Before we take a look at the effect of rake on a Formula One car, we need to explain the underside of the car. This has long been a topic of regulation given the potential downforce that can be extracted from a well-designed underbody.
Concept of Ground Effect in F1 cars
The bottom of the chassis or floor must be flat by technical regulations. It is the lower part of the chassis that extends from the beginning of the so-called tray, to the beginning of the diffuser. The lower surface of the 2 sidepods and even that of the floor itself, could originally be curved, as when Colin Chapman created the Lotus 78 and Lotus 79 (Figure 1).
When a car travels at a certain speed on a fixed surface (asphalt surface of the circuit) in a gaseous medium such as air, and there is a certain clearance distance between both surfaces, there is a significant reduction in static pressure (below the atmospheric pressure) between the duct walls and the circuit surface, which generates a vertical force or “downforce” (DWF) that pushes the chassis down. This force is proportional to the static pressure on the surface of the bottom of the car and its two sidepods, multiplied by the total section of that plate. This effect, due to the speed of the car that generates a negative pressure in the conduit with respect to atmospheric pressure, is known as the “Ground Effect”.
We must bear in mind that the reason for the Ground Effect occurs for three physical reasons or numerical simplifications of reality: the Bernoulli's Principle, the Continuity Equation and the Venturi Effect (which derives from the two previous ones).
The diffuser starts where the flat floor ends, increasing the section or passage area. The diffuser is in charge of “diffusing” the pressure and increasing it gradually until it reaches the atmospheric pressure value that surrounds the car.
The continuity equation describes the uniformity in terms of flow within a duct or tube. If there is no opening within that conduit that allows fluid to enter or exit the conduit. The mass-flow rate of air entering the conduit will be equal to the mass-flow rate of air leaving the conduit. Recall that we are dealing with speeds of the car that are of the order of Mach 0.3, so the fluid can be considered as incompressible.
Considering Bernoulli's Principle, for a constant mass-flow rate, the total energy remains constant along a flow line (or “streamline”) through the duct, so if the cross-section area decreases in one part of the duct, the air speed will increase in that part and, therefore, the pressure will decrease.
The downforce generated by the ground effect is very important because it is a force that does not have inertia. Furthermore, this force is essential since it compresses the elastic part of the suspension system and consequently compresses the tyres against the ground, increasing the friction force between the contact patch and the asphalt.
It should be remembered that before the ground effect was used, F1 cars generated accelerations of approximately 2g while cornering and 2.8g while braking. The Lotus 79 was a considerable improvement and generated 2.8g to 3g and 3.5g respectively. Those values created a great difference in efficiency and from that moment, that radically changed the aerodynamic design of racing cars.
It is important to indicate that it is NOT necessary to use a curved floor, because the most effective system is to use a flat floor, followed by a diffuser, because it allows a greater stability of the air flow that circulates under the car and maintains a lower average negative pressure. This was the reason why the Williams FW07 were more efficient than the Lotus 80, as Patrick Head was the first Engineer who designed the flat floor on both sides and a long diffuser with an angle of maximum 7 to 10 degrees, to keep the boundary layer adhered to the diffuser walls.
The pitch or “rake” is defined as the angle that the car's floor forms with the asphalt; the greater this angle, the greater the downforce the car will generate. But this angle has a limit for each car design. In order to achieve a high rake angle, it is necessary that both the floor and the diffuser work together optimally and this, logically, is complicated. There are many variables that intervene in this optimization: dimensions of the floor and diffuser, inlet and outlet areas of the floor and diffuser, heights, expansions ratio of the floor and diffuser, etc.
A bad design in the floor-diffuser assembly can produce the so-called “porpoise effect”. It occurs when a viscous air blockage under the floor is created at high speed, impeding more air from passing through the floor and, hence, losing downforce which, in turn, increases the clearance height and then it generates a high vertical force again. This creates a sinusoidal movement with a certain frequency that creates stability problems in the car, a problem that forced Colin Chapman to use very stiff springs to control this oscillation at high speed and in fast corners, which in turn created the additional problem of making the tyres work with high oscillation amplitude, not allowing to solve the problem.
As a summary, the air circulation below the bottom of the car, follows the following path: it enters from the front of the floor and accelerates as the cross-section area is reduced; it continues under the floor producing low pressure which sucks the car down (downforce); it reaches the diffuser and exits the rear of the car. But how is it possible for the diffuser to extract or produce force to pull the air flow if there is “more pressure” in the diffuser than under the floor? The answer is that, at the transition between the floor and the diffuser, right at that kind of corner, the so-called “crack pressure” is occurs, which, as its name indicates, generates a very sudden pressure drop, which is the responsible for pulling the air flow from the front of the floor, forcing the air to pass through the entire floor.
