Technical analysis of a high speed run-Part 2
Sequel of the analysis of technical aspects and aerodynamics regarding the 300mph high speed run of the Bugatti Chiron SS300+.
This is the second part of the analysis, where I try to give you a small insight of the technical aspects of modifications taken to improve the Bugatti Chiron SS300+ (shortend in the article to SS300), with regard to the mechanisms behind them and a special focus on aerodynamics.
Mercedes W125 "Rekordwagen", fastest speed achieved on public roads with 432.7km/h in 1938 till the Agera RS recently broke it
The most obvious change on the car is its elongated and tapered rear. If you would elongate and tapper it even more it would start to resemble the rear of a boat. From this resemblance this measurement also gets its name “boat tailing”. You see this on several record cars like the Mercedes W125 “Rekordwagen” (which can be seen in the picture above ), where the tapering was made mainly in the vertical direction, but the principle is the same, another car with a strongly tapered end would be the Koenigsegg Regera. Like always the target is to minimize drag. The drag at the rear of the car is mainly determined by two factors: Pressure and area. A very small physics lesson for you: A pressure difference multiplied with the area it is acting on, equals the generated force. To minimize this force acting on the rear of the car we can reduce the rear area and/or reduce the pressure difference of it. By “boat tailing” we can do both. The reduced rear area is obvious I think, but the pressure is a bit more difficult. Remember the air curtains section? At the rear something similar happens, the airflow suddenly losses its body to follow, separates and will fill the space at the rear where no airflow is. This means the air flow wants to change direction quite drastically, it will start to curl up and creating turbulences. These turbulences generate a location of a lower pressure at the rear of the car, which acts on the rear and starts to pull back the car. Basically, like a large vacuum cleaner does in a comic movie. The tapered rear end redirects the airflow so, that the redirection of the airflow is less severe, in the optimum case like on the W125 so that the airflow is smoothly guided till it is again directed in the same direction without being separated at a sharp corner at all. A simplified visualisation I tried to provide in the following picture.
Simplified airflow at the rear of a car in top-down view without and with “boat tailing”
Rear diffusor and wing/spoiler
Modified rear diffusor, also note the slots behind the fence to release the pressure from the rear wheel arches as mentioned in Part 1
In contrast to the general believe a diffusor doesn’t only create downforce, actually it also has the ability to reduce the drag of a car. With a flat underfloor the flow underneath the car has a low pressure (yes again pressure, this is something very important in aerodynamics). This flow will then be expanded within the diffusor, which reduces the air speed and especially raises the pressure of the fluid. So, when the air arrives at the rear resp. exiting the diffusor it is closer to the ambient pressure and creates less drag on the rear. The whole diffusor was redesigned in comparison to the standard Chiron with the most obvious change in the exhaust positioning, width and a general more aggressive design. The new exhaust arrangement allows to use the central part of the diffusor more, which is the most effective part due the cleanest airflow going through. At the sides the diffusor is affected by pressure differences and mainly vortices coming from the tires. To minimize the tire disturbances the stakes at the side should seal the diffusor or create a counter vortex to cancel its effect, nonetheless this reduces the performance of this part. To rearrange the exhaust away from the diffusor area can also be seen at several track-focused updates like Ferrari 458 Italia to the Speciale, the Lamborghini Aventador to the SVJ or the McLaren 570 to the 600LT. For the SS300 this rearrangement meant also, that it lost its blown diffusor. When looking at the rear of the standard car one can see that the car has actually 6 exhaust outlets from which 2 are hidden within the diffusor (like the Veyron already had or the Mercedes GTR). The hot and fast exhaust gases should increase the performance by energizing and further accelerate the airflow within this diffusor part , but this additional performance is directly coupled to the throttle condition. A few years back this was used in Formula 1, together with an intelligent ECU to control the exhaust flow also when the throttle wasn’t applied in corners.
