Hot Air Balloon Descent: Does it Keep Accelerating Until Impact?

[frankcm]

If a hot air balloon cools enough to start descending, does it keep accelerating until it hits the ground? Assume that the air inside does not cool off anymore, and pretend that the air pressure stays the same at all altitudes. I tried testing it by dropping a coin into a pool. It didn't seem to accelerate but I think it might have reached terminal velocity from the water's "wind resistance".

 

[fresh_42]

I don't know the answer for it likely depends on the initial height and whether there is a function to influence the air resistance, e.g. a valve. However, there won't be an increasing acceleration. E.g. the Millikan experiment is based upon this.

You might want to read about the terminal velocity: https://en.wikipedia.org/wiki/Terminal_velocity

 

[David Lewis]

All other things equal, the balloon will become more buoyant as it descends because atmospheric density goes up as altitude decreases. So it's possible the balloon will accelerate (in the form of slowing down).

 

[jbriggs444]

All other things equal, the balloon will become more buoyant as it descends because atmospheric density goes up as altitude decreases. So it's possible the balloon will accelerate (in the form of slowing down).

The balloon is under ambient pressure regardless. Its density increases as well. A simple comparison of balloon initial density versus atmospheric density as a function of altitude will not yield a correct answer here.

As the balloon descends and is compressed under increased ambient pressure, it does not maintain its initial temperature. It is compressed in an adiabatic fashion and heats up. One might be tempted to think that this will cause it to gain increased buoyancy. But there is a complication. All things being equal, the atmosphere maintains a temperature differential of its own -- the adiabatic lapse rate.

But all of that is irrelevant. Look back at the initial post. We are asked to consider an atmosphere with constant pressure at all altitudes.

If there is air resistance, then fresh_42 nailed the answer. If there were no air resistance (an unrealistic atmosphere with no viscosity) then indeed, the balloon would accelerate downward until finally crashing into the ground

whether there is a function to influence the air resistance, e.g. a valve.

The controls in a hot air balloon are on the propane burner (heating) and on a vent at the top of the balloon (cooling). Neither of these has a significant effect on the huge air resistance of an inflated balloon.

 

[NTW]

I don't know the answer for it likely depends on the initial height and whether there is a function to influence the air resistance, e.g. a valve. However, there won't be an increasing acceleration. E.g. the Millikan experiment is based upon this.

You might want to read about the terminal velocity: https://en.wikipedia.org/wiki/Terminal_velocity

I'm not so sure... Millikan's drops were stable in mass and volume, but a descending hot-air balloon will probably lose volume and gain mass. That must result in a continually decreasing buoyancy. Hence, the speed will increase...