Appendix II: Using the Barometer as an Altimeter

Set up Labpro:

Connect the barometer (which measures pressure) probe to the Lappro. The settings aren’t terribly important, but a setting of 10 sample/second with an over-sampling of 3 should be fine (and of course set the experiment length for a little over the time the balloon will be in the air). Refer to Appendix II on how to set the Labpro for remote data taking.

How to get the height of the balloon from the pressure reading:

Use the exponential formula for pressure vs. height, , where P is the pressure reading at the height of interest, P_o is the pressure at ground at sea level and equal to 101325 N/m² = 2116 lb/ft² = 14.69 lb/in², h is the height of the Pressure reading (i.e. height) and a = 8.42 km. -this is the height the atmosphere would have to have if its density were constant with height, and equal to r₀(r₀ = 1.225 kg/m³), in order to maintain pressure P_o at sea level. So, one can use this formula, the pressure reading P and the known value for P_o to find h. Here’s how it’s done. First decompose the equation, to solve for h. This is done by taking the natural log of both sides of the equation and solving for h.

Example: Let’s say you measure the pressure at the ground to be 0.9841 atm (thus, P_o=0.9841atm) and you measure the pressure at a certain height to be 0.9724 atm (thus, P=0.9724 atm), in order to find the height the balloon was at simply use the above equation, plugging in the values.

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Note: if you want to find your height above sea level (altitude), simply plug in 1.0 atm P_o, this is the pressure at sea level.

Accuracy: The barometer is accurate to , which roughly corresponds to accuracy in height; see below for a detailed check with a range finder.

One can also use the empirical model from NASA (this formula is derived from fitting a function to data). However, the exponential model only differs with the NASA empirical model by at 1000m altitude, and even less for smaller altitudes.

At altitudes (see Glast website, classroom resources tab) below 11km, here are the following fits for the atmosphere.

T = T₀ (1 – h / 44329 m)

r = r₀ (1 – h / 44329 m)^4.255876

P = P₀ (1 – h / 44329 m)^5.255876

Example: Let’s say you measure the pressure at the ground to be 0.9841 atm (thus, Po=0.9841atm) and you measure the pressure at a certain height to be 0.9724 atm (thus, P=0.9724 atm), in order to find the height the balloon was at simply use the above equation, plugging in the values.

.

Example: Let’s say you measure the pressure at the ground to be 0.9841 atm (thus, P_o=0.9841atm) and you measure the pressure at a certain height to be 0.9724 atm (thus, P=0.9724 atm), in order to find the height the balloon was at simply use the above equation, plugging in the values.