Analyzing Porpoising on High Downforce Race Cars: Causes and Possible Setup Adjustments to Avoid It

Abstract

The so-called porpoising is a well-known problem similar to bouncing that is affecting the dynamic behavior of basically all the field of 2022 Formula 1 racing cars. It is due to the extreme sensitivity of aerodynamic loads to ride height variations along a lap. Mid-way through the season race engineers are still struggling to cope with this phenomenon and its consequences, with regard to either physiological stress experienced by the drivers or to overall vehicle performance and stability. The paper introduces two kinds of models based on real-world chassis and aerodynamic data, where the above-mentioned downforce sensitivity has been arbitrarily recreated through the application of a decay function to aero maps. The first one is a quasi-static model, usually adopted as a trackside tool for controlling ride heights and aero balance, while the second, a fully dynamic model, recreates the interaction between oscillating aerodynamic loads and suspension dynamics resulting in a visible porpoising phenomenon. Basic setup changes have been tested, including significant static ride height variations. The paper should be seen as a proposal of guidelines in the search of a trade-off between aerodynamic stability and overall performance, without pretention of quantitative accuracy due to the highly confidential topic, which makes numerical validation impossible.

1. Introduction

The modelling of racing cars featuring high downforce levels, such as Formula 1 single-seaters and Le Mans prototypes, can offer a unique insight into the interaction between vehicle dynamics and aerodynamics. For 2022 the FIA—Fédération Internationale de l’Automobile—has modified the Formula 1 Technical Regulations completely. The change is mainly aimed at reducing downforce sensitivity to drafting (or slipstreaming) in order to make overtaking easier, thus forcing a complete changeover in terms of body shape and proportions as well as wing and underbody design. Most of the downforce is now produced by means of ground effect resulting from the presence of very large Venturi ducts built into the underbody. At the same time the peculiar shape of the 2022 front and rear wings, together with the absence of various winglets aimed at vortex generation or control, makes them less effective by far.

Start-of-season tests and the first races showed that such a one-off event is somehow a leap into the unknown: more or less all cars are suffering from severe bouncing—the so-called porpoising—along the straights. This is caused by aerodynamic instability, and can result in floor damage, driver discomfort, discontinuous tire contact patch loading, and poor high-speed performance overall. As a matter of fact, the problem was first experienced with ground-effect Formula 1 cars about 45 years ago: it is due to marked non linearities of the downforce along ride height variation induced by downforce itself. In simple words the air flow under the car stalls whenever the floor is very close to the ground, i.e., at high speed. Downforce collapses and the car bounces back to static ride heights (or even beyond), restoring downforce in turn as a consequence. Nearly half-way through the season the problem is still there, with drivers beginning to complain about potential consequences in terms of spine injuries.

Aerodynamic characteristics of Formula 1 cars are considered highly confidential and therefore they are not usually available to the vehicle dynamics community, even more so for newly designed cars of the 2022 season, where underbody aero is said to be dominated by vortex flow. Nevertheless, the porpoising phenomenon can be studied by means of a model built on the basis of a similar car with ground-effect aerodynamics, as what really counts here is ride height sensitivity.

The authors have used a lumped element model for simulating coupling between non-linear aerodynamics and suspension dynamics in [1]. The present study however describes a methodology typically aimed at performance improvements through optimization of aerodynamics and mechanical setup by means of more accurate models. This simulation approach is often used for trackside engineering [2] and for off-line lap time simulations as well [3,4,5,6,7,8,9]. Other potential applications are aimed at the design of peculiar suspension and steering systems [10,11] and advanced powertrains [12], while lap time simulation can also be addressed at the evaluation of physiological parameters when driving at the limit [13]. Lap time simulation is also used quite often for autonomous race car control [14,15] and tire performance optimization [16], and also to consider the variation of tire functional characteristics along the lap [17].

A model of a single-seater GP2/Formula 2 racing car, conceptually similar to a Formula 1, has been created for the purpose. Although featuring just four DOF and being quasi-static, the model is highly detailed. The suspension model for instance is based on suspension kinematics computation by means of a dedicated software tool described in [18,19] and provides for variable motion ratio, pressurized gas damper preload, non-linear rubber bump stops and it is coupled with a variable radius tire model taking vertical force, vehicle speed, and wheel camber angle into account. Both models are based on official information and data supplied by the vehicle and tire manufacturers respectively.

