# The Ground Effect

By Vyssion and jjn9128 on

The exact size, position, and shape of the downforce producing surfaces are dictated by regulations, initially by FISA and by the FIA themselves since 1993. Starting when wings had to be fixed to the sprung part of the car - initially wings were fixed directly to the suspension uprights which resulted in a number of high profile accidents - followed by the ban on sliding skirts, the mandatory flat floor between the axle lines, shorter diffusers, taller wings, shorter wings, longer diffusers, step planes, wooden skid planks - the list goes on.

The main mechanism for downforce on a Formula 1 car is ground-effect, with all surfaces affected by the car’s proximity to the ground. The way these important surfaces affect downforce is detailed below:

Approximate distribution of aerodynamic downforce and drag for a modern F1 car

## Underbody

Even with the mandatory flat floor and step plane the underbody and rear diffuser are the largest contributor to overall downforce, producing between 60-65% of the car’s downforce. The underbody behaves like a convergent-divergent duct, contracting air under the car, before expanding it again with the rear diffuser. As air behaves like an incompressible fluid at low Mach numbers, the mass of the airflow ($\dot{m}$) travelling through a duct will be conserved;
$\dot{m}_{1}\, =\, \dot{m}_{2}$,
while $\dot{m}\, =\, \rho\, U\, S$,
where $\rho$ is the density of air (which is constant when air is incompressible), U is the velocity of the air, and S is the cross sectional area of the duct.

The contracted volume (where $S_{1}\, >\, S_2$) between the car and the ground will cause the air to accelerate;
$U_{2}\, =\, \cfrac{U_{1}\, S_{1}}{S_{2}}$.
The Venturi effect tells us that static pressure (p) will be reduced when the air is accelerated (i.e. $U_{1}\, <\, U_{2}[/tex]),
[tex]\Delta p\, =\, ^1/_2\, \rho\, \big( U_1\,^2\, -\, U_2\,^2 \big)$
.
This is derived from the Bernoulli equation where the increase of dynamic pressure (q) will cause a reduction of static pressure,
$p\, +\, q\, =\, constant$,
where $q\, =\, ^{1}/_{2}\, \rho\, U^{2}$.

The Venturi effect is the key downforce generating ground-effect for a Formula 1 car, the negative pressure created (negative only when compared to the atmosphere, i.e. a relative vacuum) sucks the car into the ground (downforce), because downforce is equal to the integral of pressure over the planform area ($A$) of interest; $F_{z}\, =\, \int p\, dA$.

Naturally air pressure wants to return to an equilibrium state, with higher pressure regions migrating towards lower pressure ones (filling the relative vacuum). With the underbody this means the large flat area will experience an increase of pressure towards the centre of the floor, reducing downforce. The sliding side skirts used in the late 1970’s to early 1980’s helped to seal the underbody duct, preventing this flow ingress from the sides - which helped to maintain a low pressure under the car. Failure of the side skits led to a sudden and potentially catastrophic loss of downforce - if the driver turned in expecting a certain level of grip, or if the skirt failed mid-corner - and the skirts were rightly outlawed in 1983.

Since these skirts are no longer legal, teams use aggressive bargeboards coupled with the sidepod undercut to push air away from the floor. The bargeboards create lift, and therefore downwash and outwash, to mimic (though not quite recreating) the sealing effect of the side skirts, while also pushing the messy front tyre wake away from the floor. Since teams started using the sidepod undercut, circa 2000, the proportion of downforce generated by the underbody (as well as total downforce) has increased, from under 50% to around 65%.

## Front wing

The front wing is inarguably the most important part of a Formula 1 car, despite only providing between 20 and 30% of total downforce it is responsible for the quality of airflow reaching the rest of the car; generate too much downforce from the front wing and rear downforce will be reduced. Too much upwash in the front wing wake can stall the suspension members, or even cause the flow to separate at the front edge of the sidepod, which can adversely affect the rear wing and diffuser.

While the front wing profiles are shaped like a conventional wing section, a cambered upper and lower surface producing downforce, its force characteristic are dominated by ground effect, namely the Venturi effect in the convergent-divergent path under the wing, such that the air flowing on the lower surface of the wing is multiple times faster than would be the case is the wing were suspended high in the air.

