Some of you will remember my estimation of Ferrari's advantage over Mercedes in terms of Drag and Power that I made last week. The analysis was very appreciated, and many people asked me to add Red Bull to the comparison so that we could get the complete picture of the forces at work. We know that Red Bull has an excellent top speed, but is this due to the engine's power, the low drag of the car or both?
Like last time I took the speed of each car and used it to calculate the acceleration (taking the time derivative). This value is influenced, albeit to a limited extent, by the slope of the track at that point, which I calculated from the GPS altitude and distance travelled data and used to correct the previously derived acceleration.
I have therefore observed the acceleration for each speed value: each observation is a point on the graph. The higher the speed, the lower the car's acceleration: since the engine has approximately constant power, the force with which it pushes the vehicle forward decreases as the speed increases: P=F*v, so F=P/v. Furthermore, as speed increases, the force of aerodynamic resistance increases, with speed squared. The equation linking acceleration and speed is shown above.
Team engineers know the engine power P and the drag coefficient D of the car and can use the formula above to calculate the acceleration a for a given speed v. What I did was to reason in the opposite way: I already know acceleration and speed (via telemetry), but I don't know power and drag. Therefore, I can find the curve that best describes the data through regression, obtaining the values of power and drag (or rather, obtaining the values of the ratios P/m and D/m from which, assuming a value for the mass, P and D can be obtained).
We see that the Ferrari's curve is always above that of the Mercedes, which means that the Ferrari accelerates better at every speed! At medium speeds, it is favoured by the greater power, and at high speeds by the lower drag and the greater power. The regression says that the Ferrari engine has about 2% more power than the Mercedes, or about 20hp, which gives an advantage of about 0.4s/rev. It also has approximately 1% more power than the Honda engine, which is between the two (about 10hp less than the Ferrari, i.e. about 0.2s/rev). Ferrari's aerodynamic drag is also 2% less than Mercedes'. So the W13 has both a power problem and a high drag problem, confirming what we've heard discussed! What is surprising, however, is the RB's extremely low drag: the RB's drag is around 9% lower than Ferrari's and 11% lower than Mercedes'! This is due to both the car's design (which favours a low aerodynamics resistance) and the setup used in Bahrain (more unloaded rear wing compared to Ferrari). Low drag is RB's best weapon, to which Ferrari tries to respond with engine power, traction and downforce.
Does this data make sense? It seems so: Rb has -9% drag compared to Ferrari, which has 1% more power: RB's P/D ratio is therefore 8% greater than Ferrari's. Since top speed increases with the cube root of this ratio, this should translate into a 2.6% top speed advantage. RB's top speed was 322, and Ferrari's 316: a 1.9% difference, very close to the value predicted by the regression.
I hope you enjoyed the analysis; You can support the page (and request custom analysis!) here: https://www.buymeacoffee.com/F1DataAnalysis. Thank you!
Notes on methods and sources of error: for the regression, I considered sections with DRS open, 100% throttle, brakes off, and engine revs >10000rpm. In addition, I only considered acceleration values greater than -0.5m/s^2 (to avoid the phenomenon of clipping, i.e. the drop in electrical power at the end of the straight). The circuit is the Bahrain one, as the straights are numerous and cover an extensive speed range. P and D are both considered constant: obviously, engine power varies during the straight due to the electric motor's delivery strategy (an error limited, however, by the fact that in qualifying, the battery is squeezed to the maximum, so the 120kw of the electric motor is exploited most of the time) and as the number of revs varies (but negligibly, since the flow of fuel is constant above 10500 revs, so its power is more or less constant. Consequently, the gear ratios also have almost no influence. So what I get is a comparison of the AVERAGE power outputs of the various cars during the straights, which is the single power value that best describes the car's performance). In the future, I will further refine the analysis, for example, by excluding points that exceed a specific value of lateral acceleration (which would cause an increase in drag).