A more sophisticated approach has been adopted for numerical modelling of the aerodynamics characteristics, featuring strong non-linearities that make modern racing cars highly ride height- and pitch-sensitive. 3D scanning has been performed on a real-world GP2 racing car with the aim of recreating a complete CAD model of the car body surfaces, comprehensive of outboard wheel/tire assemblies, front and rear wings, various winglets, driver’s helmet, and underbody floor with Venturi ducts. The CAD model has been used for a comprehensive CFD study aimed at estimating the so-called aerodynamic maps (or aero maps) i.e., drag, downforce, and aero balance characteristics with reference to underfloor distance from the road surface along the front and rear axles. Discussions on aerodynamic properties of current F1 cars and on the CFD analysis itself go beyond the scope of this paper, which is focused instead on the effect of ride height sensitivity on vehicle dynamics.

After a thorough comparison with original data supplied by the vehicle manufacturer for validation, the aero maps have been applied to the four DOF model to obtain quasi-static, speed-dependent ride height variations, suspension stiffness at ground, overall downforce, and its fore/aft distribution, commonly referred to as aero balance.

In order to simulate porpoising, a modification of the aero maps has been implemented by introducing further ride height sensitivity in an attempt to replicate the aerodynamic instability of the 2022 Formula 1 cars. The same aero maps—either original or modified—have been applied to a full vehicle dynamics model built within the VI-grade environment. These simulations allow for the reproduction and analysis of the porpoising phenomenon with its peculiar dynamic characteristics that trigger aerodynamic instability by interacting with the suspension system. Some attempts have been made to reduce or remove porpoising through variation of typical setup parameters like damping, spring stiffness, bump stop gaps and stiffness, and static ride heights.

Finally complete lap time simulations were carried out in order to compare the behavior of the original model with the same car affected by porpoising and with the latter car with modified static ride heights, in an attempt to identify effective solutions to the problem in terms of overall vehicle performance.

2. Materials and Methods

Since a CAD model was not available to teams, a real-world GP2 car was 3D scanned, including driver helmet, underbody, sidepod internals (basically water radiators and exhaust), engine inlet/airbox, suspension arms, and wheel assemblies with brake ducts. The car was artificially loaded in order to scan the tires with a certain level of deflection. Scan data were then processed into a digital surface model in STEP format suitable for CFD analysis, see Figure 1 and Figure 2.

A GP2/Formula 2 single-seater is a professional racing car providing full adjustability in terms of either mechanical setup (basically several suspension and steering settings, gearbox ratios, limited-slip differential) and aerodynamics, where front and rear wings can be adapted to suit circuit geometry, weather conditions and driver style, physiology, and habits. The rear wing type (mono- or bi-plane) and settings mainly define the overall level of downforce and drag, while the front flap settings mainly define the aero balance, see Figure 2b.

Add-on devices like the so-called Gurney flaps (or nolders) can also be fitted on the trailing edge of both the front and rear flaps. On top of that, the car features large underbody Venturi ducts therefore it can be defined as a ground-effect car, whose behavior and performance are not so far away from a modern Formula 1 car. As such aerodynamic actions are extremely sensitive to ride height and pitch angle, they are defined through the distances of the underbody reference plane from the ground in correspondence of both the front and rear axles: the Front Ride Height (FRH) and Rear Ride Height (RRH) respectively.

Prior to CFD analysis some assumptions were made with regard to car settings and other details. An aerodynamic baseline setup in terms of front and rear wing configuration and static ride heights was defined on the basis of the authors’ experience as trackside engineers, namely referring to a qualifying configuration for the Sakhir international circuit in Bahrain. On top of that radiator characteristics as well as the exhaust gas flow rate were also defined.

The overall aerodynamic performance of a racing car can be identified through the set of functional parameters:

$$X=C_D,C_Z,A_B,$$

(1)

where C_D is the drag or resistance coefficient, C_Z is the coefficient of downforce generated by aerodynamic devices built into the vehicle body such as wings and undertray, and A_B is the above-mentioned aero balance i.e., the fore/aft distribution of downforce expressed as percentage on the front axle.

