ASCENT RATE VARIATIONS
Ralph Wallio, WØRPK   WØRPK  at  netINS.net

The ascent rate of a high altitude balloon and payload is created by imbalance between buoyant lift and the combination of total weight and aerodynamic drag. Buoyant Lift results from the difference in density between equal volumes of lifting gas and displaced air. Total Weight includes all mass being lifted, the balloon envelope, payload, parachute, et al. Aerodynamic Drag slows ascent rate because air must be pushed aside as the balloon rises.

These factors are brought together in a formula of equilibrium,
LIFT = DRAG + WEIGHT

LIFT is calculated using Volume [m³] (equal volumes of lifting gas and displaced air), Density [kg/m³] of Air minus Density [kg/m³] of liftring gas, and the Acceleration of Gravity [9.8m s^-2]:

LIFT = (4pi/3)Radius³(Density_air-Density_helium)9.8m s^-2   (assumes balloon is spherical)

DRAG is calculated using Drag Coefficient, projected Area [m²]of balloon, Density of Air, and Ascent Rate

DRAG = C_d(pi)Radius²(Density_air)Ascent Rate²/2



High altitude balloon track and touchdown prediction accuracy is dependent on the quality of winds aloft observations and forecasts, ascent and descent rate predictions and burst altitude estimates. This discussion looks at ascent rate variations while hoping that they might be managed to improve track prediction accuracy. It is going to take all the king's horses and all the king's men to make sense out of what we find.

Current and all past versions of track prediction programs allow use of only one ascent rate value. These programs use wind direction and speed values at increasing altitudes to laterally move balloon and payload while they are ascending. Assumption of a constant ascent rate makes programs insensitive to variations in vertical velocity. The result is reduced accuracy in track and touchdown predictions.

Navigation telemetry files containing GPS based time stamp, latitude, longitude and altitude information have been collected for numerous high altitude missions. This study includes only those missions that flew after GPS Selective Availability inaccuracies were turned off on May 2, 2000. Ascent rate is calculated between consecutive GPS records using altitude and time stamps:

Ascent Rate = (New altitude - old altitude)/(New time - old time)

EXCEL charts are then constructed comparing ascent rate vs. altitude. Ten point moving average trend lines of data points are plotted and average ascent rates are given as straight lines (average for the entire ascent, release to burst). Ascent rate vs. altitude curves are then collected in monthly charts (data for any flights in January and March is not available).

We can now look through these charts attempting to find characteristics that might be useful. I have noted a few interesting details that immediately come to mind.

EOSS-50 (April) achieved equilibrium and was floating when it burst. EOSS-49 and EOSS-50 flew at the same time from the same launch site but curves are very different below 35,000ft.

BEAR-1 appears to be approaching equilibrium and float state just before burst.

NSBG1-3, NSTAR-10D and TVNSP-01D flew at the same time from the same launch site.

ANSR-2 appears to have a much tighter data point plot than HABET-L49(?)

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