Searching for Downforce: Applications of a Beam wing on an SF16 Car

Sticking to the ground: a vacuum cleaner at 350 km/h

Introduction

The goal of an F1 car is to race around a track as fast as possible, stopping the clock earlier than any other car. To accomplish this, these cars must adhere to the ground on straights as well as on corners where they are grip-limited. 

So far, this role has been demanded of front and rear wings, which were the main tools for generating downforce. However in 2022, the F1 regulations faced a revolution: the return of Ground Effect. These new cars act like vacuum cleaners that suck in the air below them to stick to the ground.

What is Ground Effect?

Let’s start from the basics. The motion of a fluid particle can be described by the conservation of mass and  the Navier-Stokes equation for an incompressible fluid as:

∇ ⋅ v = 0
ρ ∂v∂t + (v ⋅ ∇)v = -∇p + μ∇²v + ρg

For a stationary and non-viscous fluid, it can be simplified as:

ρ(v ⋅ ∇)v = -∇p + ρg

And for an irrotational fluid, neglecting the variation in height, it becomes the simple and well-known Bernoulli equation (there are many assumptions taken in this equation, but it is useful for explaining the macro behaviour of the fluid):

Ptot = Pstat + ½ρV2 = constant

The Bernoulli equation says that the sum of the static pressure and the dynamic pressure (the total pressure) is constant.

To understand what that looks like, let’s consider the flow of a fluid in a straight tube. In this case, the speed of the particles of fluid moving through the tube and the pressure of the flow are constant.

Constricting a section of the tube will increase the speed of the particles moving through the constricted section (as shown below) to maintain a constant flow rate, which in turn will lead to a reduction in the pressure in that constricted section. That’s a Venturi tube.

Source: Cadence System Analysis

Now this principle can be applied to the underfloor of the car.

If instead of a flat floor, we consider a floor with an infuser, a throat at constant section, and a diffuser we get a venturi tube under our car. The lower pressure applied to the area of the underfloor generates the so-called Downforce.

Source: Race Car Design by Derek Seward, Bloomsbury Publishing (2014) ISBN 9781137030146

For an ideal car, where the flow can not enter from the side of the floor (2D flow), a typical section reduction angle for the infuser is around 15°, as any higher angle would lead to pressure losses.

Concerning the throat, following Bernoulli it should be at constant section, but in reality, as air has a  viscous flow, it has a slight positive slope (with increasing section going downwards) to counteract the reduction in section due to the car boundary layer.

Finally, the diffuser, which is the part of the tube responsible for pressure recovery,  normally has a slope of 7°. If we increase this angle, we risk the detachment of the fluid (air) from the walls due to the adverse pressure gradient.

A crucial aim for this section of the car is to maintain the delta pressure between the floor and the outside. As we will see, this pressure can be significantly increased if a beam wing is used.

The proximity to the ground also influences the wings. Let’s consider a wing at some distance from the ground, its coefficient of lift can be considered as 

Cl = C(α + α0)

where

C = (1 + 2AR)

and AR is the aspect ratio of the wing for a finite length wing.

The coefficient of lift (Cl) reduces if the aspect ratio (AR) is lower, because the trailing vortices produced by the latter try to balance the delta pressure between the upper and lower sides of the wing.

What that looks like is:

Source: NASA Langley Research Center
Source: Aerodynamics Career Accelerator Program Course

When a wing is found in proximity to the ground, especially when  h/c<=0.5 (h=ground clearance, c=wing chord), lift increases. Coulliette & Plotkin (1996) summarised the two-dimensional effects. In their work, they separated the contributions of parameters such as thickness, camber, and angle of attack to the airfoil’s lift. 

From the race car’s point of view, the interesting observation is that for an inverted airfoil (e.g., creating downforce) all of the above effects will increase the downforce near the ground. This includes the positive effect of angle of attack and camber, which in the case of an aeroplane wing (lifting) near the ground are negative. (Aerodynamics of Race Cars, J.Katz, Annu. Rev. Fluid Mech. 2006. 38:27–63)

That’s because the reduced ground clearance reduces the strength of the vortices, virtually increasing the aspect ratio (AR).

Image source: Race Car Aerodynamics: Designing for Speed, J.Katz, 1996, Bentley publishers
Image source: Aerodynamics of Race Cars, J.Katz, Annu. Rev. Fluid Mech. 2006. 38:27–63

Enhancing Ground Effect

 Sealing the floor

As previously stated, in order to maximise ground effect, the air going under the floor from the sides in real cars has to be kept separated as much as possible from the air outside to maintain the delta pressure.

In the first ground effect era, this was accomplished by physically putting two metal sliding skirts that were in contact with the ground and preventing the air from escaping out from the sides.

Source: Photo by Giorgio Piola

Source: Race Car Aerodynamics: Designing for Speed, J.Katz, 1996, Bentley publishers

The countereffect of this method was the uncontrolled loss of downforce in the case of damage to the skirts. The safety issues connected to this problem, and the incidents that occurred, led to the disuse of those cars.

Another way to increase the floor downforce is what is used currently, which exploits a widespread method for controlling the flow: vortices.

The new regulation allows for four flow diverters, and floor fences, which can be installed in the infuser and that can be used to generate strong vortices. The latter moves from the trailing edge of the fences through the sharp edges of the floor. Their rotation produces an increase in pressure that pushes the air in the outside as well as the wheel wake outboard, preventing the mixing with the one under the floor. 