The open-source software OpenFOAM was used to perform a CFD analysis of the whole car in co-operation with the British company TotalSim. While some preliminary runs enabled fine tuning of the mesh and identification of critical areas where flow is detached from the body surface, various runs where required to sweep through the front and rear ride height range, starting from setup values all the way down to hitting the ground with the underbody. Setup or static ride heights are defined at zero speed: FRHS and RRHS.

As stated before, an in-depth description of the meshing and CFD stages is beyond the scope of this paper, as are detailed analysis of flow dynamics, boundary layer, vortex structure, and pressure fields around the car. Nevertheless, Figure 3, Figure 4 and Figure 5 show examples of some post-processing methods made available by CFD analysis.

What is relevant here is that such a sweep enabled generation of the so-called aerodynamic maps, therefore replacing experimental testing in the wind tunnel. These 2D look-up tables describe the functional properties of the car in terms of aerodynamic performance. They feature values of the products C_DS, C_ZS, as well as aero balance A_B, as a function of the combination of dynamic front and rear ride heights, FRH and RRH respectively. S is the frontal area of the car, often assumed as a nominal value of one meter squared for a single-seater racing car.

Figure 6, Figure 7 and Figure 8 show the C_DS, C_ZS, and A_B aero maps for the aerodynamic configuration under scrutiny.

Interpolation of aerodynamic maps can be performed in many different ways: from ANN (Artificial Neural Networks) to the Kriging regression method to Akima splines [20,21,22,23,24]. A common approach based on [25] is a polynomial function of the type:

$$\begin{array}{c}X=a_1·FR{H}^3+a_2·RR{H}^3+a_3·FR{H}^2·RRH+a_4·FRH·RR{H}^2+a_5·FR{H}^2+a_6·RR{H}^2+a_7·FRH\\ ·RRH+a_8·FRH+a_9·RRH+a_{10} ,\end{array}$$

(2)

where a set of coefficients a₁…a₁₀ can be computed by means of a regression technique for each of the three functional parameters C_DS, C_ZS, and A_B.

The effect of setup changes in terms of wing angle is computed as a contribution to be added to the baseline output from the look-up tables for each wing profile (mainplane and/or flaps):

$$\Delta X=b_1·{\alpha }^2+b_2·\alpha +b_3+c,$$

(3)

where a is the angle of attack, b₁, b₂ are the related coefficients and c is the further contribution of any add-ons. This formula is not suitable for modeling the stall phenomenon often occurring for large values of a, which should be avoided anyway.

Overall drag F_D and downforce F_Z can then be computed for any aerodynamic setup and for any combination of front and rear ride heights by means of the well-known expressions:

$$F_D=\frac{1}{2}\rho C_{D}S{V}^2,$$

(4)

$$F_Z=\frac{1}{2}\rho C_{Z}S{V}^2,$$

(5)

where r is the air density and V is the vehicle speed. Downforce on the front axle F_Zfrt and rear axle F_Zrr can be respectively computed as:

$$F_{Zfrt}=F_Z·A_B,$$

(6)

$$F_{Zrr}=F_Z·\left(1-A_B\right) .$$

(7)

While aerodynamic efficiency is computed as the ratio between downforce and drag as usual:

$$Eff=\frac{F_Z}{F_D} .$$

(8)

The peculiar shape of the efficiency map—which is obviously a function of front and rear ride heights too—is emphasized in Figure 9.

These functional characteristics have a massive impact on tire vertical loads, and hence on racecar drivability, performance, and ultimately lap time. Especially aero balance is of particular interest for the trackside engineer: even apparently small changes can affect cornering balance in terms of understeer/oversteer and vehicle stability, especially in the turn-in transient phase. According to the authors’ experience a 0.2% aero balance variation can be easily perceived, at least by a professional driver.

All the three aerodynamic parameters are therefore non-linear functions of dynamic ride heights:

$$X=F_D,F_Z,A_B=f\left(FRH,RRH\right) ,$$

(9)

Dynamic ride heights are in turn a function of static ride heights, overall downforce, and aero balance, hence they are strongly dependent on vehicle speed on one side, and on parameters related to chassis settings, such as tire and suspension stiffness at ground level, on the other side.