## Rear wing

The rear wing is a downforce generating device in its’ own right, producing 15-25% of total downforce, but it also part of a mutually beneficial system with the rear diffuser. The low pressure under the rear wing helps to create a region of low pressure behind the car which in turn helps to draw more air from the front of the floor - known as diffuser pumping. The low beam wing, which was removed in the 2014 rules, created an even lower base pressure, which helped to connect the upper rear wing to the diffuser. In 2014 McLaren tried to recreate the beam wing effect with mushroom shaped rear suspension, while on current cars the Gurney flaps and winglets on top of the rear diffuser are important for creating a lower pressure behind the car.

The rear wing is the second highest single source of drag on the car, after the exposed wheels, so trimming the rear wing is vital for races where a high top speed is required, for example Monza/Spa.

Comparison of rear wing angle for high and low downforce circuits (2017 Mercedes W07).

## Chassis & bodywork

It is a common misconception that the only force aerodynamicists purposely create on a Formula 1 car is downforce - in fact strategically producing lift can have a net benefit for overall downforce. Nowhere is this more true that the vanes under the drivers legs and ahead of the sidepods (bargeboards). Lift generated in this region helps to produce the downwash and outwash flows which effectively “seal” the underbody, as discussed above, while also pushing the front tyre wakes away from important areas of the car.

Approximate circulation around a Formula 1 race car.

Not all of the lift generated around the middle of the car is produced deliberately, and the top surface of the monocoque stands out as an example of where this lift is a negative. Since the maximum nose tip height of 220mm was introduced in 2014 the nose surface has risen steeply to meet the maximum chassis height, with a tight curve used in the transition. This tight curvature creates a sharp region of low pressure (lift) which also serves to thicken the boundary layer on the top of the monocoque. Most teams now use the S-duct nose design to introduce a high velocity airflow after the transition to ease the pressure gradient.

## Wheels

The exposed wheels are the biggest source of aerodynamic drag on a Formula 1 car, responsible for between 25% and 40% of total drag (depending on the regulations and the circuit in question). The wheels also produce a lift force due to the contact with the ground (ground-effect is not always beneficial). If the wheels were suspended in the air, the direction of rotation would mean they create downforce because of the Magnus effect, where the direction of the rotation would accelerate the air on the bottom surface, creating a lower pressure underneath than above. The ground contact means the rotating flow on the surface is constrained by the ground, instead rolling up at the front face of the contact patch before jetting around the sidewall - tyre squirt. Where the rotating boundary layer at the top of the wheel opposes the direction of travel, the air air separates, creating a region of low pressure above (lift) and behind (drag) the wheel.

## How much downforce do F1 cars generate?

Downforce ($F_{z}$) as a measure is a moving target because it squares with speed - a 2018 car will exceed its dry weight (733kg) in downforce above ~165km/hr (~105mi/hr), twice the dry weight at ~235km/hr (~145mi/hr), three times the dry weight above ~285km/hr (~180mi/hr)...etc - so aerodynamicists use non-dimensional coefficients to describe the forces, which also removes the effect of the atmospheric conditions;
where $C_{z}\, =\, \cfrac{F_{z}}{^{1}/_{2}\, \rho\, U^{2}\, S}$*,
and $C_{x}\, =\, \cfrac{F_{x}}{^{1}/_{2}\, \rho\, U^{2}\, S}$.

*In the motorsport and automotive sectors a constant frontal area is used for both drag and downforce measurements; normally between 1.5m² and 2m² depending on the team. This isolates the change in force coefficient from any change of frontal area.

Formula 1 constructors are engaged in a perpetual tug-of-war with the FIA, improving performance week-on-week only to have that work nullified by a change of the regulations. For example the rumour is that the 2019 regulation changes will cost the teams 1.5s per lap, which equates to a loss of downforce of ~50 points (~15%), or an increase of drag of ~25 points (~25%) - most likely some combination of the two.

