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A New Method for Analysing the Effect of Environmental Wind on Real World Aerodynamic Performance in Cycling^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{φ}) and wind speed (p

_{Vw}) for a given vehicle speed. This method is the origin of the SAE Wind Averaged Drag but will be applied differently for cycling in this paper.

_{φ}) and wind speed (p

_{Vw}) as well as a magnitude weighting term for speed (V*). These will be addressed individually.

#### 2.1. Wind Direction

_{φ}as a constant value where;

#### 2.2. Wind Speed

#### 2.3. Velocity Magnitude Weighting

#### 2.4. Application

_{D}A*, to distinguish it uniquely from the SAE Wind Averaged Drag (WAD).

_{D}A* for Sample 1 and Sample 2 can be calculated as 0.092 and 0.089 respectively. This highlights the importance of yaw weighting as Sample 1 has significantly lower drag at high yaw but this is offset by poor performance at the dominant low yaw angles. This approach scales with the number of sample points (j), ensuring that the magnitude of C

_{D}A* is not distorted, regardless of yaw resolution of experimental data. The key difference to the SAE WAD approach is that this method applies the weighting value to drag values at the measured yaw angle from wind tunnel results, making it directly applicable to experimental data. The SAE approach requires interpolation of drag to a set of prescribed yaw angles.

## 3. Results

_{R}) of 25 mph (40.23 km/h, 11.18 m/s) as this is provides a balance as an attainable speed for amateur cyclists and is close to the average speed of elite stage races. For consistency, V

_{W}= 7 mph (3.13 m/s) is proposed so as to align cycling with the automotive industry. This value was reviewed as a part of SAE J1252 [12] and was measured to be 7.45 mph for North America. J1252 retains the 7 mph for historical consistency and is therefore a logical choice for cycling applications. Table 1 provides values of the normalised weighting function using V

_{R}= 25 mph and V

_{W}= 7 mph at a common wind tunnel yaw sampling schedule; symmetric about 0°.

## 4. Conclusions

_{D}A*), is presented as a method for condensing drag and yaw angle data into a single numeric that can be used to simplify the understanding of drag performance across all yaw angles. A yaw weighting curve with a wind speed of 3.13 m/s (7 mph) and road speed of 11.18 m/s (25 mph) is proposed as a candidate for industry standard practice for all cycling applications. The combined outputs of this method will assist in simplifying the analysis and interpretation of complex drag and yaw distributions for a wider audience including athletes and coaches.

## Conflicts of Interest

## References

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**Figure 1.**Yaw Angle (ψ) as a function of road speed (V

_{R}), wind speed (V

_{W}) and wind direction (φ).

**Figure 2.**(

**a**) Example of two different drag curves for arbitrary bicycles; (

**b**) The normalised weighting function for yaw angle. The product of these two curves generates a weighted drag curve (see Figure 3).

**Figure 3.**Weighted drag curve; the product of the normalised weighting function and raw output from wind tunnel drag measurement. Note the change in vertical axis scale.

**Figure 4.**(

**a**) Probability of yaw angle with varying road speed (V

_{R}); (

**b**) Probability of yaw angle with varying mean wind speed (V

_{W}).

**Table 1.**Single sided yaw weighting function for V

_{R}= 25 mph (40.23 km/h, 11.18 m/s), V

_{W}= 7 mph (3.13 m/s). Function is symmetric about 0°.

Yaw Angle (°) | 0 | 2.5 | 5 | 7.5 | 10 | 12.5 | 15 | 17.5 | 20 |

Weighting Function (W) | 1.000 | 0.952 | 0.857 | 0.683 | 0.543 | 0.377 | 0.237 | 0.158 | 0.090 |

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**MDPI and ACS Style**

Barry, N.
A New Method for Analysing the Effect of Environmental Wind on Real World Aerodynamic Performance in Cycling. *Proceedings* **2018**, *2*, 211.
https://doi.org/10.3390/proceedings2060211

**AMA Style**

Barry N.
A New Method for Analysing the Effect of Environmental Wind on Real World Aerodynamic Performance in Cycling. *Proceedings*. 2018; 2(6):211.
https://doi.org/10.3390/proceedings2060211

**Chicago/Turabian Style**

Barry, Nathan.
2018. "A New Method for Analysing the Effect of Environmental Wind on Real World Aerodynamic Performance in Cycling" *Proceedings* 2, no. 6: 211.
https://doi.org/10.3390/proceedings2060211