The above Figure 6, Figure 7, Figure 8 and Figure 9 show that downforce tends to increase dramatically when the car gets closer to the ground, especially at the front end, thus moving the aero balance forward with increasing speed. It is therefore mandatory for the trackside engineer to master the interaction between aerodynamics and mechanical setup by means of proper simulation tools.

2.1. Quasi-Static and Full Vehicle Models

A comprehensive vehicle model is therefore required, where speed and static ride heights are the input variables, parameters defining aerodynamic items and chassis setup in terms of overall vertical stiffness enter the equation, and aerodynamic actions result in the computation of dynamic ride heights, contact patch forces, and aero balance as a function of speed. A typical tool for trackside vehicle management responding to the above requirements is the well-known quasi-static, four DOF vehicle model taking heave and pitch as well as front and rear tire radial deflections into account.

Suspension stiffness at ground is mainly a function of suspension kinematics and spring stiffness, the latter being either a traditional coil spring or a torsion bar, as it is the case of the GP2 front axle. Pressurized dampers—a standard in motorsport—play a role as well: the gas preload PG is set by the pressure in the floating chamber and by the geometry of the damper piston and shaft. It can be around 400–500 N or even more hence its effect is not negligible.

The spring preload PS should be taken into account as well if some form of rebound stop is present. The overall spring rate is therefore

$$K_{Spring}^{\prime }=\left\{\begin{array}{cc}\infty & if F_{Spring}\le \left(P_S+P_G\right)\\ K_{Spring}& if F_{Spring}>\left(P_S+P_G\right)\end{array}\right\},$$

(10)

where K_Spring and F_Spring are the stiffness and force of the coil spring alone. A linear spring stiffness however is not suitable for the requirements of a high-downforce, ride-height-sensitive racing car with strongly non-linear aero maps. The spring-damper unit therefore is usually complemented by a “progressive” bump stop working in parallel with the spring. The force vs. deflection curve of a typical rubber bump stop can be described by means of a fourth-order polynomial going through the coordinate origin, see Figure 10. As such it is defined by a set of coefficients e₁…e₄ and comes into play once a free gap d is covered by the spring deflection D. The overall springing force is therefore

$$F_{Spring}^{″}=\left\{\begin{array}{cc}{K}_{Spring}^{\prime }·D& if D\le d\\ K_{Spring}^{\prime }·D+e_1\left(D-d\right)+e_2{\left(D-d\right)}^2+e_3{\left(D-d\right)}^3+e_4{\left(D-d\right)}^4& if D>d\end{array}\right\},$$

(11)

where the gap d can also be set to a negative value.

Suspension kinematics can be considered by means of the so-called Motion Ratio MR, to be defined as

$$MR=\frac{dW}{dD}=f\left(W\right)$$

(12)

where W is the wheel displacement and D is the corresponding spring deflection, or the equivalent linear deflection of the torsion bar. Being a function of wheel displacement, the Motion Ratio is directly related to ride height for each axle. In the case of a GP2 car however MR(W) is nearly linear, and in addition to the limited suspension travel typically used on a racecar, it can be assumed to be a constant value MR₀ linearized around the setup ride height. The overall force at the wheel is therefore [26]:

$$F_{Wheel}=\frac{1}{M{R}_0}·F_{Spring}^{″}.$$

(13)

Additional items like the so-called third element can be added with their own, linear or non-linear stiffness and motion ratio. Tire radial stiffness characteristics play a major role hence they must be considered. The tires do not only act as a spring in series with the suspension: they are subjected to growth due to centrifugal force as well. Camber angle g and eventually cornering forces F_Y also affect tire radius. According to refs. [27,28] the tire loaded radius can be computed by means of the empirical expressions:

$$R=R_0-dR,$$

(14)

$$dR=\frac{F_{Wheel}}{t_1·IP+t_2·V^2+t_3·V+t_4+t_5·\left|\gamma \right|+t_6·F_Y^2/F_{Wheel}}+t_7·V^2+t_8·V,$$

(15)

where R is the tire loaded radius under dynamic conditions, R₀ is the nominal tire radius in static conditions, and dR is the radial deflection, IP is the inflation pressure, V is the vehicle speed, and finally t₁…t₈ are a set of coefficients describing dimensional tire properties under vertical load for a certain speed, to be determined (usually by the tire manufacturer) on a dedicated test bench. Front and rear tires feature different dimensions and a specific structure hence two sets of coefficients are required for a single-seater racing car.