Source: Race Analysis
Source: Aerodynamics Career Accelerator Program Course Slide

Along with sealing, fences provide another benefit: in combination with the trailing edge, the leading fence produces a vortex. The latter is characterised by high rotational speed and low pressure; directing air to the Venturi tunnel, which strengthens suction and thus increases downforce.

Beam Wing

Increasing the ramp angle of the diffuser would lead to a possible detachment of the flow from the walls. So, how is this issue addressed? Adding a beam wing at the back of the car can fix this problem.

What does a beam wing do, exactly?

Source: F1 Sport

The lower side of the latter creates a low-pressure area right above the diffuser, which enhances the extraction of air from the floor acting like an elongation of the diffuser. By adding the beam wing, the ramp angle of the diffuser can be further increased as the pressure gradient is reduced.

The counter effect is an increase in drag due to the low efficiency of the wing.

What happens if we apply a beam wing to an SF16-like car?

As part of the final project for the Aerodynamics Career Accelerator Program course, I developed a beam wing to be applied at the back of a SF16 to see if this would improve its performance.

The wing was designed with CATIA and positioned by studying the flow around the baseline car.

Images and data from the author’s final project (with use of Bramble CFD and CATIA 3DX)

The goal was to place the beam in the most high-energy area, but not too close to the rear wing avoiding influencing it too much. 

A lower AoA was given to the sections at the extremity due to the dirty air coming from the bodywork and the junction with the endplate. Along with the AoA, the chords were increased in the midsections. 

Starting from the endplate sections, the longitudinal position was shifted to the back, the purpose was to leave the endplate sections closer to the structural support while maximising the effect above the diffuser. The z variation was chosen with the aim of putting the sections in the high energy flow.

Created using Bramble CFD

I have run my simulations thanks to Bramble CFD software and made a Postpro of the relevant views.

The wing gave the expected results of increasing the extraction in the underfloor along with an increase in pressure at the entrance.

Created using Bramble CFD
Created using Bramble CFD

Here we can notice that the vortex generated at the entrance of the floor by the turning vane has been energised by the wing, consequently increasing suction under the floor.

Created using Bramble CFD

The top of the car faced an overall increase in pressure up to the front wing and suspensions.

Created using Bramble CFD
Created using Bramble CFD

The back of the car, the bodywork exit area, faced an increase in pressure as well. This is likely caused by the high-pressure side of the beam wing and may negatively influence the cooling capacity.

The plots of the streamlines at y= –0.275m (0.1 m from the endplate) show the upwash given to the fluid by the wing, meaning that the concept was working.

In terms of numbers, results reflect what was expected: a positive increase in Downforce equal to 1.71% and an increase in drag higher than the DF gained, which results in a loss in efficiency. Concerning the lap time, let’s consider the Track Ratio, which is a way to determine if a part can be sent to the track or not, it is calculated considering a delta laptime equal to 0.

TR = dCzdCx

If we consider a track like Monaco with a TR around 0.9, we can calculate the efficiency of this beam wing:

E = dCzdCx = 0.520.45 = 1.16

Being the latter greater than the track ratio we can send this part to the track to improve the lap time. 

Looking more in detail, the rear wing, which takes into account the beam wing, faces the biggest increment, while the diffuser doesn’t seem to be strongly influenced by the wing considering the small increase in downforce. The balance marginally shifts to the rear.

Following the positive results obtained, I increased the AoA of the sections to test how far I could have gone with the design.

Run 2 Design (created in CATIA 3DX)

Unfortunately, the modification was too extreme, leading to a drop in performance and a stall of part of the wing.

Created using Bramble CFD
Created using Bramble CFD

The chart below shows the degradation in performance of Run 2.

Run 2 results pushed me to reduce the AoA of the sections where it was too extreme in a second attempt to improve the design.

Run 3 Design (created in CATIA 3DX)

Remarking on the difficulty in getting the correct configuration and design, these modifications didn’t bring improvements and instead enlarged the stalled region.

Created using Bramble CFD
Created using Bramble CFD
Created using Bramble CFD

Conclusions

As a conclusion of the analysis, I can state that adding a beam wing above the diffuser of an F1 Car effectively improved the downforce, although it was not efficient in terms of drag. 

Furthermore, optimising the design was not as easy as expected, and to properly design a wing a higher number of control sections or better guidelines should be drawn to have better control over the design.

Finally,  the Beam Wing cannot be simply added but should be considered in the preliminary design of the car for the best results. Another important aspect is that fresh air from the bodywork should be provided to the wing and the diffuser angle should be increased to maximise results.

What have I learnt?

This project let me learn by doing, putting into practice what I was taught during the Aerodynamics Career Accelerator Program, and getting a taste of what it is like to be an Aero Engineer in F1: design, test, fail, repeat until success!

Thanks to the introduction to CATIA I managed to design and modify my wing and the invaluable theoretical knowledge from the course, I was able to do a detailed analysis of the results and learn from them.

Interested in mastering Aerodynamics like Alessio? Enrol today in our Aerodynamics Program, and rev up your career!

Check out our Aerodynamics Career Accelerator Program HERE!

Meet the Author

Alessio Giudice is an Aerospace Engineer specialising in Aerodynamics and Hydrodynamics. He holds a Master’s degree in Aerospace Engineering from Politecnico di Torino and currently works as an Aerothermal CFD Engineer. Alessio’s achievements in motorsport engineering include participating in international regattas, improving performance through innovative design, and contributing valuable insights to the engineering community. You can follow him on LinkedIn here.

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