Right from the first race, a reversal of power between the Ferrari engine and the Mercedes has been noticed: the higher pace of the F1-75 compared to the W13 is, in fact, also due to greater engine power, as is evident from the better acceleration in the first half of the straight compared to the second. But how much is the power difference? And which of the two cars has the least drag?
To do this, I took the speed of both cars and used them to calculate the acceleration (doing the time derivative). This value is clearly affected by the track's slope at that point, so I calculated this slope from the elevation and travelled distance GPS data and used it to correct the previously derived acceleration.
At this point, I observed the acceleration for each speed value: each observation is a point on the graph. As I expected, 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. So, I can find the curve that best describes the data using regression and derive the power and drag values.
So we see that Ferrari's curve is always above Mercedes', which means that Ferrari accelerates better at every speed! At medium speeds, it is favoured by its greater power, and at high speeds by its lower drag and its greater power. From the values from regression, I can say that the Ferrari engine has about 2% more power than the Mercedes, or about 20hp, which gives an advantage of about 0.4s/rev. The aerodynamic drag of the Ferrari is also 1.6% less than that of the Mercedes. So the W13 has both a power problem and a high drag problem, confirming what we've heard discussed! Now we probably have more accurate numbers.
For the regression, I took sections with DRS open, 100% throttle, and brake off into account. The circuit is Bahrain, as the straights are numerous and cover an extensive speed range.
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