Aerodynamic downforce produced by the cars has varied over the last 20 years, reaching a peak in 2008 (Cz =3.27) after a period of fairly stable aerodynamic regulations (the front wing tips and endplates were raised by 100mm in 2005). The cars then lost some downforce in 2009 with the massive rule change, though not as much as the 50% which the FIA planned, partly because of the double diffuser loophole and in part owing to the improved understanding and manipulation of the flow field around the car. The tightening rules on the exhaust position and blowing of gases, as well as the loss of beam wing, all mean the 2014 cars were some of the lowest downforce cars of the last two decades. The 2017 rule change then created a sudden increase of dowforce - and the cars are now some of the highest downforce F1 cars ever (Cz >3.6).

The increase of downforce is mainly contributed by the underbody, for example, the Ferrari F1-2000 (according to Peter Wright) produced 41.3% of its downforce from the floor and diffuser; while the 2017/18 cars produce more than 60% of their downforce from the floor. As overall downforce has also increased from Cz ~2.6 to Cz ~3.7 this equates to more than a doubling of the underbody downforce coefficient over the past 20 years, from Cz =1.08 to Cz ~2.2. Part of this will be due to the longer wheelbase of the 2018 cars, however most will be because of the bigger rear diffusers and better “sealing” of the floor as discussed earlier.

## How does F1 compare to other race series?

The most obvious race series to compare to F1 is Indycar - as the other top tier open-wheel, open-cockpit formula. For the start of 2018 Indycar took a different tack to the 2017 F1 rule changes, electing to reduce peak downforce by about 20-30%, from Cz ~3.98 (6500-7000 pound-force at 200mi/hr) to Cz ~3.07 (~5000lbf), when the manufacturer aerokits were scrapped in favour of the new universal aerokit - albeit the IR18 still produces more downforce than the original DW12 which generated Cz ~2.82 (~4600lbf at 200mi/hr).

Like F1, Indycars race on a variety of circuits, requiring downforce level and aerodynamic balance to be tailored to each track, but no F1 event is as extreme as the superspeedways Indycar race on. Downforce in the superspeedway configuration is around half of the road course aerokit, Cz ~1.53 (~2500lbf at 200mi/hr). The aerobalance will also be moved considerably rearwards for stability, ~30% on the front axle rather than 40-45% for road courses. It is drag where the greatest saving is though, reducing by ~60% from a Cx ~0.96 to Cx ~0.35. The superspeedway package is incredibly efficient for an open-wheel race car, DF:D ~4.4:1, which is more on a par with the closed-cockpit, closed-wheel Bentley Speed 8 (DR:D =4.46:1) than a conventional open-wheel race car.

Since the 1980’s Indycar have been less restrictive in the rules on the underbody, with underbody tunnels remaining the norm through to today. Even so, while the new universal aerokit generates ~66% of it’s downforce from the underbody, Cz ~2.02, it produces ~8% less downforce the a current F1 car generates from its underbody (2.2 ≲Cz ≲2.4). While the superspeedway aerokit produces 88% of its downforce from the floor, this is only Cz ~1.35, or 40% less than a Formula 1 car floor.

Where Indycars typically perform worse than their F1 counterparts is on aerodynamic drag, despite sometimes producing more downforce the lift-to-drag ratio (DF:D) has historically been worse than in F1, closer to 3:1 than 3.5:1. The argument for a re-introduction of underbody tunnels in F1 is that the cars will be more aerodynamically efficient, but the Indycar example does not necessarily support this; it must be said though that the modern Indycar rear wing is both longer in chord and wider in span than the current F1 rear wing, which will increase drag - particularly induced drag.

Open-wheel race-cars produce tonnes of downforce at racing speeds. Downforce production is dominated by ground-effect, namely the Venturi effect, with the underbody and front wing producing most of the downforce on the car. Downforce gains in the recent past stem from improvements made generating downforce from the underbody, with the complex array of bargeboards, sidepod undercut and front wing Y250 vortex all helping to recreate the “sealing” effect of the sliding skirts.

## References

Wright P. Ferrari Formula 1. Under the Skin of the Championship-winning F1-2000.
https://ryanracing.com/the-car/
https://www.indycar.com/News/2016/06/06 ... nforce-pt1