# Selection of Posture for Time-Trial Cycling Events
## 2 Materials and Methods
### Characterization Tests: Performance
#### 2.2.1 Characterization of Resistive Forces  
The aerodynamic drag characteristics were represented by the drag area (\(C_{D}A\)). The rolling resistance characteristics were represented by the rolling resistance coefficient (\(f_{r}\)). The drag area and rolling resistance coefficient were obtained using an experimental methodology based on outdoor road tests. Further details of the methodology are described by [PERSON] et al. [37; 38]. The methodology is based on the mathematical model of the longitudinal dynamics of the rider and the bicycle presented in Equation (1). \[M_{eq}a=\eta\left(\frac{P}{v_{b}}\right)-\frac{1}{2}\rho C_{D}Av_{w/b}^{2}- mgcos(\theta)f_{r}-mgsin(\theta)-c_{1}-c_{2}v_{b}, \tag{1}\]  
where \(\rho\) is the air density, \(v_{w/b}\) is the speed of the wind relative to the bicycle, \(m\) is the mass of the bicycle and the cyclist with equipment and instrumentation, \(g\) is the gravitational acceleration, \(\theta\) is the road inclination, \(\eta\) is the efficiency of the transmission system, \(P\) is the power delivered to the pedals, \(v_{b}\) is the bicycle speed, \(M_{eq}\) is the equivalent mass, \(a\) is the longitudinal acceleration, and \(c_{1}\) and \(c_{2}\) are constants of the equivalent bearing resistance representing the dissipation originated by the bearings of the bicycle [39]. The characterization consisted of performing several one-way rides along an outdoor test route at different constant speeds. The road grade was obtained offline from altimetry. The wind speed relative to the bicycle was measured during the tests. The power delivered by the cyclist, the bicycle speed, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Rider 1** & **Rider 2** & **Rider 3** & **Rider 4** & **Rider 5** \\ \hline Type & Aero & Time trial & Endurance & Time trial & Aero \\ Mass (kg) & 10.8 & 9.9 & 11.5 & 10.2 & 10.5 \\ Frame size 1  & 55 & 51.5 & 49 & 48.4 & 52 \\ Frame material & Carbon fiber & Carbon fiber & Aluminum & Carbon fiber & Carbon fiber \\ Aerobars’ height fit window (mm) & 55 & 40 & 55 & 55 & 55 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Characteristics of the bicycles used by each rider. Figure 1: Postures included in the study. ABh/ABl: highest and lowest configurable limits of the aerobars’ height. and the ambient conditions were also registered on the route and averaged for each trial. Inertial and geometrical parameters of the rider with the bicycle were also measured or estimated. The characterization of resistive forces for each rider was performed in one test day, in which both postures were characterized. The tests were performed on a straight asphalt route, with a length of 400 m, and exclusive dedication to bicycles. Each cyclist performed ten trials in each posture. The trials were performed at constant speeds between 18 and 27 km/h. The tires of all the bicycles were inflated at 8 bar. The bicycle speed was measured with a speed sensor (Speed sensor 2, Garmin, Olathe, KS, USA) located on the rear wheel hub coupled to a GPS cycle-computer (Forerunner 910 XT, Garmin, Olathe, KS, USA). As a result that it is difficult for the riders to pedal at a constant speed in real conditions, small variations in the speed were expected. For this reason, the average acceleration of each trial was numerically computed using the bicycle speed and the total interval duration. The wind speed relative to the bicycle was measured with an onboard anemometer based on a pitot tube and developed specifically for this application [38]. The altimetry of the test section was measured with a topographical-grade Global Navigation Satellite System (GR-5, Topcon, Tokyo, Japan). The power delivered by the rider was measured with a power meter located in the pedals (Vector, Garmin, Olathe, KS, USA). The average temperature, relative humidity, and atmospheric pressure data were registered with a weather station (Weather meter 4500, Kestrel Instruments, Boothwyn, PA, USA) to estimate air density using the model presented by [PERSON] et al. [40].