## 4 Discussion
### Energy Flux of Tsukahara and Yurchenko Vaults
This finding is in line with that of [PERSON] and [PERSON] [28], who emphasized the importance of maintaining a high angular momentum during springboard contact during Yurchenko vaults. For Tsukahara vaults, increasing difficultly requires generating more AKE during springboard contact (8% more for difficult compared to simple vaults in the current study). Combined with TKE, this additional AKE represents the exploitable potential to maximize height of flight and rotation during the second flight phase. The table contact phase of difficult compared to simple Tsukahara and Yurchenko vaults is characterized by up to 7% lower PE at first table contact a shorter table contact time, and up to 15% lower AKE at push off. A fast first table contact (low PE) and a short table contact time may be crucial prerequisites for optimally oriented force production, necessary to generate an optimal counter-torque (i.e., reduction in angular momentum) at push off [11], and therefore maximize the height of flight during the second flight phase. Our data seem to confirm that, in order to perform a more difficult vault, a slightly greater counter-torque must be generated. Nevertheless, as previously discussed, the transformation of TKE may be more important for maximizing height of flight than the transformation of AKE into PE. A greater height (and longer duration) of flight increases the time in which to perform rotations around longitudinal and transversal axis (e.g., to perform a more difficult vault). In line with these findings, previous studies observed that it is crucial, in order to perform difficult vaults, that a maximum of horizontal velocity is transformed into vertical velocity during table contact [4; 29; 30; 31; 32]. Most of the significant differences between simple and difficult vaults in the current study were found for AKE during the second flight phase of Tsukahara and Yurchenko vaults. As all vaults were performed with a layout somersault during the second flight phase, the differences in AKE can be mostly attributed to the different number of rotations around longitudinal axis. In this context, we show that performing 180\({}^{\circ}\) more of rotation around longitudinal axis during the second flight phase requires between 5.6% and 5.9% more of AKE. However, AKE accounts for only up to 22% of the total energy during the second flight phase, whereas two thirds (67%) of total energy during the second flight phase consists of PE. Therefore, the necessary amount of additional AKE, in order to perform a more difficult vault, is (almost) negligible. Additionally, the requirements for PE and TKE rise slightly with increasing difficulty of the vault. This may lead to the observedincrease in total energy and to the surprisingly small difference between simple (layout) and difficult (900\({}^{\circ}\)) Tsukahara and Yurchenko vaults of 12% and 6%, respectively. Therefore, coaches and athletes must be aware that, when increasing vault difficulty, regardless of style, demands for several aspects increase slightly but simultaneously. Moreover, it can be said that if an athlete is able to perform a simple vault perfectly, he would theoretically be able to show a more difficult vault (e.g., add a half twist) with a similar amount of energy. In order to be able to show the more difficult vault, therefore, technical and/or mental progress, and not energy-related progress, is particularly necessary.