F1 PHYSICS
Formula 1® racing began in 1950 and is the world’s most prestigious motor racing competition, as well as the world’s most popular annual sporting series: The 2019 FIA Formula One World Championship™ runs from March to December and spans 21 races in 21 countries across four continents. Formula One World Championship Limited is part of Formula 1® and holds the exclusive commercial rights to the FIA Formula One World Championship™. Despite its straightforward nature of F1 at first glance, the physics of F1 is actually interesting and complex.
The Power Unit
No F1 car, whether you are Williams or Ferrari, would be able to function without a power unit.
A reliable, and powerful, power unit is the backbone to any F1 car. Over the years, the rules and regulations regarding engine rpm's in F1 cars have began to loosen, with the FIA capping it to 15,000 from 2004-2021, but giving teams the the luxuries of unrestricted rpm in 2022. To better understand the importance of power units, lets take a look at Ferrari's (illegal) power unit from 2019.
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As mentioned above, this power unit had the limit of reaching 15,000 rpm, which it was fully capable of doing. To relate engine rpm to linear speed, we must first convert engine rpm to wheel rpm:
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Engine rpm = Wheel rpm * Drivetrain transmission ratio
15,000 = Wheel rpm * 5.69
Wheel rpm = 2,637 rpm
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With this information in mind, we can now convert Wheel rpms to radians/second, where 2,637*2*pi/60 = 276.145 rad/s. Using this info, we can now relate this using the formula v =ωr, where 276.145 rad/s is ω and r (according to information offered by pirelli) is around 360mm = 0.36m. Therefore,
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v = 276.145 * 0.36
v = 99.412 m/s, which is around 357.9 kmh: the fastest speed Sebastian Vettel was able to clock down the main straight in sector one of the AUTODROMO HERMANOS RODRIGUEZ in Mexico.
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Therefore, Ferrari's power unit was able to offer them a large advantage in 2019, besting the one of their main rival Mercedes, whose top speed clocked in at 325.3 km/h.
Power Unit (Contd.)
So why was Ferrari's power unit in 2019 "illegal"? Well, to have deeper insight into this controversial topic, lets take a look at the Abu Dhabi Grand Prix of 2019. Prior to the Grand Prix, Ferrari declared that their driver Charles Leclerc would be using a total of 105 out of the allowed 110 kg of fuel to complete the race. Using this information, we can now set up an Conservation of Energy equation:
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Echem (initial) = Ke (final),
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Now, lets calculate the amount of energy in 105 kg of fuel. We can actually do this by substituting in a Kinetic energy equation, since the final and the initial are the same and calculating the energy of an E10 blend that uses 10% sustainable ethanol would be a hassle, so:
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1/2mv^2 (initial or projected) = 1/2mv^2 (final),
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We will call the initial value projected as it is projected kinetic energy of the F1 car while in motion, so lets find the initial energy. Given that the weight of the SF90 (the car) was around 743 kg, and the driver would have to compensate for around 80 kg of weight, the total energy would come to be:
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1/2(743+80+105)(99)^2 = 4547664 J
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However, the final Kinetic energy of the car as recorded totalled to around 4572166.5 J,
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4547664 J (Einitial) ≠ 4572166.5 J (Efinal).
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So where did the extra 24502.5 J come from? It was found that during a random fuel check of the Ferrari car, the reported fuel of Leclerc's car was actually around 5 kg (4.88 kg) of the accurate amount, bringing his total fuel up to 110 kg. This finding makes complete sense in the context of the Ferrari controversy, as the constructor was accused of excess fuel consumption and tricking the FIA's fuel-flow. This allowed them to push over the regulation flow rate of 100 kg/h, allowing them to gain significant advantages over other teams.
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How F1 Cars Turn
In F1, whoever dominates the turns and the car which can hit the turns the best wins the race. Due to the nature of F1 racing, every inch of an F1 car is designed to hit the turns as quickly as possible, the lack of speed when an F1 car hits turn might cause the car to spin out of the turn. F1 cars normally hit turns at speeds from anywhere between 50 kmh - 310 kmh. A good example of the faster end of the spectrum would be analyzing the famous turn "Eau Rouge" at Spa Francorchamps - the most famous turn in F1.
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To maximize lap times, an F1 driver will attempt the "apex's" of a turn, as shown above. This allows them to maximize their speed and enter/exit the turn with as much speed as possible. Normally, an F1 car enters Eau Rouge at 300 kmh. The speed of this entrance allows for the car to maximize its downforce (which is what the F1 car is designed to do). This means that the total force acting on the car downards can be equated by the following equation:
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Fnet = Fg + Fdownforce
Fnet = 743(10) + ½ (wing width in meters) x (wing height in meters) x (angle of wing) x (lift coefficient) x (air density) x (velocity).
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Taking a shortcut that a modern F1 car produces roughly 750 kg of downforce while moving at 300 kmh, we can convert this (as well as the initial Fg value) into Newtons:
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Fnet = 7430 + 7354.99 = 14,784.99 N. Therefore, a total for 14,784.99 N of force acts downwards upon the F1 car at Eau Rouge. With this conclusion, we can say that, to keep the car from sinking into the ground, the normal force of the F1 car would also have to be the same value. This, therefore, confirms our statement. Since the normal force is equated by Fn = ma, the F1 car would have to hit a certain speed in order to maintain the total normal force in order to maintain its course on a turn. An example of failure at this would be Lando Norris' crash at Eau Rouge in 2021.
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Momentum in F1
An Surprising application of Momentum in F1 can be found in the mechanisms that are used to keep drivers safe.
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With the speed and precision driving of F1 racing, the inherent danger that comes tied in with the sport cannot be ignored. Every time a driver gets into the car, he is essentially surrendering himself to driving 70 laps in a 300 kmh tin can. With this in mind, it is imperative that the safety of F1 drivers are considered to every minuscule detail, especially in the engineering of the car.
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With the consideration of other elements that bring safety to the drivers, such as the "halo", the most crucial part of an F1 car's safety would be how the car is designed to break into multiple parts very quickly upon impact against a surface. To understand why this works, we can take a look at the equation of Impulse:
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As impulse is a equated by Force * Time, and since momentum is always going to stay the same as it is always conserved, the aim of the engineers of the car should be to let the driver experience the least amount of force to keep him safe. By breaking the car into multiple parts, this increases the time value of the equation and therefore decreases the force (below):
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Therefore, by breaking the car into small pieces really quickly, engineers are able to decrease the amount of force experience by the driver in a crash, potentially saving them in the process. An example of this we can look at is Carlos Sainz's crash at Sochi, in which he experienced a total force of 46Gs. Without the crumbling of the front of the car to mitigate all of the 46Gs, it is likely that he would not have survived the incident.
