Weather Balloon Ascent Rate

See, for instance,

P.

Gluck

, “,”  , – ( );

J.

Jadrich

and

C.

Bruxvoort

, “,”  , – ( );

G.

Planinšič

, “,”  , – ();

T. A.

 

Walkiewicz

, “,”  , – ( ).

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

, “,”  , – ( ) in this issue.

M. M. F.

 

Saba

,

L. G. B.

 

Mirisola

, and

M.

 

Iguchi

, “,”  , – ( ).

A lot of information about U.S. weather balloons can be found on the National Oceanic and Atmospheric Administration website Radiosonde Observations.

Instantaneous ascent rates fluctuate wildly with altitude, as can be seen in the data of

A.

Gallice

 et al, “,”  , – () , or of

W. H.

 

Blackmore

and

R. D.

 

Kardell

, “,”  , – (), from which the quoted data were taken; the average rate is obtained by smoothing this data over, say, one minute or 10 minutes. A summary of the ascent rate variability can be seen on the NOAA website Radiosonde Balloon Ascent Rates. Some of the systematic variability is due to different balloon characteristics, but most of the minute-to-minute fluctuations arise from the very weather conditions that the balloon radiosonde is measuring.

See

K. M.

 

Lee

and

D. M.

 

Ryan

, “,”  , – ( ).

We infer this altitude-dependent c_D from weather balloon ascent data and equations presented in

Gallice

 et al (Ref. 5) and

A.

 

Sóbester

 et al, “,”  , 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 c_D = 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 c_D increases with altitude.

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.

 

Timmerman

and

J. P.

 

van der Weele

, “,”  , – ( ).

For balloon pressure, see

D. R.

Merritt

and

F.

Weinhaus

, “,”  , – ( ) , and

I.

 

Müller

and

H.

 

Struchtrup

, “,”  , – ().

A.

 

Gallice

 et al, see Ref. 5.