Professor, the aerodynamics of a racing car are completely different from those of a production car, right?

Their fundamental objectives are different. For production cars, the primary goal is to reduce aerodynamic drag. For racing cars, the goal is to maximize downforce (negative lift) while keeping drag within acceptable limits.

So the L/D ratio is the key metric for a racing car's aerodynamic efficiency.

Correct. A higher L/D ratio means you can generate greater downforce with less drag. Floor design that utilizes ground effect is key to improving the L/D ratio.

Aerodynamics of Racing Cars

Category: 流体解析（CFD） | Integrated 2026-04-06

CAE visualization for racing aero theory - technical simulation diagram

レーシングカーの空力

Theory and Physics

Overview

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Teacher, the aerodynamics of racing cars are completely different from production cars, right?

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The fundamental objectives are different. For production cars, the main goal is reducing aerodynamic drag, but for racing cars, the goal is to maximize downforce (negative lift) while keeping drag within acceptable limits.

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An F1 car generates about 3.5G of downforce at 300 km/h. This pressing force, significantly exceeding the car's weight, theoretically allows it to drive upside down on a ceiling.

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Being able to drive on the ceiling... that's incredible force.

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This downforce determines cornering speed. Since tire grip is proportional to vertical load, increasing downforce raises the cornering limit.

Governing Equations and Aerodynamic Coefficients

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Downforce and drag are expressed using dimensionless coefficients.

$$ C_L = \frac{-F_z}{\frac{1}{2} \rho V^2 A} \quad (\text{negative is downward}) $$

$$ C_D = \frac{F_x}{\frac{1}{2} \rho V^2 A} $$

$$ L/D = \frac{C_L}{C_D} \quad (\text{aerodynamic efficiency}) $$

Here $A$ is the frontal projected area. For F1 cars, $C_L \approx -3.0$--$-5.0$, $C_D \approx 0.7$--$1.2$, and $L/D \approx 3$--$5$.

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So the L/D ratio is the indicator of aerodynamic efficiency for racing cars.

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Correct. A higher L/D means obtaining large downforce with low drag. Floor design utilizing ground effect is key to improving L/D.

Downforce Generation Mechanisms

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Let's organize the main sources of downforce.

Element	Downforce Contribution	Main Principle
Front Wing	25--30%	Bernoulli effect via inverted airfoil
Rear Wing	30--35%	Inverted airfoil + multi-element flaps
Floor/Diffuser	35--45%	Ground effect, Venturi effect
Others (Bargeboards, etc.)	5--10%	Flow control via vortex generation

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The floor contributes the most?

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Ground effect increases flow velocity in the narrow gap with the ground, creating a large low-pressure area via Bernoulli's principle. It has very high L/D because drag increase is small. Since the 2022 F1 regulations, designs actively utilize ground effect.

Reynolds Number and Flow Characteristics

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The typical Reynolds number around a racing car, based on car length, is $Re \approx 10^7$.

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Flow characteristics:

Front: Bluff body flow: Stagnation point, large-scale separation
Wing: Flow around airfoils (high angle of attack)
Wheel: Unsteady vortices from rotating bluff body
Diffuser: Flow in an expanding duct under adverse pressure gradient
Wake: Interference of multiple vortex structures

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The whole car is a collection of various aerodynamic phenomena, isn't it?

Coffee Break Trivia

Why Were Ground Effect Cars Banned?

In the late 1970s, F1 teams developed "ground effect cars" that shaped the underside of the floor like a wing to generate intense downforce. Cornering G-forces exceeded 5G, and drivers raced on the verge of blacking out. In 1982, the FIA introduced flat-bottom regulations and banned them for safety reasons. When this technology was permitted again 40 years later in the 2022 regulations as a "phased return of ground effect," aerodynamic engineers reportedly cheered, "It's finally back!"

Physical Meaning of Each Term

Temporal Term $\partial(\rho\phi)/\partial t$: Imagine the moment you turn on a faucet. At first, water comes out spluttering and unstable, but after a while, the flow becomes steady, right? This "period of change" is described by the temporal term. The pulsation of blood flow from a heartbeat, or the flow fluctuation each time an engine valve opens and closes—all are unsteady phenomena. So what is steady-state analysis? It looks only at "after sufficient time has passed and the flow has settled"—meaning setting this term to zero. Since computational cost drops significantly, starting with a steady-state solution is a basic CFD strategy.
Convection Term $\nabla \cdot (\rho \mathbf{u} \phi)$: If you drop a leaf into a river, what happens? It gets carried downstream by the flow, right? This is "convection"—the effect where fluid motion transports things. Warm air from a heater reaching the far side of a room is also because the "carrier," air, transports heat via convection. Here's the interesting part—this term contains "velocity × velocity," making it nonlinear. That is, as flow speed increases, this term rapidly strengthens, making control difficult. This is the root cause of turbulence. A common misconception: "Convection and conduction are similar" → They are completely different! Convection is transport by flow, conduction is transfer by molecules. There's an order of magnitude difference in efficiency.
Diffusion Term $\nabla \cdot (\Gamma \nabla \phi)$: Have you ever put milk in coffee and left it? Even without stirring, after a while it naturally mixes, right? That's molecular diffusion. Now a question—honey and water, which flows more easily? Obviously water, right? Honey has high viscosity ($\mu$), so it flows poorly. Higher viscosity strengthens the diffusion term, making the fluid move "sluggishly." In low Reynolds number flow (slow, viscous), diffusion dominates. Conversely, in high Re flow, convection overwhelmingly dominates, and diffusion plays a supporting role.
Pressure Term $-\nabla p$: When you push a syringe plunger, liquid shoots out forcefully from the needle tip, right? Why? Because the plunger side is high pressure, the needle tip is low pressure—this pressure difference provides the force pushing the fluid. Dam water release works on the same principle. On a weather map, where isobars are tightly packed? That's right, strong winds blow. "Flow is generated where there is a pressure difference"—this is the physical meaning of the pressure term in the Navier-Stokes equations. A point of confusion here: "Pressure" in CFD is often gauge pressure, not absolute pressure. If results go wrong immediately after switching to compressible analysis, it might be due to confusing absolute/gauge pressure.
Source Term $S_\phi$: Warmed air rises—why? Because it becomes lighter (lower density) than its surroundings, so buoyancy pushes it up. This buoyancy is added to the equation as a source term. Other examples: chemical reaction heat from a gas stove flame, Lorentz force acting on molten metal in a factory's electromagnetic pump... These are all actions that "inject energy or force into the fluid from the outside," expressed by the source term. What happens if you forget the source term? In natural convection analysis, forgetting buoyancy means the fluid doesn't move at all—a physically impossible result where warm air doesn't rise in a room with the heater on in winter.

