Stratoballoon, Altitude and Pressure vs. Time

We received enough altitude data over the radio to plot both altitude and barometric pressure against time.  In fact, pressure and altitude are roughly related (things like temperature and humidity affect that relationship, but for the sake of this argument, we’ll ignore those other factors):

Palt = Psurf * (1 – 6.87535 * 10-6 * Alt)5.2561

Where

Palt = the air pressure at the nominated altitude

Psurf = the surface air pressure in hectoPascals

Alt = nominated pressure altitude, in feet

Source: https://www.brisbanehotairballooning.com.au/faqs/education/113-pressure-altitude-conversion.html

 

We used a version of this formula in the balloon Arduino sketch to calculate altitude from the pressure readings we received, so it was relatively simple to derive pressure from the altitude data we received over the radio.  Next, I plotted both pressure and altitude against time:

Charts

And stacked the graphs so you can see how they line up.  Some interesting things to note from these graphs:

  • The rates at which the balloon ascended and the capsule descended are roughly linear, while the corresponding changes in pressure are logarithmic.
  • We lost several minutes of radio contact with the transmitter right after the balloon burst, so the charts show a steep and very straight change.  The balloon really wasn’t falling that fast – we just don’t have data for that period.
  • One interesting thing about the descent is that there are a couple of places where the balloon actually ascends (see the bumps in the graph at about the 10,000 meter mark).  I double-checked the data, and those were legitimate readings – I didn’t have to massage those numbers at all.
  • The flight lasted at least 2 hours from the time of release until the last recorded transmission.
  • The balloon ascended at an average rate of 4.68 m/s, and took 1:28:40 to reach a maximum (recorded) altitude of 25,191m, or 82,647 feet.  The pressure at that altitude is 1.23 kPa, or about 1.2% the pressure at sea level.
  • The capsule descended at an average rate of 10.9 m/s, and took at least 33 minutes to fall to 3,580m, or 11,744 feet (the last recorded altitude).
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