Hot Air Balloon Time Aloft
Date: Spring 2012
My student is doing a science experiment to see if the size of a balloon (dry cleaner bags) has an affect on its flying time (being heated by a toaster with a cardboard colander over it). She has her results which support her hypothesis which shows that the larger the bag the longer it stayed afloat. Is this in line with Archemedes principal? she is wanting to do a write up to show what principal she proved but it seems complicated with density, gravity and displacement theories coinciding. she is in grade 3 so I want to keep it to this level for her.
This is a very complex concept - especially for a 3rd grader. Not only, as you suggested, is the principle of buoyancy important in this experiment (the larger the bag, the more displaced air there is), but there are other equally important concepts in play here as well. The length of time that the bag stays afloat likely depends on the air in the bag staying warm, so ideas such as: (a) the more air in the bag, the higher its heat capacity; (b) the more air in the bag, the longer for the warm air takes to diffuse out of the bag, (c) the more air in the bag, the more energy has been transferred to the bag during the heating process, (d) did she cut the bag to make it smaller? - if so, then we are also dealing with a confounding issue of the larger the bag, the more mass there is to lift, and this would actually limit the float time, etc.
Perhaps you can walk her through the different effects of mass, energy, volume, diffusion, etc. with her and then suggest further experiments that would remove other effects (make them constant) so that she can narrow down the experimental result to only one or two factors. For example, the mass of the object can be made constant by not cutting up the bag but simply tying off a portion of it so that the bags still have the same mass but can have different volumes. The amount of energy transferred to the bag can be analyzed by using the same sized bag, but vary the heating times. The diffusion out of the bag as a factor can be reduced by tying up the bags quickly after heating (you would still have to deal with effusion problems though).
Maybe this is an opportunity to discuss multivariable problems with your students and designing experiments to limit the effective factors?
There is also a safety concern here - I understand that the student has already done the experiment - but heating a dry cleaner bag with a toaster could easily lead to melting of the bag and the possibility of hot plastic sticking to children's skin. Using a toaster with a cardboard(!) colander over it is risking the cardboard catching on fire. I would strongly suggest that you talk to your students about safety issues.
Greg (Roberto Gregorius)
Archemedes’s principle just says that something is buoyed up by a force equal to the weight of surrounding fluid displaced. The size of the bag does not directly influence whether or not it will float; a bigger bag means that it displaces more surrounding air, but also that it has more weight of its own.
Two factors that you may wish to consider are
1. The weight of the bag and the weight of the air it contains both need to be overcome by this buoyancy in order for the bag to float. If a large bag contains twice as much hot air as a small bag does, it still may not weight twice as much as the small bag on its own.
2. Large and small bags may not cool off at the same rate. You might want to check how the temperature of the air inside the bags change over time.
Richard E. Barrans Jr., Ph.D., M.Ed.
Department of Physics and Astronomy
University of Wyoming
What is going on is simple but exactly why it happens is a bit more complex.
Some basic statements:
The reason the bags rise is that the warm air is lighter than the surrounding cooler air.
As long as it stays warmer than the outside, air in the bag will experience buoyancy, that is it will try to rise.
How long this goes on depends upon how fast the bag’s air cools.
The bag’s air cools by giving off heat to the outside through the plastic bag so, the rate of cooling depends upon the bag’s surface area.
The amount of heat in the bag depends upon the amount of air in the bag (volume).
Without getting into the math, and simplifying things a bit, if you double the diameter of the balloon, it loses heat 4 times faster. BUT there is 8 times more air than before!! So the larger balloon will stay warmer longer!
This relationship, I have seen it referred to as the square/cube law works on far more things than balloons. Elephants have very little surface area for their volume and would overheat quickly if not for those gigantic ears! They are super big radiators. Animals, and humans that live in the arctic tend to be rounder than those in hotter climates because they want to avoid heat loss to the environment.
I hope that helps and if I can be of more help, please write me directly.
R. W. Avakian
Click here to return to the General Topics Archives
Update: June 2012