The physics of a weather balloon is analyzed. The surprising aspect of the motion of these balloons is that they ascend to great altitudes (typically 35 km) at a more or less constant rate. Such behavior is not surprising near the ground—say for a helium-filled party balloon rising from street level to the top of the Empire State building—but it is unexpected for a balloon that rises to altitudes where the air is rarefied. We show from elementary physical laws why the ascent rate is approximately constant.
References
1.
See, for instance,
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See, for example, the following educational websites for more on high school and university weather balloon programs: http://www.aerospace.illinois.edu/news/high-altitude-balloon-class-emphasizes-hands-learning, http://www.balloonchallenge.org/education, http://www.cbc.ca/news/canada/saskatchewan/students-learn-science-with-high-altitude-balloons-1.3031597, http://www.stratostar.net/faq.html, http://www.balloonnews.wordpress.com/2013/09/15/4-websites-you-must-see-before-launching-your-first-weather-balloon/.
See also
B. N.
Fong
, J. T.
Kennon
, and E.
Roberts
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M. M. F.
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A lot of information about U.S. weather balloons can be found on the National Oceanic and Atmospheric Administration website Radiosonde Observations.
5.
Instantaneous ascent rates fluctuate wildly with altitude, as can be seen in the data of
A.
Gallice
et al, “Modeling the ascent of sounding balloons: Derivation of the vertical air motion
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4
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Kardell
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See
K. M.
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We infer this altitude-dependent cD from weather balloon ascent data and equations presented in
Gallice
et al (Ref. 5) and A.
Sóbester
et al, “Notes on meteorological balloon mission planning
,” AIAA Balloon Systems Conf.
25–28 March 2013
, Daytona Beach, FL.
Gallice et al. provide a graph and an empirical equation for drag coefficient vs. Reynolds number [Fig. 2 and Eq. (6)], and Sóbester et al. provide a graph of Reynolds number vs. altitude (Fig. 2). By combining these two, we obtain a parameterization for drag coefficient vs. altitude of the form cD = a+bz2. The spread of data in Sóbester et al. is such that the values for a and b are subject to error (I chose a = 0.40, b = 1/1400); the important point is that cD increases with altitude.8.
It is not obvious why the drag coefficient should behave this way—here we regard it as an experimental fact. We can see why drag might not be constant, however, as follows. As the balloon rises, it increases in radius and passes through air that is more and more tenuous, so it is likely that the Reynolds number (on which drag coefficient depends) changes. Drag force depends linearly on speed when the fluid flow is laminar, and quadratically on speed when flow is turbulent; the turbulence is likely to change as balloon radius and air density changes. For more on the drag force that acts on a sphere, see
P.
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and J. P.
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A.
Gallice
et al, see Ref. 5.© 2016 American Association of Physics Teachers.
2016
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