To know how much a balloon can climb first we need to understand where it is climbing: The atmosphere.
There are many points of view to describe the Atmosphere, its layers, etc... So let's use a simple model known as the ISA model.
ISA = International Standard Atmosphere.
The ISA model is the one used in aeronautics and I think it will give us a simple image of the way to follow the Rockoon during the ascent beyond 100 km of altitude.
The Trosposphere is the zone with the highest traffic density of all. It is also where practically all the humidity of the atmosphere is found, that implies that it is where practically all the atmospheric phenomenas develop.
It is highly recommended to avoid the Troposphere, used only for transit purposes.
Now the question is, how can I avoid the Troposphere? Flying over it of course! and how can I do it? Lets see:
In case of a balloon, knowing the maximum volume, the weight of a balloon and its payload we can find out how to reach the point is know as Apogee.
Now we are going to calculate the theoretical apogee ...remember I've said theoretical.
First we need to know the Temperature and Pressure, this two values are changing during the balloon climb.
The temperature in ISA atmosphere starts at Sea level at 15ºC and falls linearly until -56.46 ºC. We are able to know the decrease in temperature using the formula
Temp in celsius = 15 - (altitude in meters *0.0065)
At 11km altitude the temp is - 56.46ºC and then it keeps constant until the 20km or 25km depending the sources, after that rises linearly again until the Stratopause.
An approximate formula ( I use 20 km that is why is 20000 in the formula)
Temp in celsius = -56.5 + ((altitude in meters - 20000) * 0.001)
The temperature stops increasing at Stratopause and falls again in mesosphere and increases again in thermosphere.
Pressure never rise again but decreases in an exponential formula.
There are many websites in internet where you can find the formula of Pressure but I prefer to find altitude knowing the pressure. This formula relates each altitude at a given pressure.
Altitude = 8430.153 * LogN (1013.25/pressure))/(1+(0.095*LogN(1013,25/pressure))
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