## 4 Discussion
### Aerodynamic Drag Models  
Since the bodies of individual skiers differ, we chose to express data as dimensionless, relative/normalized values wherever possible, in order to allow a more general application of our experimental models (Figures 2 and 3). In contrast to previous findings in connection with downhill skiing [12; 14; 15], our present data indicate clearly that when applying models of aerodynamic drag to the technical disciplines, it is necessary to distinguish between the positions taken during more intense turns (which are more frequent in the technical disciplines) and those adopted during less intense turns or on flat terrain. In these disciplines, transitions from one position to another usually occur quite rapidly; during the transition from a higher to the tuck position and vice-versa, \(\mathrm{h_{n}}\) can be estimated here to be \(\cong\)0.6, which is almost exactly the mid-point of the individual values for the higher and tuck positions (Figures 2 and 3). Our first model allows direct calculation of the product \(\mathrm{C_{d}}\)-S from the relative shoulder height \(\mathrm{h_{n}}\) using two linear regression functions (Figure 2). If the skier is equipped with a global navigation satellite system (GNSS) with the antenna positioned at shoulder height [17], this model, in combination with skiing speed, provides the aerodynamic drag directly from the Rayleigh equation. Thus, in this case, only the relative shoulder height (corresponding to the absolute distance between the shoulders and skis) and skiing speed need to be measured or calculated. A calculation of the product \(\mathrm{C_{d}}\)-S as a function of neck height or various joint angles was common in previous investigations on downhill skiing [12; 14; 15] and, in particular, the relationship to joint angles provides deeper insight into the effects of posture on aerodynamic drag. However, the determination of joint angles as independent variables requires equipment that is more technologically complex. Since this simpler experimental model calculates the absolute value of the product \(\mathrm{C_{d}}\cdot\mathrm{S}\) from the relative height \(\mathrm{h_{n}}\) alone, this approach might be expected to provide less reliable values for skiers whose height differs from those of our subjects. Therefore, we created another experimental model that, in addition to \(\mathrm{C_{d}}\), incorporates the relative cross-section \(\mathrm{S_{n}}\), which is also dependent on \(\mathrm{h_{n}}\). On average, this latter model resulted in lower limits of agreement (LoA) and coefficient of variation (CV) (Figures 2 and 3). Here, the reference cross-sectional area (\(\mathrm{S_{f}}\)) of each skier was obtained from iDEXA images, which are often available for elite skiers. Alternatively, when such scans are not available, the skiers can be photographed in an upright and extended position against a wall using a conventional camera and \(\mathrm{S_{r}}\), subsequently obtained by processing the resulting image with the same click-based interactive segmentation utilized here [18]. In general, the determination of the aerodynamic drag associated with skiing utilizing our models involves an error of 3.9-7.7% (CV). On the other hand, the division of the LoA (Figures 2 and 3) for each parameter by the average value for this same parameter to obtain a relative error that includes 95% of the values measured results in a range of 4.5-16.5%. These levels of accuracy are only slightly poorer than those reported previously utilizing a model requiring more complex three-dimensional measurements of multiple segments of the skier's body [10]. By employing our new experimental models in combination with the methodology described in a previous report [11], the energy dissipation caused by aerodynamic drag can be determined as a numerical integration of the product of \(\mathrm{F_{d}}\) and the distance travelled. Subsequently, these energy losses can be divided by the total energy losses to obtain the relative energy loss associated with aerodynamic drag.