# Determinants of Top Speed Sprinting: Minimum Requirements for Maximum Velocity
## 3 Results  
Data across a range of top speeds for the three hypothetical runners of varying leg lengths are presented in Tables 1-3 and Figure 2. These values are calculated from the equations and simplifying assumptions presented in the Methods. The predictive lines illustrated in Figure 2 are based on the outcomes listed in Tables 1-3. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline _Speed_ & \(t_{c}\) & _SR_ & _SL_ & _SL/L\({}_{0}\)_ & _F\({}_{Zagg}\)/mg_ & \(\theta_{total}\) & \(\omega_{avg}\) & \(\kappa_{max}\) \\ (m/s) & (s) & (steps/s) & (m) & (ratio) & (ratio) & (deg) & (deg/s) & (deg/s\({}^{2}\times 10^{3}\)) \\ \hline
7.00 & 0.121 & 4.14 & 1.69 & 1.99 & 1.99 & 84.5 & 349.8 & 7.15 \\
8.00 & 0.106 & 4.42 & 1.81 & 2.13 & 2.13 & 89.2 & 394.3 & 8.60 \\
9.00 & 0.094 & 4.66 & 1.93 & 2.27 & 2.27 & 94.1 & 438.6 & 10.09 \\
10.00 & 0.085 & 4.88 & 2.05 & 2.41 & 2.41 & 99.0 & 482.8 & 11.62 \\
11.00 & 0.077 & 5.07 & 2.17 & 2.55 & 2.55 & 104.0 & 526.9 & 13.18 \\
12.00 & 0.071 & 5.24 & 2.29 & 2.69 & 2.69 & 109.0 & 571.1 & 14.77 \\
13.00 & 0.065 & 5.39 & 2.41 & 2.84 & 2.84 & 114.0 & 615.2 & 16.38 \\ \hline \end{tabular}
\end{table} 
Table 1: Calculated values across a range of speeds for a hypothetical athlete with \(L_{0}\) = 0.85 m. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline _Speed_ & \(t_{c}\) & _SR_ & _SL_ & _SL/L\({}_{0}\)_ & _F\({}_{Zagg}\)/mg_ & \(\theta_{total}\)_ & \(\omega_{avg}\) & \(\kappa_{max}\) \\ (m/s) & (s) & (steps/s) & (m) & (ratio) & (ratio) & (deg) & (deg/s) & (deg/s\({}^{2}\times 10^{3}\)) \\ \hline
7.00 & 0.136 & 3.91 & 1.79 & 1.88 & 1.88 & 81.0 & 316.9 & 6.12 \\
8.00 & 0.119 & 4.19 & 1.91 & 2.01 & 2.01 & 85.2 & 356.9 & 7.38 \\
9.00 & 0.106 & 4.43 & 2.03 & 2.14 & 2.14 & 89.5 & 396.6 & 8.68 \\
10.00 & 0.095 & 4.65 & 2.15 & 2.26 & 2.26 & 93.8 & 436.3 & 10.01 \\
11.00 & 0.086 & 4.85 & 2.27 & 2.39 & 2.39 & 98.2 & 475.8 & 11.38 \\
12.00 & 0.079 & 5.02 & 2.39 & 2.52 & 2.52 & 102.6 & 515.3 & 12.77 \\
13.00 & 0.073 & 5.18 & 2.51 & 2.64 & 2.64 & 107.1 & 554.8 & 14.18 \\ \hline \end{tabular}
\end{table} 
Table 2: Calculated values across a range of speeds for a hypothetical athlete with \(L_{0}\) = 0.95 m. \begin{table}
\begin{tabular}{c c c c c c c c} \hline _Speed_ & \(t_{c}\) & _SR_ & _SL_ & _SL/L\({}_{0}\)_ & _F\({}_{Zagg}\)/mg_ & \(\theta_{total}\)_ & \(\omega_{avg}\) & \(\kappa_{max}\) \\ (m/s) & (s) & (steps/s) & (m) & (ratio) & (ratio) & (deg) & (deg/s) & (deg/s\({}^{2}\times 10^{3}\)) \\ \hline
7.00 & 0.150 & 3.70 & 1.89 & 1.80 & 1.80 & 78.3 & 290.1 & 5.30 \\
8.00 & 0.131 & 3.98 & 2.01 & 1.91 & 1.91 & 82.0 & 326.4 & 6.41 \\
9.00 & 0.117 & 4.23 & 2.13 & 2.03 & 2.03 & 85.8 & 362.6 & 7.56 \\
10.00 & 0.105 & 4.44 & 2.25 & 2.14 & 2.14 & 89.7 & 398.5 & 8.74 \\
11.00 & 0.095 & 4.64 & 2.37 & 2.26 & 2.26 & 93.6 & 434.4 & 9.95 \\
12.00 & 0.088 & 4.82 & 2.49 & 2.37 & 2.37 & 97.6 & 470.2 & 11.18 \\
13.00 & 0.081 & 4.98 & 2.61 & 2.49 & 2.49 & 101.6 & 505.9 & 12.44 \\ \hline \end{tabular}
\end{table} 
Table 3: Calculated values across a range of speeds for a hypothetical athlete with \(L_{0}\) = 1.05 m.  
Figure 2: Calculated data across a range of top speeds for the three hypothetical athletes of different body dimensions. Illustrated lines based on values in Tables 1–3, arranged by athlete leg length (\(L_{0}\)). (**a**) ground contact time (\(t_{c}\)), (**b**) step rate (\(SR\)), (**c**) step length (\(SL\)), (**d**) ratio of step length to leg length (\(SL/L_{0}\)), (**e**) ratio of stance-averaged vertical force to body weight (\(F_{Zang}/mg\)), (**f**) total thigh range of motion (\(\theta_{total}\)), (**g**) average thigh angular velocity (\(\omega_{avg}\)), (**h**) modeled maximum thigh angular acceleration (\(\alpha_{max}\)).