# Aerodynamic Benefits by Optimizing Cycling Posture
## 4 Application to Ironman Hawaii
### General Bike Split Model  
By using the Nabla Flow CFD simulation tool AeroCloud, a dimensionless CdA coefficient at a flow velocity of \(U_{x}\) of 10m/s was extracted. In addition, drag force \(F_{d}\) at the specified yaw angle \(\beta\) was also derived. These two parameters are sufficient to calculate the necessary power to overcome the aerodynamically drag. To have a more accurate estimation of \(P_{total}\), we needed to add the rolling resistance \(P_{roll}\), the power to climb \(P_{elev}\) and mechanical losses \(P_{mech}\) (mechanical losses of 3% of the total power output were considered). Therefore, our model is summarized in Equation (1):  
\[P_{total}=\left[\frac{1}{2}\cdot\rho\cdot CdA_{0^{\circ}}\cdot U_{x}^{3}\cdot cos (\beta)+c_{r}\cdot m\cdot g\cdot U_{x}+\frac{m\cdot g\cdot dh\cdot U_{x}}{ds} \right]\cdot 1.03 \tag{1}\]  
As velocity \(U_{x}\) is represented in Equation (1) with the 3 rd power, its accuracy is important. The temperature T also deserves a special discussion. A higher temperature results in a lower air density and cannot be neglected over the whole course of 180 km, nor can the change in altitude (which has the largest influences on the density and humidity). Sample calculations show that all effects--when taken together--result in changes in density of less than 2% Here we rely on data from one of the author's races at IM Hawaii on 13 October 2018, stored in a TCX-file. (Bike computers record all relevant data, including distance, speed, elevation, etc., and store them in TCX files). For all the following calculations, an average air temperature of 27 \({}^{\circ}\)C (300.15 K) was used. The variables used were: \(\rho\), density of air; \(c_{r}\), rolling resistance coefficient; \(m\), total mass; \(g\), earth acceleration (9.81 m/s\({}^{2}\)); \(dh\)/\(ds\), local slope of cycling path.  
Other decisive factors are the elevation profile and the system mass of the cyclist and the bike. In this case, the system weighed 94 kg (83 kg athlete + 11 kg equipment). The elevation profile of the course was extracted from the TCX file, and the overall course was cut into 20 distinct segments; see Table 3. Segment 5, for instance, marks the short and steep climb at Palani road in Kailua-Kona, so it was not mixed up with another segment, as the average speed for a set power output at this climb is highly affected by \(P_{elev}\) and therefore, by the system mass. Segment 12 and 14 will be highlighted as well. They mark the 10 km climb up to Hawi, and in reverse, the fastest part of the course: the 10 km downhill after the turning point. Looking closer at the table, we can also see that the long part on the Queen K Highway is symmetrical (segment 7 to 19) and can be regarded as rolling hills, as previously mentioned. In the downhill segments with negative slope angles \(\alpha\), \(P_{elev}\) is of particular interest. The so-called downhill slope force will add a negative value to the equation, and therefore allow one to increase the remaining values. Downhill segments are therefore much faster than flat or uphill segments with the same power output.  
Figure 9: Probability of wind yaw at IM Hawaii.  
The last important parameter showing a high impact on the overall performance is the CdA value within the aerodynamic drag expression. As the focus of this work is the optimization of cycling posture to go faster, substantial savings can be seen within the improvement of the CdA value. Considering the different CdA values from the four positions, a bike split calculation was performed for each one of them to determine time saving on the IM Hawaii bike course. The cubic equation, shown in Equation (1), was solved by a simple fixed-point iteration for each increment ds from Table 3. The input power \(P\) was set to 300 W constantly. Equation (1) was then solved for \(U_{x}\), and the increment in time dt for an increment in path ds was calculated via \(dt=U/ds\).