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We know that the Romans invented or used simple machinery like waterwheels, crank mechanisms and even simple steam and atmospheric engines, as well as what we would recognize today as clockwork, but for a variety of reasons, the Romans never got beyond individual pieces of bespoke machinery for particular applications, and certainly never triggered an industrial revolution in the first century AD, or any time.

What I would like to know is, assuming no large scale discontinuities like civil wars or the fall of the Empire, would it be possible for the Romans to have built a simple flying machine at any time, and what circumstances would possibly allow this?

Edit to add: For clarification, could the Romans have developed a heavier than air flying machine either with the technology available after the first century AD or evolved form beyond that point?

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    $\begingroup$ What is your definition of simple flying machine? Does a balloon count? Must it be manned? $\endgroup$ – kingledion Dec 24 '17 at 4:49
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    $\begingroup$ I don't really understand what the question is. Are you asking if a flying machine could've been constructed with known roman technological capacities at a certain point in time? Or if romans could've evolved their tehnology enough for this, given certain circumstances? In the first case, you'd have to be more precise about what period of roman civilization you're refering to and in the second case, the question would not have a correct answer (predicting events in a alternating history is hard if not impossible) $\endgroup$ – user44285 Dec 24 '17 at 9:28
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    $\begingroup$ They could probably manage a hot air balloon. They have air, wicker, flame and materials strong enough for an envelope. They might have problems that their fuels have lower energy density than ours but they should be able to get airborne. $\endgroup$ – Bellerophon Dec 24 '17 at 9:52
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    $\begingroup$ They never would have actually gotten around to it because, assuming that culture and religion are maintained, no one would dare cross the line between the mortal and the immortal and risk incurring the wrath of gods. $\endgroup$ – Varad Mahashabde Dec 24 '17 at 20:31
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    $\begingroup$ If we relax the definition of "Romans" and allow for sufficient time, we can say that they already did. Spain, France, Italy and Romania are all splinters of the once mighty empire, they all speak badly mangled forms of Latin, and they all have aeronautical industries which are building heavier than air flying machines. (I don't know whether Belgium and Portugal are producing aircraft, sorry.) $\endgroup$ – AlexP Dec 26 '17 at 19:01
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According to answers to this question, the Romans could possibly have manufactured an early pulsejet, which may be strong enough for powered flight. The reason no-one did before the early XXe century is that to even think about it, they needed modern scientific advances.

However, assuming some genius inventor like Archimedes reproduce the jam-jar design discovery, with a nearly empty alcohol pot set on fire with a small hole on top, and dedicates enough time, resources and cleverness to study it further, it may be possible for someone in the Roman Empire to have access to empirically-developed pulsejet designs.

Wings would probably be bat-like and rather inefficient to our standards, so the pulsejet would have to bruteforce itself into the air. I suspect its performances would be bad, its autonomy terrible and the noise truly awful (though that last one may be an advantage in some contexts). Veteran pilots would probably be deaf and develop serious health problems due to vibrations, but I doubt that would stop the Roman Empire, given the benefits of even such a crude flying machine.

Comments evoke hot air balloons as another, simpler option. They would probably not have access to enough silk to use it, so the performances would not be as good. I suspect it wouldn't fly when air is too humid. Charcoal would probably be the fuel of choice, being relatively high energy-dense per mass. Still, even a clear-weather, tethered hot air balloon would give serious military benefits.

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Yes or probably, depending on your definition of machine.

Does anything that is artificial and able to stay airborne count? If so, the ancient chinese did it. From the wikipedia article on kites:

The kite has been claimed as the invention of the 5th-century BC Chinese philosophers Mozi (also Mo Di) and Lu Ban (also Gongshu Ban). By 549 AD paper kites were certainly being flown, as it was recorded that in that year a paper kite was used as a message for a rescue mission.

Even if a kite doesn't count, I believe they could have built a primitive hang glider. They certainly had materials for a prototype, such as silk and many kinds of wood. The reason they never did is probably because they lacked the science and the motive. The very idea for something like that was only thought as feasible in the western world around da Vinci's time, during the 1500's. It would take a handful more centuries before someone could actually build a workable one. But once again, romans were one-upped by ancient China:

The earliest forms of gliding had existed in China. By the end of the sixth century A.D., the Chinese had managed to build kites large and aerodynamic enough to sustain the weight of an average-sized person. It was only a matter of time before someone decided to simply remove the kite strings and see what happened.

(I love the last sentence for all the scientific spirit contained in it).

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