In Figure 2 and 3 there are some views of the car (a Formula-E) used to verify the pressure distribution under the floor-diffuser system explained above, by means of CFD analysis (test conditions: air speed = 250 km/h, rake angle = 1°, rotating tyres and rims).
Figure 4 shows the pressure distribution at the centre line under of the car, where "A" corresponds to the floor section, “B” is just the aforementioned “Crack Pressure” or “braking line” and “C” is the diffuser section. It can be notice exactly what has been explained before: "B", a noticeable low pressure, a greater average pressure in "C" than in "A"; in fact, the diffuser produces little total load, compared to the floor.
A surface (static) pressure plot is shown in the bottom view of the Formula-E model depicted in Figure 5 where the aforementioned zones (A, B and C in Figure 4) can be clearly distinguished. The low-pressure areas are represented in coloured blue, that is, the beginning of the floor (where the air flow accelerates) and the Crack Pressure area at the separation line between the floor and the diffuser.
Global analytical comparison between a “double-setup” car (high rake), compared to a “single-setup” car (low rake)
The analysis is carried out based on the setups, represented in Figures 7 and 8 (1 rake angle) and in Figures 8 and 9 (3° rake angle), that are imposed on a basic model of an F1 car.
Other images of the analysed car are shown below. Technical data of the CFD simulations is exposed at the end of the document.
Car in high-rake condition (double setup)
The system of a high rake or aerodynamic double-setup racing car consists of a car that presents a basic change in the Concept of the racing car design, since it is a car that works with two aerodynamic setups in the same car, so it needs a rear suspension system that works with a double vertical stiffness and a front suspension that allows precise control of the clearance height, provided with a combined damping system to act in the 3 states: 1) movement in heave (vertical movement of the suspended mass without rotation in the Y-axis) and in braking (controlled by the 3rd element); 2) movement in a curve, to damp the movement in roll; and 3) movement to control the damping of each wheel at high frequency and the impact against the kerbs.
The elastic system of the front suspension is provided with two torsion bars installed on the shaft of each rocker, which support the static load of the car and the variations in dynamic loads from the downforce, the circuit disturbances and the braking, cornering, acceleration states and their combinations, allowing precise control of the clearance height. The group of shock absorbers allow the accumulated energy to be dissipated by the different load variations that the car undergoes in its movement along the circuit. It also has an anti-roll bar to minimize the roll angle of the car.
It should be noted that all these elements are commonly used for several years in competition cars, but, in the case of this car, they must allow a correct operation both in the low-rake state (in the straights) and in the high-rake state (at the initial braking moment and when cornering, specifically in low-speed corners), because this car allows a large variation of the rear clearance height.
The rear suspension also has similar elements to control the height of the rear axle, firstly the control of the static load, plus the variation of the DWF and the variations of the dynamic loads when moving the vehicle on the circuit, similar to the case of the front axle, but with different values due to the distribution of static and aerodynamic loads, plus the control of the clearance height of the rear axle, due to the considerable variation in height when driving the car on straights and when braking and cornering (which is a function of the car speed). The car must have a suspension with two different values of vertical stiffness, a soft one, to work at a clearance height that ranges from 165 to 85 mm of the rear sprung mass and another with greater vertical stiffness to control the height of the rear sprung mass when it is between 85 and 45 mm.
When braking, before entering low-speed corners, the vehicle increases the rear height due to both the load transfer and the loss of speed. This reduces the DWF, increasing, at this time, the height of the rear Centre of Gravity, reaching approximately 165 mm rear height and 3 mm of front splitter clearance. Due to the longitudinal weight transfer under braking, the lower front lip of the chassis floor approaches the pavement surface, to the point of hitting or leaving a 3mm gap, reducing the clearance height of the front wing, increasing the front DWF, due to the Ground Effect. That reduces the possibility of understeer in the front axle by means of the 3rd element of the front suspension that does not allow the clearance height of the front wing to touch the asphalt. The roll moment created by the centrifugal force, acting on the sprung mass at the height of the Centre of Gravity, which increases due to the greater clearance height of the rear axle, must also be controlled (it should be remembered that by increasing the rake angle, the height of the engine and the gearbox increases, relative to the asphalt surface due to the roughly 3-degree rake angle that the high-rake car takes).
