Exploring the atmosphere using smartphones

Abstract

The characteristics of the inner layer of the atmosphere, the troposphere, are determinant for the earth's life. In this experience we explore the first hundreds of meters using a smartphone mounted on a quadcopter. Both the altitude and the pressure are obtained using the smartphone's sensors. We complement these measures with data collected from the flight information system of an aircraft. The experimental results are compared with the International Standard Atmosphere and other simple approximations: isothermal and constant density atmospheres. The international standard atmosphereThe atmospheric conditions exhibit strong variations at different points and different times. To provide a unified frame of reference, an atmospheric model, the International Standard Atmosphere (ISA), has been established 1 . It consists of tables of pressure, temperature, density and other variables suitable at mid latitudes over a wide range of altitudes. The ISA is used for several purposes ranging from altimeter calibration to comparison of aircraft performance among others. The ISA is divided into layers with simple temperature variations. The inner layer is the troposphere, from the surface until 11 km of height, in which the temperature presents a linear gradient, named lapse rate, C= -0.0065 K/m. The pressure p as a function of the height h according to the ISA is shown in Fig. 1.We also consider two additional atmospheric models. Firstly, a rather crude approximation consists of considering the temperature constant in the inner layers. This model is called isothermal atmosphere. The flight information system usually available to the passengers in many aircrafts provides an clever way to quantify the relationship between temperature and pressure. In Fig. 2 we plot the temperature as a function of the altitude using data collected by a passenger. The linear fit, and g gives a temperature gradient of about C= -0.0072 K/m. Of course, this value highly depends on the particular atmospheric conditions during this flight and does not necessarily represents accurately the ISA. This exercise can be proposed as a homework to students about to travel on a plane.The second approximation is obtained neglecting air density variations. Under this approximation valid at small altitudes (a few kilometers), ρ is constant and the atmospheric pressure obeys the hydrostatic equation

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