## 1 Introduction  
Wind energy systems have gained much attention for their ability to provide clean and environmentally friendly energy resources in contrast to fossil fuels [1, 2]. Recently, the geometric dimensions and capacity rate of wind turbines have been getting larger in order to meet the required reduction of LCOE (levelized cost of energy). This became possible due to the evolution of technologies, such as materials, structural designs, systems, aerodynamics, and so on. It is possible to capture more energy from incoming wind with an increased rotor size since power production is proportional to the square of the rotor diameter [3]. Furthermore, the paradigm shift to offshore wind from onshore wind has been accelerating the growth of wind turbine size and capacity due to steadier and more stable wind resources, not to mention having the advantages of being far away from artificial obstacles and potential noise issues [4, 5]. However, the CAPEX (capital expenditure) of huge wind turbine structures, which includes the material cost, installation cost, transportation cost, and operational and maintenance costs, is becoming increasingly unfavorable. Therefore, the sizes of wind turbines are now approaching an economically feasible limit under current technologies [6].  
There have been many innovative concepts developed to harvest wind energy efficiently with a fraction of the traditional wind turbine cost. As an emerging technology, airborne wind energy systems (AWES) utilize steadier and stronger wind resource resulting from the high altitude [7, 8, 9, 10, 11]. Figure 1 shows two different concepts of AWES, Ground-Gen systems, and Fly-Gen systems [12].  
As shown in Figure 1, both airborne wind energy systems use a tether structure to connect ground systems (mobile or fixed) to flying devices without a tower to capture wind energy at high altitudes above those of traditional tower-based wind turbines. By controlling tether length, the harvesting height can be adjusted to maximize wind resource availability [13]. That is, the tether structure plays the role of transferring the traction force of the AWES to the fixed or mobile ground system with less motion. Therefore, its design life should be able to operate under the cyclic load caused by the repeated reeling motion and to endure the specific breaking strength limit entailed by a certain form of snap loading caused by unexpected impulsive forces [14]. Since the tether is an extremely critical component, it should be designed according to a fail-safe rule [15]. To avoid the accidental failure of the tether under unexpected snap loading, the tether should be designed to increase the capacity of energy dissipation.  
In this paper, the AWES is simply modeled as a two-point mass structure with a tether connection, where the small mass represents a flying airborne system such as a kite or flying aircraft, and the other big mass corresponds to a ground station with little movement. The benefit of this tailoring concept, applicable to the airborne wind turbine system under impulsive tensile loading, was analytically investigated in a previous study [16]. Often, there are cases in which the tether length can increase to up to 1000 m to access wind resources at extremely high altitudes above 500 m. In this work, an approximate technique for such a long tether was developed in order to reduce the computational costs dramatically while providing good accuracy, even when compared to the original full modeling. The approximated tether modeling developed in this paper could be applicable to the mooring systems of floating wind turbine systems. The efficient and light design will be possible by applying optimization techniques such as genetic algorithms or gradient-based optimization to maximize the energy capacity or to find the advanced tether geometry [17; 18; 19; 20; 21].