A reader asks this question: “I have a question about helium, lift and an idea I have. First, please assume an efficient design with little gas loss. Compressed helium is in a storage tank and connected to an deflated balloon. The gas is released into the balloon, inflating it to be full enough to provide lift to the attached empty (or partially full) tank, and the assembly floats up. Connected to this system is a battery-powered air compressor. Turned on, the compressor extracts the helium gas from the balloon causing deflation, and the gas is returned back into the tank. As the helium returns to the tank in compressed form, the assembly starts to float down. So… once again assuming this is an efficient assembly with relatively minor loss of gas, could this method be used to control the ascent and decent of the assembly?”
The short answer is yes. The more detailed explanation follows.
Archimedes’s principle, which states that the buoyant force on an object in a fluid equals the weight of the fluid displaced by the object, applies here.
What does this statement mean?
To start, scientists define a fluid as either a liquid or a gas, rather than the everyday use of the word fluid we use to mean a liquid. Hence the air around a helium-filled balloon is a fluid. That means Archimedes’s principle applies to balloons in air, as well as the more familiar idea we have of boats floating in water.
The buoyant force is an upward force that pushes an object suspended in a fluid upward. The object will also have a gravitational force equal to its weight pulling it downward. The object will accelerate in the direction of the greater force. That means if the object is heavier than the fluid it displaces, it will sink. Conversely, if the object weighs less than the fluid it displaces, it will move upwards, or if it is at the top of the fluid, it will float.
If an object is less dense than the fluid, the fluid it displaces will weigh more than the object. Hence the buoyant force will be greater than the object’s weight and the object will rise in the fluid or float on the top of the fluid.
If the object is more dense than the fluid, the reverse occurs. The fluid displaced weighs less than the object, the upward buoyant force is less than the downward gravitational force, and the object sinks.
As a result of Archimedes’s principle, an object will rise in a fluid if it is less dense than the fluid and sink in the fluid if it is more dense than the fluid.
Ascent and Descent
As the helium gas fills the balloon, the balloon becomes larger, and therefore displaces more air. Eventually the balloon can become large enough to displace an amount of air that weighs more than the total of the balloon and the apparatus described in the question.
Even though the pumping apparatus is much more dense than air, a large enough helium filled balloon can reduce the average density of the balloon and pumping apparatus to less than the density of air. When this happens, the buoyant force will become larger than the downward gravitational force on the balloon and apparatus.
The balloon will then begin to rise, as the balloon effectively floats on air.
Balloon Apparatus Limitations and Capabilities
The main limitation here is the fact that the apparatus described in the question is likely to be fairly heavy. Hence there must be enough helium, and the balloon must be large enough, to displace enough air to weigh more than the apparatus.
Pumping the helium gas from the balloon back into the storage tank reverses this process. The balloon and apparatus will therefore sink back down towards the ground as the questioner speculates will happen.
Air is thinner and less dense at higher altitudes. When the helium-filled balloon rises, it will rise to the altitude where the weight of the air displaced equals the weight of the balloon and apparatus. At this point the balloon will float at a stable altitude.
If a small additional amount of helium enters the balloon, the balloon will rise a small amount. If the pump returns some of the helium from the balloon to the storage tank, then the balloon will sink a small amount.
So, yes – one can control the height of the balloon by adjusting the amount of helium in either the balloon or storage tank.