I really enjoyed reading this thought process; it is (was) a very creative and clever project proposal. My initial thought was, "controlling a combustible on a small scale...this guy has gone mad in all the right ways!", but then I did see your renewed approach using a lightbulb, or any other heating source, which I thought was clever. I wonder though, ignoring the lift-constraints and specific heat conversions, if you used a lighbulb, or heating element other than a combustible, would you achieve the same lift? I don't know anything about thermodynamics, but I am making the assumption that a combustible produces a more directional heat (eg. up), while other heating sources would produce a more radial heat. Without the upward "drive" created by a combustible, would you need more heat? Or would it simply take longer to achieve the lift?
Out of curiosity, did you weigh the Arduino and potential battery packs required? Do you think it is possible, even at large scale to produce a hot-air balloon using batteries as the power source? For instance, I'm guessing there is an equation for a lithium-ion battery that can provide available power output based on weight (roughly)? For example: (made up numbers here) a 500g lithium-ion batter is capable of producing 2000mAh of power, 2000mAh power can be converted into X-amount of heat using my heat source, which can achieve a maximum lift of 400g. I am mostly curious if the relationship is linear in that you would never be able to achieve enough lift regardless of heat source since the batteries output is never enough to overcome the weight of itself.
Also, what were you going to use as the altitude sensor? Does such a thing exist, or were you going to program a sonar sensor to compute the distance and adjust accordingly?
This is a great thought-provoking proposal. As you had mentioned, it is too bad you couldn't get it off the ground!
Hey Josh, good questions and points. You're right, there are differences in heating with an open flame and a mostly radiant source like a light bulb.
The flame heats the air immediately surrounding it (and the CO2 released by its own chemical reaction) in a process called conduction or diffusion, which then flows up due to the very buouncy forces we are investigating in a process called advection, then swirls around a bit in a chaotic fashion. Together, this is called natural convection. The flame also radiates heat with photons streaming out and being absorbed partially by the air it encounters and primarily by the balloon wall, at which point the heat is diffused or reflected back into the air inside the balloon, spread through to the outside of the balloon wall, and outside of the balloon.
The light bulb is a hot filament that does the same thing as the flame but in different proportions -- there is more radiation being emitted than convective. This means there is less "swirling" or mixing than with the flame.
Convection heats the air in the balloon more effectively than radiation, just like a convection oven cooks more evenly than those without forced air. Radiation from a light bulb heats objects better than air as it emits mostly infrared, which is not well absorbed by air (see Wikipedia: Infrared Window). This means it heats the surface of the bulb and the balloon material first, then the glass bulb and the material heats the air. Reflective material helps reflect heat back into the balloon. In the end, both methods heat the air in the balloon, but convection is more efficient.
The lifting effect of the initial upward draft from an open flame is cancelled out in a closed system (the rising air mass has an equal portion of lowering air), but it does allow placing the heating element below the heated chamber while maintaining high heat transfer ratios compared to the amount of heat that would escape with a radiative source in the same location.
Another practical consideration you mention is that a light bulb would need a lot of electrical energy, namely batteries. The maximum energy density of available batteries is around 0.5 kWh/kg or 1.2 kWh/L. By comparison, that of paraffin wax is around 12 kWh/kg (42 kJ/g) or 6.1 kWh/L, at least five times more energy dense. Without taking into account system efficiencies, a battery operated heater would require at least 5 times more fuel mass (batteries) than a paraffin wax heater (candle). Batteries could still be used, however, with a sufficiently small time scale (batteries die) and a sufficiently large volume of air. Although fuel weight (and volume) to energy output is linear, including batteries or paraffin wax, air volume to material weights is not, so scaling up the size does work. The only limiter is fuel suitability -- can you release and spread the energy quickly enough to heat the air? I leave this up to the hot air balloon pilots... :)
Cheers
I forgot about your other questions, whoops.
I did weigh the Arduino and estimated other componenets: SparkFun RedBoard (Arduino) with all SIK components 173g; balloon envelope 17.3g per square meter; and 50g for the frame, tea light, flame flue, and battery (I hadn't planned on using the battery to heat the air, only to power the microcontroller and flue). This was a high estimate for total weight.
Altitude sensor would have indeed been a sonar sensor.
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