Calculating CdA

The aerodynamic drag coefficient (C_dA) is calculated using the power output and other parameters. The calculation involves several steps, including determining the apparent wind speed, the yaw angle, and the aerodynamic power.

Step 1: Calculating Apparent Wind Speed

The apparent wind speed (v_app) is calculated using the bike speed and wind speed.

$$v_{\text{app}} = \sqrt{v_{\text{bike}}^2 + v_{\text{wind}}^2 + 2 \cdot v_{\text{bike}} \cdot v_{\text{wind}} \cdot \cos(\theta)}$$

where:

• v_bike is the bike speed.
• v_wind is the wind speed.
• $\theta$ is the angle between the wind direction and the bike direction.

Step 2: Calculating Yaw Angle

The yaw angle ($\phi$) is the angle between the direction of the bike and the apparent wind.

$$\phi = \arctan \left( \frac{v_{\text{wind}} \cdot \sin(\theta)}{v_{\text{bike}} + v_{\text{wind}} \cdot \cos(\theta)} \right)$$

where:

• v_wind is the wind speed.
• v_bike is the bike speed.
• $\theta$ is the angle between the wind direction and the bike direction.

Step 3: Calculating Aerodynamic Power

The aerodynamic power (P_aero) is calculated using the effective power output, rolling resistance power, and elevation power.

$$P_{\text{aero}} = P_{\text{eff}} - P_{\text{rr}} - P_{\text{elev}}$$

where:

• P_eff is the effective power output.
• P_rr is the rolling resistance power, calculated as $P_{\text{rr}} = F_{\text{rr}} \cdot v_{\text{bike}}$.
• P_elev is the elevation power, calculated as $P_{\text{elev}} = F_{\text{gravity}} \cdot v_{\text{bike}}$.

The rolling resistance force (F_rr) and gravitational force (F_gravity) are given by:

$$F_{\text{rr}} = C_{\text{rr}} \cdot m \cdot g$$$$F_{\text{gravity}} = m \cdot g \cdot \sin(\theta)$$

where:

• C_rr is the rolling resistance coefficient.
• m is the total mass (rider + bike).
• g is the acceleration due to gravity.
• $\theta$ is the slope angle.

Step 4: Calculating CdA

The aerodynamic drag coefficient (C_dA) is calculated using the aerodynamic power and other parameters.

$$C_dA = \frac{2 \cdot P_{\text{aero}}}{\rho \cdot v_{\text{app}}^3 \cdot \left( \cos(\phi)^2 + 1.2 \cdot \sin(\phi)^2 \right)}$$

where:

• $\rho$ is the air density.
• v_app is the apparent wind speed.
• $\phi$ is the yaw angle.