Our last two posts, were about that fascinating Google attempt to provide internet access to our planet's remote areas. Project Loon.

First we wanted to find out, what a balloon needs in order to fly, so we added a Hot Air Balloon Lift calculator to fxSolver's database. Then, we wondered how the electronics each balloon carries, will survive the low temperatures of the Stratosphere. We decided that we can use fxSolver to calculate the thermal resistance of the insulation material.
Now, we definitely should understand more about the stresses that the circuit board must sustain. Circuit boards which were soldered in room temperature and have to operate in very low temperature conditions.
In order to calculate that, we should use the linear and the surface thermal expansion coefficient.

Linear goes first.
Thermal expansion is the tendency of matter to change in volume in response to a change in temperature through heat transfer. When a substance is heated, the kinetic energy of its molecules increases. Thus, the molecules begin moving more and usually maintain a greater average separation. To a first approximation, the change in length measurements of an object (“linear dimension”) due to thermal expansion is related to temperature change by a “linear expansion coefficient”. Linear thermal expansion is given by the formula on the left, where Δ_L is the change in length (m), a_L is the coefficient of linear expansion (K^-1), L the reference length measurement in meters, and Δ_T the change in temperature (K).

The degree of expansion divided by the change in temperature is called the material’s coefficient of Area thermal expansion and also varies with temperature.
The area thermal expansion coefficient relates the change in a material’s area dimensions to a change in temperature. It is the fractional change in area per degree of temperature change (ignoring pressure). The equation on the left is the one you are looking for, and a_A is the area thermal expansion coefficient (1/K), A the area of interest on the object (m²), δ_Α the change in area (m²) and δT is the change of temperature (K).

Have fun in the solver with all the formulas in our "Project Loon post trilogy". If you have the time and desire, check out our fxSolver video.  
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