When driving the car in low-speed corners, it generates a high lateral weight transfer from the inner to the outer wheel one on the rear axle, due to the high roll moment (as mentioned above), unloading the inner wheel and causing the car to turn practically on three wheels (the two front wheels and the external rear wheel). That facilitates the car to turn, due to the reduction of the mechanical grip on the rear axle, because it practically works on the external wheel (which has a grip potential of the order of 60 % to 70 %, according to the radius of the curve). To avoid slipping of the internal wheel (wheelspin), it is necessary to use a high percentage of locking in the self-locking differential (approx. 60 % to 65 %). To prevent the front wing, which is very close to the ground, from touching the ground (as this would cause it to lose downforce) its height is controlled by the third element and its roll is controlled by a rather stiff roll bar (in order not to lose downforce on the part of the wing on the inside of the corner).
Ultimately, the concept of a high rake allows the reduction of understeer in low-speed corners. With this, the car has a controlled lateral grip (at the limit of lateral slipping of the rear), controlled by braking deceleration and the steering wheel angle given by the driver, thus keeping the percentage of oversteer (controlled oversteer) of the rear end and minimizing the understeer (min. understeer) of the front end. So far, not all drivers can drive this type of car as correctly as Max Verstappen can, because Adrian Newey allowed him (almost from his start in F1) to learn and develop the driving technique of a high-rake car (Figure 10).
For this reason, the high-rake car can be very fast in low-speed corners, by allowing a fast change of direction, without practically understeer. But there is the problem that, as the cars works with practically a single wheel on the rear end in low-speed corners, the external rear tyre is overstressed, which increases external tyre wear, probably causing a greater degradation than in a traditional low-rake car. The latter has a smaller vertical load difference on both rear tyres in low-speed corners, and does not overstress the rear tyres when cornering, allowing a greater number of laps with the same tyre set compared to a high-rake car. Low-rake cars put more stress on the front axle tyres, because they have a greater clearance height in the front wing in low-speed corners and this causes less ground effect than the high-rake cars do, so they are closer to the critical understeer.
Analysing now the high-rake car during the moment of acceleration, at the exit of low-speed corners and at the start of a race together with its behaviour in a straight line at high speed, the following points are observed:
• In the case of starting the race (on dry or wet ground), as well as at the exit of low-speed corners, the high-rake car has the clearance height in the rear end of around 165 mm at the start of the race and between 145 and 150 mm at the exit of low-speed corners. So it is understood that the rear end is still supported by the elastic system with less vertical stiffness (remember that the high-rake car has two vertical stiffness values as explained above). This makes it possible to generate a greater linear acceleration, because as the rear end is supported, at that moments, on a low-stiffness suspension system, at no time will the car be at a point of high vertical stiffness in the rear axle, which would cause the rear tyres to skid, losing longitudinal acceleration, since the softer suspension with allows higher longitudinal acceleration, with greater progressiveness in the application of power under acceleration. This allows a more efficient acceleration on wet floors and floors with little mechanical grip.
• At the moment of acceleration (when changing to higher gears), it also allows a greater acceleration efficiency between gears. But remembering that the DWF grows in quadratic proportion to the increase in vehicle speed, the increase in DWF will quickly compress the softer elastic system of the rear suspension, leaving the car, after the 5th gear, supported by the stiffer elastic system, so the rake angle gradient will begin to tend at a constant angle of approx. 1.0 to 1.3 degrees. As the DWF continues to increase, that will bring the clearance height of the rear sprung mass below 70 mm, reducing the “Cd × A” product and the angle of incidence of the rear wing, which reduces the drag of the car as a result of the reduction of the car's master section (A) and its Cd coefficient. At the same time, the DWF on the rear axle increases due to the increase in ground effect because of the proximity of the asphalt tape to the rear diffuser due to the reduction of the clearance height of the rear axle.
• The reduction of the “Cd × A” product increases the vehicle speed and the car enters a similar aerodynamic setup field of a traditional low-rake car, so the car does not recover the consumed power compared to low-rake cars, where the final speed depends on the BHP value of the power unit (PU). Therefore, if a traditional car has a higher BHP value, this car will be faster on straights, because, as both cars have a similar “Cd × A” product. The highest speed will be performed by the car with the highest power, although the high-rake car is faster in slow corner zones.
• In high-speed corners, there is not big efficiency difference between both cars (traditional or low-rake cars and high-rake cars), because both will have a very similar rear axle clearance height. In the high-rake car, its rear sprung mass will be already supported by the stiffer elastic suspension system, which is similar to that of the traditional car and the DWF is high and very similar. Therefore, the rear diffuser will generate a very similar ground effect value, as well as the rear wing, because the angle of incidence at that position of the circuit is quite similar (taking into account that, in order to simplify the study, we are considering that both cars work with similar ailerons that generate similar DWF, drag and aerodynamic efficiency).
