I think the Wright brothers had a significant conceptual breakthrough. Most aviation pioneers had though of traveling through the air as the equivalent of traveling on water. They saw lift and steering as two distinct operations. They saw the purpose of lift as keeping the plane up in the air but they visualized its movement as level - the way a boat would travel on the surface of a body of water. So by analogy, they visualized steering systems that worked with some equivalent of a rudder, which is not an efficient way to steer an airplane.
The Wright brothers saw that you could use lift to steer. Traveling through the air is three-dimensional unlike two-dimensional boat travel. They realized if you tilted a plane off the level, the lift would then effectively become movement to the left or right rather than just up and down.
It’s been speculated that the Wrights, being bicycle mechanics, saw an analogy in the way a bicycle is turned: you first tilt it off vertical, then the “banked” cycle turns itself. AFAIK, nothing in their (rather extensive) writing proves this, but it makes sense.
The Wright brothers, yes started with a wind tunnel to find that the literature they relied on about wing lift was wrong - and so they produced appropriately shaped airfoils through experimentation. They developed wing-warping for flight control. In fact they built a dynamically unstable aircraft - I saw a movie taken from a Wright Flyer doing a demonstration flight in France around 1908 (Saw it in Bell Labs, no less). The lecturer pointed out that you could see the horizon going up and down as the pilot constantly adjusted the canard trying to get level flight.
They then proceeded to sit on their patents and stifle competition - to the point where while Europe - immune from Wright lawsuits - had a flourishing aviation business.
I’m not sure banking into a turn was such a major innovation since it would have been apparent in not just bicycles, but other vehicles, ships, even people running. What was innovative would be the eventual discovery of the explanation for spins in slow banked turns.
Which is why the first Montgolfier balloon had a smoke generator instead of a hot-air generator. Montgolfier thought it was the “smoke” that rose, so he built a burner that generated a lot of “smoke”.
Hot-air balloons came first, with the Montgolfieres. IIRC these balloons burned straw in a brazier to stay aloft. Not many years later, balloonists switched over to gas balloons which were superior in almost every way.
I agree that the best strength-to-weight ratio is what you want, but I’m not sure I agree that what will work for a 1-m balloon will work for a 25-m balloon. ISTM that the top of the balloon is supported by the bouyant force of the air inside the balloon, but the side walls and bottom of the balloon are hanging from the top; at some point it seems that the weight of the bottom half of the balloon would exceed the tensile strength of the material.
I don’t know how to figure out what the tension forces are on the different parts of the balloon envelope, especially since the balloon is not a closed pressurized sphere.
My physics knowledge isn’t that advanced (I have no formal training after high school) but I assume this is the same “square-cube law” that makes it difficult for things to stay structurally sound as they get larger. Except in this case, since the volume of the balloon is lighter than air and providing lift rather than pulling down it works to your benefit.
But the number of threads increases linearly with increasing radius, while the weight of the dependent material increases as the square (because it’s determined by surface area).
Another way of thinking about it: for a given thread at the equator of the balloon, the weight it must support goes up linearly with increasing balloon radius, but the thread strength remains constant. At some point the weight is too much, and the thread snaps.
Silk may well be strong enough to work for all practical balloon sizes (ie you can’t heat a balloon so big that it rips under its own weight) but the scaling issues are still real.
If there’s any material that will work for balloons, then silk will, since silk has a better strength-to-weight ratio than the vast majority of fibers. It’s certainly better than paper. If you can afford enough of it.
In the Roman era, a yard of silk could cost as much as a year’s pay for a soldier, or a quarter of an ounce of gold. So the silk for a hot air balloon would cost about as much as paying 1500-2000 soldiers for a year. In that era, that was a lot of money to spend on wild hairs. And just acquiring that much silk would have been difficult.
Actually, I got the numbers wrong, and missed the edit window. A good example of the price of silk in the ancient era was the Edict of Diocletian, or the edict on prices, which set the price of a pound of silk to be equal to a quarter pound of gold. So in today’s prices, that’s more like $20,000 per pound. A modern hot air balloon envelope weighs about 250 lbs, so if a similar one could hav been made in the ancient world, the equivalent cost would be about $5 million dollars. GDP in that era was about $570 per capita, so the silk for a hot air balloon would cost the equivalent of 8771 annual average salaries.
That sounds a little expensive for playing around with balloons.
People tried repeatedly in myth and reality for millennia to fly by imitating birds. Taking flight with the use of a balloon would only occur to those who had seen very small hot air balloons, and the few who considered a larger human carrying device rapidly were disabused of the notion. I doubt anyone ever plunged to death from a burning balloon, or even burned up on the ground because it was such a large enough and complex enough task. I think it’s perfectly reasonable that human flight in hot air balloons did not occur until the Industrial Revolution was well underway.
There were medieval kings and emperors who had tapestries and tents made out of silk. Sure they were expensive - but showing off their wealth was the point they were making. It’s the same reason they spent fortunes building places and monuments. Spending the equivalent of five million dollars on a status symbol is the kind of thing people do.
Once again, I don’t see how this is plausible. As you note, people have long dreamed of flying. And they looked for inspiration in natural things that they could see flying like birds. So why not be inspired by seeing smoke going up in the air?
I don’t see any reason to assume that people suddenly became more intelligent in the eighteenth century.
Instead of assuming that the price of silk in ancient times was the same as it is today, as Little Nemo did, you are assuming that the price of gold in ancient times was the same the price of gold today - but the one assumption is just as false as the other.
As for the supposed GDP in the 3rd century… :rolleyes:
There is no way to make meaningful conversions between ancient and modern prices, because a) the relative prices of goods were very different, b) the structure of society, and c) the whole economy were very different. The problem with calculating GDP in the past has been discussed at length in another thread.