# Duty Factor Reflects Lower Limb Kinematics of Running
## 1 Introduction  
In both well-trained athletes and recreational runners, a U-shaped curvilinear relationship between running economy and self-selected stride length [1; 2; 3; 4; 5; 6; 7], stride rate [3; 7], and contact time (\(t_{c}\)) or leg stiffness [8] has been reported. This highlights that runners seem to self-optimize their running gait to minimize the metabolic cost of running [1; 9; 10; 11]. An emergent area of research is focusing on the individual runner to try to identify how the person's structure and functional abilities influence performance, running economy, or running-related injuries [12]. For instance, self-organizing map [13] or hierarchical cluster analysis [14] approaches identified different running gait strategies within a given sample of runner. Based on a subjective evaluation of the spontaneous overall running pattern, other researchers categorized runners in two groups with kinematic differences, called terrestrial and aerial runners [15; 16]. Using the duty factor (DF; an objective parameter representing the proportion of time spent in contact with the ground during a running stride), [PERSON] et al. (2019) observed global biomechanical differences when classifying runners in two groups called DF\({}_{\rm low}\) (a low mean DF (\(\overline{\rm DF}\)) averaged over different running speeds) andDF\({}_{\rm high}\) (a high \(\overline{\rm DF}\)) [17]. In their analysis, the authors divided the running cycle in several subtimings, namely, braking (\(t_{b}\)) and pushing (\(t_{p}\)) times, which are defined from footstrike (FS) to mid-stance (MS) and from MS to toe-off (TO), respectively, and elevation (\(t_{e}\)) and dropping (\(t_{d}\)) times, defined as the time from TO to mid-flight (MF) and from MF to FS of the contralateral foot, respectively. MS and MF events were calculated to divide \(t_{c}\) and flight time (\(t_{f}\)), respectively. The authors observed that the two subcomponents of the contact phase (\(t_{b}\) and \(t_{p}\)) were statistically longer for DF\({}_{\rm high}\) than for DF\({}_{\rm low}\) and that both \(t_{e}\) and \(t_{d}\) were statistically shorter for DF\({}_{\rm high}\) than for DF\({}_{\rm low}\). In addition, the authors showed that the vertical displacement of the center of mass (COM) during the elevation phase (\(\Delta z_{\rm COM,\emph{e}}\)) was statistically greater for DF\({}_{\rm low}\) than for DF\({}_{\rm high}\), but no statistical differences were obtained for the vertical displacement of the COM during braking (\(\Delta z_{\rm COM,\emph{b}}\)), pushing (\(\Delta z_{\rm COM,\emph{p}}\)), and dropping (\(\Delta z_{\rm COM,\emph{d}}\)) phases. Similar subgroupings of participants were obtained based on the DF measured at 12 km/h than based on a subjective evaluation of the spontaneous overall running pattern [18]. The two groups of runners have the same running economy, but with a different running pattern: aerial and DF\({}_{\rm low}\) favor a long \(t_{f}\) together with a midfoot to forefoot strike pattern. On the contrary, terrestrial and DF\({}_{\rm high}\) favor a long \(t_{c}\) associated with a rearfoot strike pattern [17; 19]. Moreover, grouping runners based on their DF reflect their global running pattern, which takes into account not only the FS pattern but also vertical oscillation of the head, antero-posterior motion of the elbows, vertical pelvis position at ground contact, and antero-posterior foot position at ground contact. Similarly to what was observed when grouping runners based on their global running pattern, no difference in running economy has been reported while using more local and finer parameters, such as the FS angle [20] or strike pattern [21; 22; 23]. Beyond metabolic cost, different FS patterns are providing different impact loading rates. Using a forefoot strike pattern does not eliminate the passive impact peak at the ground contact [22].