# Kinematic Determination of the Aerial Phase in Ski Jumping
## 1 Introduction  
Ski jumping is a popular winter sport, with an Olympic history dating back to 1924 [1]. In previous research, the consensus has been to divide a ski jump into four main phases: inrun, take-off, flight, and landing, where the flight phase is subdivided into three phases: early flight, stable flight, and landing preparation [2], as shown in Figure 1. A ski jumper aims to gain the highest speed possible through the invnn [3], while establishing the best possible conditions for the phase considered to be most influential on performance, the take-off, where the initial conditions for the flight are created [2, 4, 5]. The early flight phase spans from where the ski jumper is airborne until a steady flight posture is reached. The aim of the early flight phase is to reach stable flight as quickly as possible, with minimal speed loss [6, 7, 8, 9]. The stable flight phase is the part where the ski jumper maintains a fairly constant flight posture, i.e., from the end of early flight to the start of landing preparation. In this phase, the aerodynamic forces are highly influential and the ski jumper intends to achieve as high of a lift-to-drag-ratio (\(LD\)-ratio) as possible [2]. From a physics point of view, a ski jumper must produce a force, counteracting the gravitational force in order to be flying. However the aerodynamic forces do not counteract the gravitational forces, and the ski jumperdoes not provide any propulsion or thrust. Therefore, a more accurate description would be 'gliding', as the ski jumper glides through the air, and descends gradually without supplying force. Performance is to a great extent determined by the initial conditions determined by the take-off and the gravitational and aerodynamic forces through the glide phase [10; 11; 12]. The term'stable' is probably derived from the limb motions of the ski jumper, which are relatively static during this phase compared to the take-off and landing phases. The dynamics of the athlete is not as tightly coupled to the flight characteristics as the effect of the athlete's action is. Therefore, this phase should be described as 'isometric-static' or'steady', i.e., the rate-of-change of aerodynamic forces is close to zero. Hence, the term'steady glide' will be used for the'stable flight' phase (3.2 in Figure 1) through this article. While much research has examined factors influencing take-off and early flight, research on the steady glide phase is scarce. This was partly caused by the difficulties in establishing valid methods to collect data from this phase, since the ski jumper moves through a large volume at high speed. Currently, researchers have used computational fluid dynamic simulations and wind tunnel measurements, and there have been a small number of studies using video analysis to examine how the glide posture can influence glide parameters, such as the aerodynamic relationship between the lift (\(F_{L}\)) and drag forces (\(F_{D}\)), i.e., \(LD\)-ratio [9; 13; 14; 15; 16; 17; 18; 19]. In recent years, wearable sensors as inertial measurement units (IMUs) have shown promising results when measuring kinematics and kinetics from the start of the irnum to the landing [20; 21; 22; 23; 24; 25; 26; 27; 28]. A suitable method used to provide accurate field data from the steady glide phase is differential global navigation satellite system (dGNSS) technology. Measurements with dGNSS are extensively used and validated in alpine skiing for position, velocity, and acceleration-related parameters [29; 30; 31; 32; 33], but have rarely been used in ski jumping [34]. However, a recent study has shown the possibilities dGNSS provides to efficiently collect data from the start of the irnum to the landing [35]. The use of this method allows measurement of the trajectory with \(\pm 0.05\,\mathrm{m}\) global position accuracy [36].