The overall springing rate at contact patch level is therefore strongly non-linear and “progressive”: it is mainly a function of suspension jounce and vehicle speed among other variables. It requires careful design on both axles in order to keep pitch angle hence aero balance under control with increasing speed, while avoiding bottoming at high speed and on road surface irregularities. Most of all, it means that static ride heights and setup parameters affecting springing rates front and rear are all powerful tools for setup adjustment, car balance optimization and finally for performance improvement.

Typical output graphs are displayed in the following images (Figure 11, Figure 12 and Figure 13) and explained in the captions.

The quasi-static, four DOF model described above was thoroughly developed and validated across four years of race engineering activity at international level, via comparison with on-board data acquisition and with the help of subjective feedback from professional drivers, especially with regard to the aero balance, which is one of the key parameters for overall performance. More recently, a full vehicle model was built from scratch in the VI-grade simulation environment and compared to the four DOF model for validation, following the very same approach for modeling suspension and aerodynamics in particular. All the various non-linearities were thus taken into account, including the ride-height-sensitive aero maps. Suspension kinematics for instance was fully modelled by means of a proprietary design tool [18] and included non-linearities like variable motion ratio and progressive bump stops. An official .tir file-based tire model was used as supplied by the tire manufacturer, for loaded radius and radial stiffness properties and for in-plane lateral and longitudinal forces, governing handling, acceleration, and braking. The vehicle model was then tested in steady-state mode with increasing longitudinal speed along a straight line and around a Formula 1 circuit like Sakhir in Bahrain, in order to check for model robustness and lap time accountability, although without claiming full correspondence between the GP2 car model and a highly performant, modern Formula 1 car complying with new technical regulations for the 2022 season. This model is referred to as Setup #1 later in the text.

2.2. Triggering the Porpoising Phenomenon

Different types of arbitrary decay functions were applied to the original aero maps and tested in order to reproduce the peculiar bouncing dynamics due to extreme sensitivity of downforce to front and rear ride heights from the ground: the infamous porpoising, as Formula 1 drivers, technical staff, and journalists have named it. The following function was chosen according to the criteria listed ahead, where F_{Zfrt_Porp} for instance is the front portion of downforce modified by means of the arbitrary decay curve:

$$F_{Zfrt\_Porp}\left(FRH\right)=F_{Zfrt}·{\left(\frac{FRH}{FR{H}_S}\right)}^{\left(\frac{1}{d}\right)},$$

(16)

so that in static conditions:

$$F_{Zfrt\_Porp}\left(FR{H}_S\right)=F_{Zfrt}\left(FR{H}_S\right),$$

(17)

and whenever the underbody panel is in contact with the ground:

$$F_{Zfrt\_Porp}\left(0\right)=0,$$

(18)

while similar decay function is applied to the rear downforce:

$$F_{Zrr\_Porp}\left(RRH\right)=F_{Zrr}·{\left(\frac{RRH}{RR{H}_S}\right)}^{\left(\frac{1}{d}\right)}.$$

(19)

Parameter d was set to a value of 7 in order to represent an abrupt loss of downforce whenever the underfloor drops all the way down to the ground. Figure 14 and Figure 15 show the above decay functions for front and rear downforce and the effect on ride heights as a function of vehicle speed as computed in the four DOF model i.e., statically, as well as on aero balance and efficiency. Because of the decay function, downforce is abruptly reduced once the car underfloor gets very close to the ground at high speed, resulting in turn in higher ride heights as well as heavily modified aero balance and efficiency curves. In steady state the aero balance trend appears more consistent, while efficiency is reduced at high speed.