On top of the extended rear on can spot a spoiler (side note: a spoiler is a device on which a flow only passes on one side, whereas on a wing the flow passes over and under the device). Spoilers are used on cars since a very long time to reduce the rear lift or depending on the vehicle even create downforce. Generally, on a notchback designed car you have over the roof, rear window and trunk a low pressure due the air passing over it or in the worst cases seperation and vortices creating lift, by adding a spoiler you can change the pressure distribution and create overall higher pressures over the rear of the car and by this reducing the lift force. A nice additional effect of spoiler and rear wing also is that they interact with the diffusor and underbody flow and can improve them if engineered right. I couldn’t find out till now, if the active rear wing still is usable on the car. For the high speed run it is most certainly retracted. I personally would assume it is still operating because you still see the outlines on the bodywork, which you would otherwise cover to reduce gaps disturbing the air and to balance out the aerodynamic if the front diffusor is opened (personal assumption).
Engine and drag coefficient calculation
The SS300 got the same engine upgrade as the Centodieci, which means 100PS more power. This doesn’t sound that much regarding to the base power, but still is the power of a small compact car(!). A certain person doubted this number and stated that the car needed much more power to achieve this top speed. It is true that the competition has partially more power available to beat this speed maybe in the future (SSC Tuatara 1750hp  or the from M2K modified Ford GT which achieved 300mph in a standing mile with over 2500PS), but some also have the same amount as for example Koenigsegg with the Jesko  running on E85. In the following I wanted to check how much the aerodynamics had to improve over the standard car to achieve this higher speed, assuming they really produce “only” 1600PS and neglecting power train losses (which are actually not insignificant). The number WON’T be an exact number, because it is based on several assumption due a lack of information, but it can put it maybe a bit in perspective.
In a steady state (also when the car doesn’t accelerate) you can write the general power balance as followed (I won't explain how it is derived in detail here, otherwise you would stop reading I presume):
Power balance for a vehicle moving with a constant speed
The main power of the car has to work against the resistance coming from the aerodynamic drag (blue part) and the rolling resistance from the tires (red part). We can assume there was no inclination (the Ehra-Lessien test track is basically completely flat), so the yellow part representing this vanishes. The values taken for the aerodynamic part are a velocity of 135.9m/s (490km/h), an air density of 1.2133kg/cubic meters (the air density is based on the standard atmosphere at 100m above sea level, where the test track is placed) and a frontal area of 2.1squarmeter (the Veyron had one of 2.07 , but the Chiron is slightly larger and the assumption is close to the value I computed by comparing pictures). For the resistance from the tires, I’ve taken the empty weight of 1995kg and the assumption, that it creates no lift/downforce as stated in Part 1 (so the second part representing the aerodynamic force on the tires in the red box also vanishes). The rolling resistance coefficient of the tires is a bit more complex. The coefficient is usually taken as constant, even if it is dependent on temperature, tire pressure, load acting on the contact patch and of course the compound. But above a speed of around 100km/h this assumption isn’t any longer valid, because the coefficient is also dependant on the speed the tire is moving with. Next to the fact that the moving speed influences the other parameters (temperature, pressure), additional resistance arises due aerodynamic effects and vibrational waves which are formed within the tire. So I calculated the coefficient based on the most commonly used fourth-polynomial approximation of the speed dependency  (don't worry if you don't know what this means, you are perfectly fine) and corrected it slightly downwards. The so calculated value for the rolling friction coefficient was 0.1 (this is around 10x the value for low speeds). If you put all those numbers in the equation, add a bit mathematic and a portion unicorn magic you end up with a drag coefficient of 0.28. This doesn’t tell you much I suppose. The standard car has a drag coefficient of 0.36 in top speed mode , this would mean they reduced the drag by around 25% (like I said, this is just a very rough approximation to get a feeling of the magnitude), this would show that they had to put quite some work in the project, but I think it wouldn’t be completely impossible. Anyway more power would have been most certainly helpfull. To put the number in wider relation, SSC claims that the Tuatara has a drag coefficient of 0.279 to achieve over 300mph and the currently most aerodynamic production car is the Mercedes CLA with a drag coefficient of 0.23 .
