1. Total Aerodynamic Downforce ($F_L$) & Drag ($F_D$)
F_L = ½ · ρ · v² · A_ref · C_L(α_fw, α_rw, h_f, h_r)
F_D = ½ · ρ · v² · A_ref · C_D(α_fw, α_rw, h_f, h_r)
• ρ (Air Density): Adjustable in simulator (Standard sea-level = $1.225 \text{ kg/m}^3$).
• v (Velocity): Airflow speed in $\text{m/s}$ ($v_{\text{m/s}} = v_{\text{km/h}} / 3.6$).
• A_ref (Reference Area): Frontal reference surface area set to $1.60 \text{ m}^2$.
• Dynamic Pressure ($q$): $q = ½ \cdot \rho \cdot v^2$.
2. Wing Angle of Attack ($\alpha$) & Lift Coefficients ($C_L$)
C_{L,fw} = C_{L0,fw} + \frac{dC_L}{d\alpha} \cdot \alpha_{fw} = 0.45 + (0.045 \cdot \alpha_{fw})
C_{L,rw} = C_{L0,rw} + \frac{dC_L}{d\alpha} \cdot \alpha_{rw} = 0.65 + (0.052 \cdot \alpha_{rw})
Derived from Thin Airfoil Theory ($\frac{dC_L}{d\alpha} \approx 2\pi \text{ rad}^{-1} \approx 0.11 \text{ deg}^{-1}$), adjusted for low aspect ratio ($AR \approx 2.8$) multielement Formula 1 wings.
3. Induced Drag ($C_{D,i}$) & Parasitic Drag
C_{D,induced} = \frac{C_L^2}{\pi \cdot AR \cdot e}
C_D(total) = C_{D,base} + C_{D,fw}(\alpha_{fw}) + C_{D,rw}(\alpha_{rw}) + C_{D,ground}(h)
As wing angle ($\alpha$) increases, the lift coefficient ($C_L$) grows, generating higher wingtip vortex intensity and induced drag penalty governed by the Oswald efficiency factor ($e \approx 0.82$).
4. Underbody Ground Effect & Venturi Throat Pressure
p_1 + ½ \cdot ρ \cdot v_1² = p_2 + ½ \cdot ρ \cdot v_2² \text{(Bernoulli's Principle)}
C_{L,floor} = C_{L0,floor} \cdot \left(\frac{h_0}{h_{avg}}\right)^{0.55} \text{where } h_{avg} = \frac{h_f + h_r}{2}
Decreasing ride height constricts underfloor area. According to the continuity equation, airflow accelerates underneath, creating low static pressure ($p_2$) that produces downforce via ground-effect suction.
5. Aerodynamic Efficiency ($L/D$) & Engine Power Required
L/D = \frac{F_L}{F_D} = \frac{C_L}{C_D}
\text{Power}_{\text{required}} = F_D \cdot v \text{(Watts)}
Power needed to overcome aerodynamic drag scales with velocity cubed ($v^3$), demonstrating why high-speed straight-line performance requires low drag or DRS activation.
Academic References & Sources Used
- 1. Katz, J. (2006). Race Car Aerodynamics: Designing for Speed. Bentley Publishers.
- 2. Wright, P. (2001). Formula 1 Technology. SAE International.
- 3. McBeath, S. (2015). Competition Car Aerodynamics: A Practical Handbook. Veloce Publishing.
- 4. NASA Glenn Research Center Aerodynamics Fundamentals: Lift and Drag Coefficients.