## 4 Metabolic Power Savings and Performance Predictions  
To calculate the power consumed by the core race walker against the aerodynamic drag, the basic kinematic equations and an empirical mathematical model of mechanical power output are utilized. [PERSON] (1977) conducted an experiment with race walkers on a force platform to establish an empirical model of mechanical power output [PERSON] (1977). This model considers the power generated by moving the center of mass, limb movement, and the work required to overcome aerodynamic drag, enabling the expression of mechanical power output. \[P_{R}=(9.42+4.73v+0.266v^{1.993})\frac{4.1868m}{60}+P_{areo}, \tag{6}\]  
where \(v\) is the speed, \(P_{R}\) is the mechanical power output, \(P_{areo}\) is the work required to overcome aerodynamic drag, \(m\) is the mass of the core race walker. The formula for overcoming the work required by aerodynamic drag is  
\[P_{areo}=F_{areo}.v, \tag{7}\]  
where \(F_{area}\) is aerodynamic drag. The metabolic power \(P_{mech}\) can be expressed as:  
\[P_{mech}=\frac{P_{R}}{\epsilon}, \tag{8}\]  
where \(\epsilon\) is the metabolic efficiency. Race walking, while similar in form to walking, requires athletes to sustain a fast pace for extended periods, demanding significant physical fitness. Metabolically, it shares more similarities with running than traditional walking. [PERSON]'s experiments involved walking speeds ranging from 2.5 to 8 km/h, considerably slower than race walking's pace at 4 m/s (equivalent to 14.4 km/h), aligning it more closely with running in terms of speed. [PERSON]'s findings suggest that running speeds between 10 and 15 km per hour primarily rely on aerobic processes, consistent with the metabolic demands of race walking. Within this speed range, running efficiency typically ranges from 0.4 to 0.5. Therefore, this study adopts a metabolic efficiency \(\epsilon\) value of 0.488, corresponding to a speed of 4 m/s [33]. The sports economy \(RE\) can be expressed as [34]. \[RE=\frac{P_{mech}}{m}, \tag{9}\]  
In accordance with the drag coefficient calculations presented in Section 2.3, the work required by aerodynamic drag \(P_{areo}\), the mechanical power \(P_{R}\), the mechanical power \(P_{mech}\), and sports economy \(RE\) of core race walker in different drafting formations are computed utilizing Equations (6)-(9), as depicted in Table 2. According to Table 2, the optimal double, triple, and quadruple drafting formations result in \(\Delta RE\) increases of 4.4%, 4.9%, and 5.7%, respectively, compared to race walking alone. [PERSON] (2019) observed that in high-level racing events, speed increases with \(RE\), as shown in Figure 14 [34]. When \(RE\) increased by 3% relative to the 2:04:00 time of the Berlin Marathon in 2015 (with the introduction of a more economical running shoe), the speed increased by 1.97%, resulting in a time of 2:01:36. This time is remarkably close to the recent world record set by [PERSON], thus confirming the accuracy of [PERSON]'s model [34]. Figure 14 indicates that at a speed of 4 m/s, an increase in \(RE\) by 1% corresponds to a 0.82% increase in speed. \begin{table}
\begin{tabular}{l c c c c c c c} \hline
**Drafting Formations** & \(F_{area}\)**(N)** & \(P_{areo}\)**(W)** & \(\Delta P_{areo}\) & \(P_{R}\)**(W)** & \(\Delta P_{R}\) & \(P_{mech}\)**(W)** & \(RE\)**(W/kg)** & \(\Delta RE\) \\ \hline Race walking alone & 7.5 & 45 & & 675.3 & & 1383.8 & 22.61 & \\ Double formation & 2.6 & 15.6 & 65\% & 645.9 & 4.4\% & 1323.6 & 21.62 & 4.4\% \\ Triple formation & 2.1 & 12.6 & 72\% & 642.9 & 5.1\% & 1317.4 & 21.53 & 4.8\% \\ Quadruple formation & 1.1 & 6.6 & 85\% & 636.9 & 5.7\% & 1305.1 & 21.33 & 5.7\% \\ \hline \end{tabular}
\end{table} 
Table 2: Aerodynamic power \(P_{areo}\), mechanical power \(P_{R}\), metabolic power \(P_{mech}\), and sports economy \(RE\) of core race walker in optimal drafting formations.