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In my world, one of the main methods of transportations is via hot-air balloon. These balloons are propelled by aluminum(or other lightweight metal, it doesn’t really matter) steam engines, and the steam and heat produced by the engines also serve as the fire that heats the air in the balloon. Would the heat produced by an engine that favors being lightweight over being efficient be enough to lift some amount of passengers and cargo? (The airship does not need to travel quickly; 3-4 mph is enough)

EDIT: Some stats: The balloons are spherical with a diameter of 20 feet. They are expected to carry up to 450 pounds of passengers/luggage, in addition to the engine.

Also, changing the atmosphere density is an acceptable last resort.

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  • $\begingroup$ How big are these balloons? What weight are they expected to carry? The expected size and load of these balloons are important details we'd need in order to answer the question properly. The smaller the balloon, the less lift capacity it will have and the hotter it must be inside the balloon for it to fly. $\endgroup$
    – overlord
    Commented Oct 9, 2019 at 16:45
  • $\begingroup$ Related question, but about airships instead of hot-air balloons: worldbuilding.stackexchange.com/q/127474/32016 $\endgroup$
    – F1Krazy
    Commented Oct 9, 2019 at 16:53
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    $\begingroup$ In addition to overlord's questions, when you say "same amount of passengers and cargo", are you asking about steam-heated balloons in comparison to modern hot air balloon which use propane burners to heat the air, or in comparison with hydrogen or helium filled balloons or dirigibles, or in comparison with other historical forms of balloon flight? The "Further milestones" section of that wiki article I linked mentions there was an early dirigible with a steam engine but it was "too slow to be effective". $\endgroup$
    – Hypnosifl
    Commented Oct 9, 2019 at 16:57
  • $\begingroup$ @F1Krazy yes, I looked at that question, but those airships were lifted by hydrogen rather than hot air. The premise of my question is if a steam engine could produce sufficient heat to lift the engine and passengers. $\endgroup$
    – Snorka
    Commented Oct 9, 2019 at 16:58
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    $\begingroup$ The air displaced by a spherical balloon with a diameter of 20 feet weighs about 220 pounds (100 kg). Before you can make that balloon lift 350 pounds + engine + water + fuel you must go back in time to the 3rd century BCE and kill Archimedes. $\endgroup$
    – AlexP
    Commented Oct 9, 2019 at 18:56

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You would not use steam as a lifting gas, for a number of reasons. First, you'd have to make the steam engine open-cycle, which means you'd have to carry lots of extra water. Second, the some of the steam would quickly condense on the surface of the balloon, removing any lift.

You could use a closed-cycle steam engine, with the condenser heating the air in the envelope, but this wouldn't be efficient.

A more reasonable design would be to have a closed-cycle steam engine for propulsion, having the condenser in the air stream, and using the exhaust from the engine to heat the air in the balloon. That is, if you think of a traditional steam locomotive, the exhaust from the smokestack heats the air in the balloon, while the steam driving the wheels instead turns a propellor.

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  • $\begingroup$ The water weight consideration is the reason I think this is the right answer $\endgroup$
    – Mathaddict
    Commented Oct 9, 2019 at 17:55
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    $\begingroup$ You can recycle the condensation, making the envelope double as the engine's condenser. Insulation can help control the rate of condensation. Steam as a lift gas has been thought of several times, but only recently has actually been experimented with: flyingkettle.com/index.html $\endgroup$ Commented Oct 11, 2019 at 10:40
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According to this Wikipedia article, the Union Pacific Big Boy locomotive, with tender car, was about 175 pounds per horsepower. Supposing that's not too far off, and supposing you only needed 10 horsepower to push this thing, you would need to carry about 1 ton of engine. You would need to factor in something about impeller blades, fuel, and water as well. So, using the numbers from Slarty's answer, you would need something like 130,000 cubic feet of balloon just to carry the engine. That's a 62 foot diamer balloon just for the engine, no cargo or passengers.

According to this web site relating to the Chester County Balloon Festival, hot air balloons range from 19,000 to 200,000 cubic feet. You would have about 1000 pounds left over with the very largest. So you would need something in the range of 70 foot diameter by 100 feet tall.

Steering a balloon is a challenge because the structure is just a big bag. You would need to put in some allowance for some kind of structure to the balloon. Supposing you changed over to some sort of dirigible. According to this web site on dirigibles, the weight of the dirigible is something in the range of 40 percent of the weight it can lift, using Helium. (Very rough figure.) So with hot air it will be less. So you would probably have to double the volume again to put in some kind of structure. But you could likely make quite good speeds with such a rig.

On the other hand, I have never heard of anybody operating a "hot air dirigible." So maybe there's some technical issue with such a thing that I have not thought of.

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According to this link, 65,000 cubic feet of hot air balloon can lift around 1000lb weight. The greater the volume the greater the potential lift, however there are problems with very large balloons in terms of stability.

The amount of heat that can be generated and its controllability might be an issue with a steam engine and a very slow moving hot air airship would be at the mercy of the wind, but in principle a steam engine could be used to provide both locomotive force and hot gas for the envelope.

However the balloon that you specify could not take off as it would not have sufficient lift. A 20 foot diameter balloon only has a volume of around 2300 cubic feet.

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Yes, it is perfectly possible, but you have to change the dimensions.

The steam engine will have to have a closed cycle, meaning steam exiting engine will be condensed and reused. The balloon will work as a condenser.

The buoyancy would be 0.4 kgm$^{-3}$, meaning that for a 200 kg cargo, the balloon would need to be 500m$^{3}$, not counting the weight of the balloon, engine, water, fuel, etc. This is 200 kg on the light side, which is probably space-age technology.

So, a balloon with 1000m$^{3}$, meaning a radius of 6.2 meters (~20 feet). That should work.

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  • $\begingroup$ Welcome to Worldbuilding SE! I've cleaned up some of your grammar, but this question could be greatly improved by adding more information on how you got the numbers you did. For example, you could include the equations you used so that the OP, who has more information on the requirements, can do their own calculations. Good luck! $\endgroup$ Commented Sep 3, 2021 at 2:03
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    $\begingroup$ The answer looks good apart from using superscript and things which I'll do in a moment but you really should provide sources for your data points so they can be reviewed and applied more generally by other users. $\endgroup$
    – Ash
    Commented Sep 3, 2021 at 2:06
  • $\begingroup$ Welcome Chris, take our tour and read-up in our help center about our ways, enjoy the site. $\endgroup$ Commented Sep 3, 2021 at 2:22

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