Totally useless thought, but did the technology and materials exist in ancient Rome for some clever Roman to have built a functioning hot air balloon? They had canvases and cloth, but did the technology exist to make them air-tight enough, without making them too heavy, so that they could lift a man in a basket?
No China:
But the man in the basket didn’t come until Europe in 1783
Yes. Hot air balloon material doesn’t have to be all that airtight, but it helps. They could have treated fine linen with oil or pitch to do it, or just use enough untreated cloth. Maintaining the heat with the fuel available at the time would make it difficult to have a long or controlled flight, not that you have that much control anyway. At least they wouldn’t hit any power lines. Just getting enough hot air into the balloon to lift it’s own weight would be difficult. Even knowing that a small bag of hot air rises might not convince them to try to lift a man, the size of any balloon that big would seem daunting to construct.
Funnily enough I was discussing something like this with my father in law yesterday, he’s a qualified and experienced balloon pilot amongst other things.
He mentioned that ballooning as we know it certainly seems to have started with the Montgolfier brothers, but it ceased to a “thing” until the late 1960s. The reason wasn’t the materials for making the balloon, it was because it was only then that compressed propane for heating the air became realistically available. Prior to that, heating had to be with normal methods (eg wood) which required a huge amount of material (note the Montgolfier balloon was tethered over a bonfire) or through petrol, which was very dangerous. However, once propane burners in small sizes became available the floodgates opened. YMMV.
The flammability of such material makes the thought make my hair stand on end.
“Let’s build a fire-powered vehicle out of CANDLE WICKS!”
The OP didn’t ask if it was a good idea.
The OP also didn’t ask whether the passengers had to survive until landing.
Actually, the OP didn’t even ask whether the man had to start the flight alive.
Up and down alive, 100 ft in the air, and travel at least 2 miles. If the Romans put all their resources to it, could it be done with the stuff they had. Don’t care if they had to build a huge scaffold to keep the balloon away from the flames, then the scaffold could be pulled away by hundreds of slaves once the balloon was inflated (slaves could die).
I would say it is possible if they had the will and basic knowledge. Hot air balloons are very low-tech. If the Romans could build complex engineering project like aqueducts, they could certainly make a hot air balloon big enough to carry one or more people.
Once you have the idea figured out, all it takes is a whole lot of tightly woven cloth, a large basket and a burner. The first two are just very labor intensive but they had the technology to make those. The burner is harder but your specified requirements aren’t very difficult. I would use fires well away from the balloon to do the initial inflation. You could send hot air into the balloon through a system of ducts and simple manual air pumps. Maintaining the hot air inflation is harder but this is a one-off attempt and doesn’t have to be that efficient. A fire-proof chamber fueled by coal and/or wood should be provide enough heat for a little while at least. Again, you might need simple manual air pumps like bellows to force the hot air into the balloon but manpower isn’t an issue.
If Romans could build fairly large ships, simple hot air balloons should be fairly easy by comparison as long as they understood the basic principles.
The problem is they didn’t, at least at the beginning. They thought it was the smoke that made them rise, not the hot air that was causing the smoke to rise.
With modern lightweight fabric, the smallest hopper (just a seat, no basket) balloons are approx 30,000 cubic feet. Heavier fabrics from ancient times would require even larger envelopes to get off the ground.
Actually I think oil would be the fuel to which Romans would have had access and which has a higher energy density.
It certainly could have been done, it’s very low tech. They would have to know how to control descent with a flap to open at the top or they’re not landing alive. Their ability to travel 2 miles depends on that flap, a decent heat source, and wind. They’ll have to exceed 100 feet to do it reasonably which means they need to control the heat during descent. Failure is likely, but it could be done.
A 10MPH wind will get them there in 12 minutes, if they can fill the envelope with hot enough air to start they’ll shoot up well over 100 feet rapidly, and then it’s just a matter of balancing the release of hot air from the top with just enough additional heat to keep from crashing.
As already stated, this is so tricky that hot air balloons weren’t used much for close to a century after the first hot air flight.