Car in low-rake condition
To simplify the study of the double-setup car in comparison with a single-setup car (those with low-rake aerodynamics), an aerodynamic study in CFD has been carried out, considering the same car and varying only the rake angle from 1.0 to 3.0 degrees to determine the aerodynamic response to the change in rake angle, as it happens in high-rake cars in braking moments and in low-speed corners. On the other hand, a change in the rake angle from 3.0 to 1.0 degrees has been considered for the car when driving on high-speed straights (where it works with a low rake angle). Only CFD simulations in both angle values has been performed, that is, it has been considered two fixed and constant states.
It is important to note that, when varying the rake angle from 1.0 to 3.0 degrees, the aerodynamic “Centre of Pressure (CoP)” is shifted forward (in this particular case, from 43.4 % at the front for the 1.0° rake angle to 53.1 % at the front for the 3.0° rake angle). As can be observed, by varying the ground effect value in the front wing (and in the front part of the floor) due to the reduction of the front clearance height and the consequent loss of the DWF in the rear axle because the increase in clearance height in the rear end, makes the rear diffuser lose ground effect, so the aerodynamic balance varies, due to the proportional increase in the DWF in the front end and the loss in the rear end.
In Figure 11 surface pressure plots are depicted for a F1 car CFD model with a rake angle of 1.0° (top view) and 3.0° (bottom view). Low-pressure areas are represented in coloured blue and high-pressure in red. It is evident that at 3.0 degrees, blue areas increase substantially, indicating that the front wing is generating more downforce due to ground effect.
In addition, not only does the load on the front wing increase, but as said before, so does the lower part of the nosebox, that works as a front diffuser. With this, the CoP position with respect to the X axis can be calculated, where it is observed that, in the 3.0° rake angle car, the CoP moves forward with respect to the CoP position of the 1.0° rake angle car (Figure 16).
This difference in load distribution, because of different CoP location, can be appreciated by calculating the streamlines underneath the floor-diffuser assembly (Figure 12).
It can be noted that the double-setup car (the one with 3.0° rake angle), when driving on straights, or when exiting low-speed corners and increases speed, or also in fast corners, reduces its rake angle, but in these corners has a slightly higher rake angle than the single-setup car. Analysing in this way, it possible to clarify the physical fact of the aerodynamic behaviour of the car when varies the rake angle because of the increase in DWF as a consequence of the increase in vehicle speed. Looking at the pressures underneath the bottom of the car, in particular at the diffuser, large differences are observed. Three different pressure distributions have been calculated along three longitudinal sections (A, B and C) as shown in Figure 14.
The resulting pressure distributions are shown in Figure 15 (for the case of the 1.0° rake angle car) and Figure 21 (for the 3.0 rake angle car). Starting from the left of the plots, the first part of each curves corresponds to the beginning of the flat floor, whereas the end part corresponds to the end of the diffuser (if applicable).
One of the most interesting things that can be seen is the great low crack pressure (green peak down at the transition between the floor and the diffuser) that occurs in the case of 1.0° rake angle (Figure 15). On the contrary, in the case of 3.0° rake angle (Figure 16), the downward peak is much smaller and, hence, its crack pressure value is higher (less negative). As explained before, in the latter case, the diffuser does not work as well as in the former case, due to the greater clearance height at the rear axle of 165 mm due to the rake of this setup. In reality, the floor-diffuser assembly generates less DWF than in the case of the 1° rake angle car. This difference in pressure distribution is also reflected in a different distribution or evolution of the streamlines underneath the car floor as shown in bottom (Figure 17) frontal (Figures 18 and 19) and rear views (Figures 20 and 21).
For that reason a single car model is used as a reference model, without making modifications or aerodynamic corrections in parts of the body, ailerons and/or flaps, nor are special developments carried out to improve the efficiency of each set-up (whether with high or low-rake) only the response of the aerodynamic behaviour of the car is evaluated in its values of total DWF, drag, aerodynamic efficiency, percentage aero-balance of the front and rear DWF (with respect to the values of the clearance heights of the front and rear axles), the pressure diagrams on the car body and pressure fields around the car, diagrams of velocity, vorticity, position of the CoP (for high and low-rake conditions), streamlines at the top and the bottom of the car and also on the surface of the circuit track, vortex generations and other additional verifications, to determine the maximum efficiency of each set-up.
