I'm trying to calculate the acceleration of a high altitude balloon at different altitudes. In excel I've got the temperature, air pressure, and air density for a given altitude (thanks to NASA). Right now I am calculating the net force on the balloon with: F_{net}= F_{b}-F_{m} F_{b} = Buoyant force = density of air*volume*9.81 F_{m}= (mass of balloon+mass of payload+(volume*density of helium))*9.81 For whatever volume I put in for the balloon I only get a positive net force until about 55,000 feet. I'm thinking it is because I am not taking into account the increase of air that will be displaced by the balloon as it gets higher and higher, but im not sure how to model that mathematically. Any insight as to how to do this would be appreciated.
Isn't the buoyant force: density of air*volume*9.81 ? High altitude balloons will start out partially filled, so their volume will increase. What won't increase is the mass of the helium used. F_m will be a constant unless you let out helium
Yes it is. I guess I wasn't paying attention when I was typing that in. Its been fixed in the original post. I'm aware that the volume of the balloon will increase as it climbs which is my problem since the amount of air displaced will also increase. I just don't know how to model the change of volume. As for the helium, the mass of the helium in my excel sheet is constant (it uses the initial volume of the balloon)
Im using these equations: http://www.grc.nasa.gov/WWW/K-12/airplane/atmosmet.html I'm still getting a constant buoyant force for some reason. If someone could take a look at my excel sheet that would be great. The ideal gas law is being used to calculate the baloons volume at different altitudes. thank you
At very high altitudes, the strength of gravity will be a bit less. Eventually it's mostly helimum and hydrogen at the outer edges of the atmosphere without any of the heavier elements.
Yes, these a minor effects. But at some point the balloon is fully inflated, so it cannot reduce its density to float into less dense regions.
But if it was constant than its acceleration would be constant so it would be going close to 300 m/s at a certain altitude. This of course is without the drag force accounted for.