Once the decay functions are also applied to the full vehicle model, the effect is clearly visible and appears quite similar to porpoising, recalling what happens on current Formula 1 cars. Figure 16, Figure 17 and Figure 18 show a comparison between the baseline GP2 car model with original aero maps (Setup #1, in blue) and the model with decay functions applied to aero maps (referred to as Setup #2, in red) in terms of straight-line behavior with increasing speed. What appears a simple effect when observed in quasi-static mode turns into a complex, cyclical combination of axle jounce and body pitch, where axle jounce is in turn a combination of damped suspension jounce and underdamped oscillation on tires. Validation with a real-world case unfortunately is not possible because Formula 1 vehicle data recorded on-board are not available outside the teams themselves, nevertheless a reference for the typical porpoising frequency can be easily estimated with the help of many videos available on the web by simply counting the number of bouncing cycles in a time interval, while a reference for the amplitude of vertical acceleration oscillations is available on [29]. Both numbers are extremely similar to what was achieved with the full vehicle model; hence we can say that porpoising is reproduced in a reasonably correct way.

It can also be stated that a vertical oscillation frequency around 6 Hz (see Figure 15) falls in a range where tolerability for the human body is low [30,31]. This is basically confirmed by various F1 drivers actually complaining of extreme discomfort, fatigue, loss of driving focus, and potential neck and spine injuries.

3. Results

Availability of the full model together with its capability for approximating the porpoising phenomenon makes it possible to search for a trial solution, although within the domain of the so-called mechanical setup only, since changes in terms of aerodynamics are certainly outside the scope of this paper. Given the intrinsically dynamic nature of porpoising, the very first variable that appears as a potential improvement is damping: front and rear damper curves were therefore modified separately, just by multiplying damping force values by two. Needless to say, in the real world such a massive change would imply detrimental effects in other areas of vehicle behavior—riding on kerbs for instance—but these consequences can be neglected at this modeling stage; in any case both changes were effective to a certain extent only. For the sake of simplicity Figure 19 and Figure 20 show the results for front bumping modification only, as rear damping returns a very similar trend.

The reason is that porpoising dynamics are basically caused by underdamped tire deflection, as shown above in Figure 18. In other words, hydraulic dampers cannot provide enough damping in the system to control body oscillations.

A second, straightforward attempt was an increased rubber bump stop stiffness, meaning in turn an overall larger wheel rate once the bump stop gap has been covered by suspension jounce. This change was tried at the rear only, as porpoising seems to be triggered by the rear axle or at least it seems to start there. Figure 21, Figure 22 and Figure 23 show however that the effect is not in terms of system dynamics but only in terms of downforce-related dynamic ride heights: porpoising is basically delayed until a higher vehicle speed is reached simply because the dynamic ride heights are higher. A change in bump stop characteristics can be seen therefore as a tuning item, but not as a solution. Similar results were achieved by increasing spring stiffness or by changing the gap d.

The Effect of Static Ride Height Variations

All the above seems to suggest that a significant improvement can be achieved by increasing the static ride heights, in turn affecting dynamic ride heights as well. At first a variation was tried separately on the two axles. The front was raised by 10 mm, which is quite a change for a ground effect car. Bouncing amplitude is reduced significantly at the front, and the rear also benefits from the change (see Figure 24), although average downforce is also reduced.

The rear end was raised by 20 mm instead. In this case the effect on the rear axle is significant as bouncing is nearly removed. The front end also benefits significantly (Figure 25).

Now in order to achieve a similar aero balance in the medium speed range, at least in quasi-static conditions, a 1:2 proportion between front and rear variations in terms of ride height is required. The next step is therefore the following variation: FRHS +5 mm, RRHS +10 mm, referred to as Setup #3. This time the result is satisfactory: the onset of porpoising is delayed until 260 kph, and the average downforce is higher, see Figure 26 and Figure 27.

A second attempt with the following variation relative to the baseline setup: FRHS +10 mm, RRHS +20 mm, referred to as Setup #4, was finally successful in removing porpoising completely, although at the expense of overall downforce and efficiency. Figure 28, Figure 29 and Figure 30 compare the latter configuration with the baseline and the baseline with decay functions.

4. Discussion

Full lap time simulations were then performed in the VI-grade software environment in the search for a reasonable tradeoff between vehicle performance and aerodynamic stability, in other words for assessing the impact of static ride height variations on outright lap time. The virtual driver adopted for the simulation is based on MaxPerformance, a proprietary algorithm for vehicle control during closed-loop driving maneuvers developed by VI-grade and tuned according to the authors’ experience.

