This paper presents analytic equations modelling the main physics and cost of a generic Airborne Wind Energy System flying crosswind. The power equation of a system that can handle ground and on-board generation is presented, under the assumption of steady-state flight. A structural and a take-off model are used to derive the key equations for the flying mass estimation of a hard-wing kite. A modification of the power equation is carried out to show how to include gravitation forces in the power estimation. Finally, an economic model is introduced. The model presented in this paper is intended to describe the key behavior of the system based on basic principles. It is suitable to be coupled with system design tools. (C) 2020 Elsevier Ltd. All rights reserved.