This paper presents a mathematical model of the vertical forces acting on an airship during vertical motion. The main effort is the definition of an airship model, which move only vertically by ballast, and buoyancy effects, with a much reduced energy consumption for take-off and landing operations. It has been considered a disc-shaped airship, which can operate using the open balloon airship architecture defined to operate safely with hydrogen. This architecture does not require internal ballonets, because of the connected increased fire dangers that they create even if vented.Several models of airship based on vertical forces have been presented in literature. They often consider only the US or International Standard Atmosphere models and they neglect effects of weather conditions. The latter are connected with the location and with the season. These environmental and climatic factors have a large influence on behaviors of the airship system, because it is well known that the internal buoyant gas changes pressure and density condition because of external temperature. This paper defines the lifting behavior in terms of speed and acceleration. It evaluates the load factor as a function of the buoyancy and the ballast on board as a function of climatic conditions.A very simple methodology has been also presented on daily basis, authors neglect the effect of overheating of the gas due to solar radiation on the surface of the balloon, which can support the predefinition of climatic effects. The proposed methodology corrects the International Standard Atmosphere model by considering climatic data such as temperature, density and pressure of the air dependent on seasonal factors and location on annual basis.