Assumptions and Applicability Limits

Continuum assumption: Valid for Knudsen number Kn < 0.01 (mean free path ≪ characteristic length)
Newtonian fluid assumption: Shear stress and strain rate have a linear relationship (non-Newtonian fluids require viscosity models)
Incompressibility assumption (for Ma < 0.3): Treat density as constant. For Mach number ≥ 0.3, consider compressibility effects
Boussinesq approximation (Natural convection): Consider density variation only in the buoyancy term, using constant density in other terms
Non-applicable cases: Rarefied gas (Kn > 0.1), supersonic/hypersonic flow (requires shock capturing), free surface flow (requires VOF/Level Set, etc.)

Dimensional Analysis and Unit Systems

Variable	SI Unit	Notes / Conversion Memo
Velocity $u$	m/s	When converting from volumetric flow rate for inlet conditions, pay attention to cross-sectional area units
Pressure $p$	Pa	Distinguish between gauge and absolute pressure. Use absolute pressure for compressible analysis
Density $\rho$	kg/m³	Air: approx. 1.225 kg/m³ @20°C, Water: approx. 998 kg/m³ @20°C
Viscosity coefficient $\mu$	Pa·s	Be careful not to confuse with kinematic viscosity coefficient $\nu = \mu/\rho$ [m²/s]
Reynolds number $Re$	Dimensionless	$Re = \rho u L / \mu$. Indicator for laminar/turbulent transition
CFL number	Dimensionless	$CFL = u \Delta t / \Delta x$. Directly related to time step stability

Numerical Methods and Implementation

Analysis Method Selection

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What analysis methods are used in racing car CFD?

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RANS, DES/DDES, and LES are all used appropriately.

Method	Scale	Application	Team Usage
Steady RANS	50 million--100 million cells	Design exploration, Parametric studies	All teams
Unsteady RANS	100 million--200 million cells	Unsteady aerodynamic characteristics	Top teams
DDES	200 million--500 million cells	Wake interference, tire vortices	Top teams
LBM (PowerFLOW/XFlow)	Several hundred million voxels	Full-car unsteady analysis	Some teams

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How much computational resources do F1 teams use?

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FIA regulations limit CFD usage (ATR: Aerodynamic Testing Restrictions). As of 2024, the champion team has an annual limit of 25 Teraflop-hours. This roughly corresponds to a 2000-3000 core HPC cluster running at full capacity for one year.

Mesh Strategy

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The following are important for full-car mesh generation.

Wall Prism Layers: $y^+ \approx 1$, 20--30 layers. Especially critical for wings and floor
MRF (Moving Reference Frame): Models wheel rotation
Ground Boundary: Moving wall condition. Moves at the same speed as the car
Refinement Zones: Wing tips, diffuser exit, wake region
Total Cell Count: RANS 50-100 million, DDES 200-500 million

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The ground is set as a moving wall?

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In actual driving, the car moves forward, but in CFD, the car is fixed and the ground is moved at the flow velocity. If you forget this and set the ground as a fixed wall, the ground boundary layer develops and ground effect is not correctly reproduced.

Turbulence Model

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What turbulence models are recommended for racing car CFD?

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SST k-omega is the industry standard. The SA model is also used, but SST is superior for predicting separation under adverse pressure gradients.

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Detailed wing analysis:

SST k-omega: Steady RANS. Good for predicting wing surface pressure distribution and separation location
SST k-omega + gamma-Re_theta: When transition prediction is needed (low Re airfoils)
DDES (SST based): Analysis of unsteady vortex structures in wing wake

Rotating Wheel Treatment

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How is wheel rotation modeled?

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There are three methods.

Method	Overview	Accuracy	Cost
MRF (Frozen Rotor)	Steady calculation in rotating reference frame	Low--Medium	Low
Sliding Mesh	Physically rotates the rotating region	High	High
Overset Mesh	Overlays rotating mesh	High	Medium--High

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MRF is common in the design exploration phase with steady RANS. To accurately capture unsteady vortex structures in the tire wake, use Sliding Mesh or Overset Mesh. STAR-CCM+'s Rigid Body Motion is user-friendly.

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How is tire deformation (flex) handled?