2017 Academic High Altitude Conference

Applying Newton’s Law of Cooling When The Target Keeps Changing Temperature, Such As In Stratospheric Ballooning Missions

Newton’s Law of Cooling describes how a “small” system, such as a thermometer, comes to thermal equilibrium with a “large” system, such as its environment, as a function of time. It is typically applied when the environment is in thermal equilibrium and the conditions are such that the thermal decay time for the thermometer is a constant. Neither of these conditions are met when measuring environmental (i.e. atmospheric) temperature using a thermometer mounted in a payload lofted into the stratosphere under weather balloons. In this situation the thermometer is in motion so it encounters layer after layer of atmosphere which differ in temperature, and the changing environmental conditions can influence the thermal decay time “constant” for the thermometer as well. We have used Newton’s Law of Cooling in spreadsheet-based computer simulations to explore how thermometer readings react under these conditions, to better-understand how logged temperature records from stratospheric balloon flights during both ascent (relatively slow) and descent (much faster, especially at altitude) are related to actual environmental temperatures at various altitudes.