It is observed that this type of double-setup cars behave like a total DRS (Drag Reduction System), different from the FIA DRS that acts only on the rear wing to reduce the angle of incidence of the upper flap and reduce the drag of the rear wing, increasing vehicle speed to allow it to overtake the car in front. The angle of incidence of the double set-up car, varies mostly with the increase of the vehicle speed, with respect to the single setup cars, that have a much smaller variation of the angle of rake.
Remembering that the high-rake car (when it is braking or when cornering in low-speed corners), thanks to the reduction of the front wing clearance height with respect to the track surface, is able to generate a higher DWF value in the front axle, due to the increased ground effect on the lower part of the front aileron, its flaps and the lower part of the nosebox. Because of its inclination, the entire front wing assembly works as a front diffuser, rather than a wing, allowing to brake more deeply into the corner and to reduce the degree of understeer. This reduces the braking and traverse times on low-speed corner, due to the increased driving speed with the car under control. In this way, it is possible to anticipate the application of power on corner exit, as the higher DWF of the front wing means that it does not suffer from critical understeer on entry and exit of slow corners, allowing it to accelerate before fully exiting the corner. At this point, the car has a lower vertical stiffness in the rear axle than the stiffness on a straight line (and a lower value than that of the low-rake cars), which allows the vehicle to develop power in a more progressive way, without reaching the sliding limit of the rear tyres (as explained in the first part of this report).
In other words, the potential advantage is at the moment of braking, where the high-rake car, in the first moment of braking, increases the rake angle almost instantaneously, thereby increasing the drag by increasing the rear clearance height, increasing the incidence of the chassis and especially that of the rear wing. The car is very effective when braking and reduces the possibility of locking the rear tyres because the car is, at that moment, supported by the softer of the 2 vertical stiffnesses of the rear axle.
This is just a basic study to understand the dynamic effect of a double-setup (high-rake) car versus a single-setup (traditional low-rake) car. There is still a lot to study, analyse and develop in order to achieve a highly efficient double-setup car. Considering that Adrian Newey began to develop this idea in 2009 and has already been working on this concept car for almost 12 years, it is very difficult for other designers to achieve a similar efficiency in their projects, since a lot of study and development work is needed to define an excellent vehicle dynamics: in aerodynamics, in the study of lateral load transfer in low-speed corners and when braking and accelerating, to make this double-setup car system work properly.
Also, as a final consideration, the numerical results of both simulations, and their variations with respect to the change of setup (rake angle), are presented. Many conclusions can be drawn from this first and quick analysis. Especially it can be seen that varying the rake angle from 1.0° to 3.0° the front DWF increases, however, the total DWF suffers a small variation (of the order of 1.7 % lower), so the efficiency in the car with 1.0° rake angle (since the drag is much higher than that of the 3.0° case) is bigger than that of the car with a 3.0° rake angle (see Table 1). It is also observed that the increase of front DWF shifts the CoP forward.
Note that the car on which the analysis has been performed is not optimised to work with a 3.0 rake angle; therefore, by carrying out a good development and optimisation work, the total DWF and the aerodynamic efficiency could be increased considerably.
With regard to the efficiency of the Red Bull car, it is observed that, in order to be as efficient in straight line speed as the Mercedes F1 car, it needs an increase of the current power output of its engine/PU by an estimated value of 4 to 4.5 %. It remains to be seen whether this will be achievable by Red Bull’s engine/PU supplier during the current championship.
It is interesting to note that the teams that have developed high-rake cars have lost less lap time compared to last season. The teams that have kept the low-rake concept, by changing the FIA 2021 regulations (basically by cutting the floor size), have lost even more lap time. Whilst Red Bull has lost around 1 second of lap time, Mercedes has lost around 2 seconds or so.
Being able to increase the rake angle of the car, allows increasing the DWF, because, if the FIA regulation reduces the DWF load in the order of 10 %, those teams that designed cars "capable" of having high-rake angles, can compensate for the loss of load by increasing the rake. Simple, isn't it?
Data of each CFD simulation
• Test speed: 250 km/h.
• 65 million cells.
• Boundary layer composed of 20 layers.
• Rotating tyres and rims.
• Moving floor.
• Radiators on sidepods.
• Engine intake.
• Gas mixture and temperature in the exhausts: 120 m / s.
• Front wheel brake disc and calliper.
• Heat transfer in engine block, exhausts, radiator and brakes.
• 72 hours of calculation on a PC with 256 GB RAM and 56 cores.
Nacho Suárez - PhD Electronics Engineer Vehicle Dynamics, Virtual 7-post rig, Simulation, Autonomous Vehicles, Embedded Systems, Control
email@example.com - https://www.linkedin.com/in/nachosuarezphd/