The comparison was carried out taking the Sakhir circuit in Bahrain (Figure 31) as a reference because of its nature of combined slow, medium- and high-speed corners, making it representative of a vast selection of Formula 1 circuits.

Table 1. Configurations tested with related lap time. Faster lap time gaps in green, slower in red.

Car Setups and Configuration	Lap Time	Gap from (#1) Baseline	Gap from (#2) Porpoising
(#0) Real-world GP2 car, 4th position in 2013 Qualifying session (Bahrain circuit)	1:40.58	+0.8%
(#1) Full model, Baseline setup	1:39.79	=	−1.03
(#2) Baseline with porpoising	1:40.82	+1.03	=
(#3) FRHS +5 mm/RRHS +10 mm	1:40.32	+0.53	−0.50
(#4) FRHS +10 mm/RRHS +20 mm	1:40.71	+0.92	−0.11

shows the configurations tested, each with the related lap time.

The standard vehicle configuration with baseline Setup #1 was tuned with real-world data. Such a process is not within the scope of this paper hence it is not dealt with here, in any case the final difference with the real car in terms of lap time is negligible (+0.8%) hence this model can be considered validated and capable of a 3rd or 4th position overall in the 2013 Qualifying session in Bahrain [32].

For the sake of clarity, it should also be stated that the other configurations were not fine-tuned after the modifications, in order to avoid the introduction of additional variables in the loop. The setup configuration with decay functions #2 is much slower than the baseline and would qualify in 22nd position. Massive porpoising appears along all the straights, see Figure 32. It is worth noting that the amplitude of oscillations at the rear axle is even larger than the “normal” amplitude of suspension jounce due to downforce, while the front end appears less prone to aerodynamic instability. The average downforce is reduced accordingly, while vertical acceleration levels at the center of gravity exceed 1.5 g, making them a severe hazard for the driver’s body (see Figure 33).

Configuration #4 with static ride height variations FRHS +10 mm, RRHS +20 mm is capable of removing porpoising completely, although at the expense of downforce. As a matter of fact, such a car would qualify in 20th position in 2013. Configuration #3 with static ride height variations FRHS +5 mm, RRHS +10 mm is finally a reasonable tradeoff: porpoising appears only at the end of the straight i.e., at top speed (see Figure 34), while the amplitude of vertical accelerations experienced by the driver is reduced to 0.8 g and just for a few seconds, resulting into an appreciable improvement in terms of comfort. On top of that lap time would be good for a 16th position in the 2013 starting grid, and this improvement is largely due to fairly consistent downforce levels (see Figure 35).

The above improvement is even clearer in Figure 36, where configurations #2 (with decay functions/porpoising) and #3 (FRHS +5 mm, RRHS +10 mm) are compared directly.

5. Conclusions

Insiders and professionals in the motorsport world know very well that the so-called porpoising, which is heavily affecting the dynamic behavior of 2022 Formula 1 racing cars, is very difficult to deal with both for the drivers (complaining about back and neck pain and increased physiological stress during grand prix races) and for the race engineers trying to maximize vehicle performance. Mid-way through the season all the teams are still struggling with this problem, caused by extreme sensitivity of aerodynamic loads to dynamic ride heights. The paper presents two kinds of models where such an aerodynamic sensitivity has been arbitrarily recreated: a quasi-static model, usually adopted as a trackside tool for controlling ride heights and aero balance, and a fully dynamic model, where the interaction between oscillating aerodynamic loads and suspension dynamics results in the porpoising phenomenon.

Basic setup changes have been tested on the second model, resulting in no or limited benefits. Only a significant increase of static ride heights proves resolutive as it can delay or remove porpoising, although at the expense of downforce levels hence performance, in accordance with typical statements often issued by Formula 1 teams. Finally lap time simulations have been carried out with the aim of assessing such a performance loss and to offer guidelines in the search of a tradeoff between aerodynamic stability and overall performance.

Future work will be about transferring the model to the real-time environment for DIL (Driver-In-the-Loop) testing on a professional driving simulation, with the aim of taking subjective aspects into account. The effect of properly tuned devices like a mass damper and an inerter on porpoising will be investigated as well, regardless of the fact that they are both forbidden by the current Technical Regulations issued by the Formula 1 governing body, the FIA.