passes someone standing by the tracks or road, the sound of the approaching vehicle is higher pitched than when it is moving away from the listener. There is an abrupt change in frequency of the sound as the vehicle passes, and it is only at the moment when it is opposite the listener that the true frequency is heard.
Thus it would be no use to sense the sound of an engine using trackside microphones; the microphone must be placed on the car itself. While most teams would object to a competitor mounting a microphone on their car, they cannot object to the microphones fitted to the video cameras they carry for transmitting on-board views for TV programmes. The researchers found that the sound track from pay-TV channels produced a rich sound source for their analysis.
Quasi-steady state analysis of the sound of the engine at the end of the straight, using the short-time Fourier Transform method, over a period of 0.2 seconds during which RPM hardly changes, shows the harmonic content of the signal. Figures: 1 and 2 show the 1998 Ferrari and McLaren-Mercedes respectively, at 16,000rpm on the Pit straight at Imola.
At 16,000rpm, the combustion frequency is 1,333Hz, and engine speed is 1/5 of that, i.e. 266.6Hz. The difference in the spectra of the sound intensity signals from the two engines is due to different amplitude harmonics, possibly caused by different exhaust pipe geometry. However, the interpretation of the spectra of Figures: 1 and 2 is Iimited to the understanding that they are valid only for a very short time duration, during which it is assumed that the engine speed is constant. To extract information about the speed of the engine as the car drives around the circuit, including fast transients as gear-changes occur, non-stationary signal analysis methods are used. These are known as joint time-frequency signal analysis, and permit the estimation of the instantaneous frequency of a signal with a time-varying spectrum.
Figure: 3 shows the time-frequency analysis of the Ferrari accelerating out of the last corner at Imola, down the Pit straight and then lifting-off for the first corner. Each curve represents a harmonic, the sound intensity controlling the resolution of the plotted line. For greater clarity, the 4 lowest harmonics are shown in Figure: 4, and in this figure the y-scale represents the RPM (calculated from frequency) of the topmost curve. The vertical lines of the "tooth forms" are the almost instantaneous changes in RPM due to gear-changes. At around 1.5seconds, the RPM rises suddenly, probably due to wheel spin, and then stabilises as the driver lifts the throttle to control it.
Figures: 5 and 6 show the same analysis for the Ferrari at Curva Tossa and the double corner, Curva Rivazza, respectively. The data was taken during the race, and peak RPM from these plots is 17,450rpm (lift-off for Curva Tossa), while RPM in the corner can be as low as 7,250rpm (apex in Curva Tossa). The pronounced vertical line at around 1second in Figure: 6 is probably caused by the car passing under a bridge over the track, and the microphone picking up reflected sound waves from the exhaust.
While rich in information about the engine and the way the driver uses it in corners, the authors' analysis does not yield car speed directly. However, all the information is available. The speed of all the cars is measured at 3 places on the track during a GP event, by the TAG-Heuer timing system. A similar system can easily be set up by a team during a test session, and usually is. By relating speed at a given point to the engine RPM derived from acoustic analysis, the overall gear ratio, in the gear selected at the measurement site, can be calculated. All the other ratios can then be calculated from the RPM drop between gears during gear changes. With the RPM and the gear ratios known, it is a straightforward task to calculate speed at all points around the circuit.
Just a speed profile is not sufficient to calculate an opponent's power, aerodynamic downforce and drag, and balance. However, the differences between Formula1 cars, particularly those at the front of the grid, are quite small - maybe only 2 or 3%. All teams know their own cars intimately, and have data banks of all the parameters that describe its performance. Lap Simulation software is used extensively to calculate the cars predicted lap time around a track using these data files as inputs, and the simulation can output a speed profile. This profile is compared and simulation inputs changed by small adjustments to tyre coefficient of friction (for temperature, track condition and compound effects), ambient conditions (air density and humidity affect power and aerodynamics), and wind (aerodynamic downforce and drag corrections), until they match the actual speed profile.
Armed with a competitor's actual speed profile, derived from acoustic analysis, his own actual speed profile and a matched lap simulation speed output, the simulation engineer can set out to determine the source of the differences between the competitor's speed and that of his own car. The process is made very much quicker if it is known that the two comparison cars are on the same tyres, or that the differences in tyre characteristics are already calibrated. Likewise it simplifies the calculation if the car weights are the same, as in Qualifying when the vehicle weight can be assumed to be 600kg, plus enough fuel for 3 or 4 laps, or in the closing laps of a race after the last pit stops, when all cars have the same fuel i.e sufficient to finish the race. Qualifying lap comparisons are also the best for comparison because it is likely that the respective drivers are driving at the limit of their cars' performance. This may not be true towards the end of a race. The competitors gear ratios are already known and will be input to the simulation.
Two approaches to quantifying the main performance parameters of the competitor's car are possible. Either expert trial and error, or a technique called parameter identification. Using trial and error, an experienced engineer can adjust the power curve, downforce, drag, weight distribution and aerodynamic centre of pressure, starting with the settings for his own car, until the simulation speed is a reasonable match to the competitor's actual speed. He will analyse the differences in full-throttle acceleration of the cars, with respect to speed, and deduce how much of the differences are due to power differences and how much due to drag differences - greater acceleration at low speed is mainly a result of greater power, while greater acceleration at high speed will also be affected by reduced drag. Consistently higher cornering speeds in low speed corners will tend to indicate a good balance (weight distribution and aerodynamic centre of pressure), while greater cornering speed in high-speed corners is likely to be a function of more downforce. Braking performance at different speeds can also indicate relative levels of downforce and drag. An engineer who really understands the performance of a Formula1 car should be able to close in on a good match within about 10 iterations.
Parameter identification effectively automates this process. Those parameters that most affect the speed are systematically varied until the best possible match between the lap simulation model and the actual car are achieved. Suitably intelligent algorithms can speed up the process by cutting down the number of variations necessary to arrive at the optimum match. The values for the performance parameters that provide this match are then output. To achieve a detailed power curve and an aero. map may involve thousands of variations and millions of calculations, but this is just what computers are best at.
All Formula1 teams and their engine manufacturer partners, if they are truly serious about winning, strive to push the performance of every component a little bit more each year. To do so requires major R&D effort into every aspect, searching for tiny gains that add up to a measurable whole. It is extremely hard to set actual targets for this research, and the results are a product of effort, expertise and even luck. If the Technical Director can walk into the engine R&D department and show the researchers their competitor's power curve, he can then set an immediate target of matching it and a longer term one of beating it. Knowing exactly what a competitor is using to win is an immensely strong incentive, and it can focus the mind wonderfully!