Effect of altitude
Another statement of Bugatti claimed that the run is even more impressive, because they performed it close to sea level with a little sting to the run from Koenigsegg. As mentioned in the last section Ehra-Lessien, where the test track is located, is placed around 100m above sea level. The official record run from Koenigsegg was driven on the Nevada State Route 160 at around 1100m above sea level. As you can see in the blue part of the formula in the last section, the aerodynamic drag is directly proportional to the air density. If we take the standard atmosphere and compare the densities, we see that the air is around 9% less dense and with this you have also an equal amount less aerodynamic drag. This makes a large difference, especially if you think about that the aerodynamic drag is responsible for nearly 80% of the overall resistance, as follows from the calculation before, which you have to overcome. One could argue that also the engine losses power, because there is less oxygen in the same volume of air, which is feed into the engine. However, modern supercharged engines can compensate this at least partially by changing their ECU, injection and turbocharging pressure parameters.
Interiour of the prototyp at the public presentation with the roll cage, the racing seat, additionaly there is the data recording equipment, which seems to be already removed
At this kind of speed even small defects or mistakes can lead to a fatal crash. For a company like Bugatti and VW behind them, they are not allowed to make a mistake, otherwise the consequences for the public image and media response could be devastating. This means they have taken several measurements regarding safety. One of it is that they drove on their own test track even if it is a handicap regarding the air density, but they have their experience on it and have placed medical teams along the straight, which reduces the time in which they arrive in a case of fatality. Further they cleaned the whole track before the run, so that there are no sharp pieces around which can damage the already stressed tires. Speaking of the tires they x-rayed them before mounting them on the car to ensure, that the metal treads are placed in the right manner and are not touching each other, otherwise they would rub on each other due the tire movement and create a lot of located heat. Heat was also the problem why they didn’t run in the other direction. The pavement has a grain which is patterned in one direction due the years of driving cars in one direction on it. If you now drive in the opposite direction, you would drive against this very rough pattern and increase the friction and heat generation. The most controversial safety measurements they have taken is the removal of the seats and replacing them with a racing seat respectively the whole recording/measurement equipment (supposedly not only for the run, but it is a prototype, so they collected a lot of general vehicle data), together with the installation of a roll cage . It has to be said, that the additional weight of this components outweigh the normal seats. On a lap record the roll cage could provide additional stiffness, but on a high speed run these changes don’t affect the result. It was a prototype and prototypes are driven over the limit and with untested components installed. That’s why most of prototypes you can spot have race seat and cage installed, to guarantee the safety of the driver even with the much higher probability of a crash or failure of a component. Further as far as I heard is the roll cage even an option for the costumers to install.
Bugatti stated this was the last time they will attempt a top speed run. As awesome the technical/engineering side of this cars are and I love the achievements, I think we arrived at a point where the power figures and top speeds get slightly out of hand. However, this won’t stop the competition from battling for new records and I’m sure we will see their attempts in the future and am also curious how they approach it. I only hope they look for the safety of the driver and persons involved. I’d like also to add something to the “Zero-Lift” section in the last part, to which I was addressed to in the comments. It is unlikely that the car really produces zero net-Lift/downforce, most likely it will create a small amount of downforce to ensure stability, independent of changes in rake angle or environmental influences and also because it would be very difficult to exactly balance the car at every driven speed. For this input and insightful comment, I’d like to thank @JoshS.
This is the end of the second and last part of this article. I hope you enjoyed it as much as I did and you could learn something new. Again, if you have questions regarding the statements or would like to add something, feel free to do so in the comments. It further is to note that I'm still not a native English speaker so I'm sorry for grammatical mistakes. In the following there are the sources for the numbers I used in the calculations and statements.
7) Essentials of Vehicle Dynamics, Joop Pauwelussen; Chp.2
11) Books : Fahrzeugaerodynamik, Schütz; Race Car Aerodynamics , Katz; Rennwagentechnik, Trzesniowski
12) Pictures of the Bugatti Chiron SS300+ from netcarshow.net
13) Further: several interviews with Andy Wallace on Youtube and general public media information
EDIT: This are all educated guesses from me. It could be that the engineers had another or additional goal with a certain solution. In aerodynamics, small changes for example at the front can lead to large effects further down the car.