The Steam Walrus lurking in my brain
It should be noted that there are some questions among aviation historians regarding the Andrews' Aereon airships. As I understand, most of the primary sources are contemporary newspaper articles (and newspapers then often carried fanciful stories of progress in developing airships and airplanes). The account was popularized in a mass-market history of airships written by the journalist John Toland in in the 1950's or 1960s. Like many mass-market books written at that time, it is a well-written and very entertaining book based largely on secondary sources that is replete with inaccuracies and exaggerations to make the history more interesting.
To my knowledge, there are no official government records that would absolutely verify the supposed test flights for Lincoln ever really occurred.
Another problem with the story is that, if the unpowered Aereon worked as well as it did - and if was actually demonstrated for the President in the midst of a Civil War where aerial scouting would be of great value - why was the concept not further developed, since it supposedly provided dirigibility at least as effective as early Santos-Dumont airships in the early 1900's, entirely without a motor...
You might well be right--I suppose it's possible the whole story of the amazing Aereon was exaggerated or even had parts made from whole cloth. I frankly have never considered this.
But one reason I accepted it was that the physical mechanism whereby such a craft can work is pretty straightforward. Airships in practice rely on dynamic lift all the time; it's how they can keep a course in a side wind, how they can stay airborne when heavier than their gas lift alone can support; how they can avoid rising uncontrollably up to pressure height when lighter. The USS Akron and Macon, the aircraft carrier naval scout rigids that were nearly as big as the Hindenburg, often flew as much as ten tons overweight (their static lift being somewhat less than 200 tons). Clearly the mechanism can be reversed, and a static imbalance can be leveraged into thrust.
But I wouldn't expect much thrust! It's all very well for maneuvering in light winds; they could hardly prevail against a strong headwind. (To be fair, neither, sometimes, could even such big and powerful ships as Akron or Macon!

) Then too the range would be rather limited; an aerostat might possibly be designed to rise to say 10,000 feet, 3 kilometers--to do so you have to either vent a quarter of the lifting gas you started with at sea level or start out with less than 75 percent full to allow for such a pressure height. (A ship that starts out full has a pressure height of zero; it needs to begin valving gas immediately, or else the pressure of the gas will burst the necessarily light structure, however that structure is laid out). Actually airships, and still more balloons, have risen a lot higher than that--I threw that height out because that's the altitude where human beings start to suffer from low air density and pressure. Press on much above that height without supplemental oxygen or pressurized living spaces and more and more people would start to suffer various problems; much higher than 3 kilometers and everyone begins to suffer from the insidious effects of anoxia. Some people are acclimated and won't, that low, but everyone has a limit. And beyond that limit, as with drunkenness one of the first things to go is judgement, so people are quite likely to get far into the danger zone before they realize they have a problem, and by then their ability to solve it is seriously impaired...so it doesn't pay to make an unpressurized vessel go a whole lot higher than 3 kilometers.
But 3, 5, whatever--clearly an Aereon type system can only take you so far before you have to vent whatever excess lift you have left and begin the sinking leg of the trip. Then you have the same limit, where you better drop ballast or else hit the ground. I can't see these iterations taking a craft much more than say 100 miles, in good weather, and doing so involves loading the craft up with lots of extra lift gas and lots of ballast--much more than the payload I'm guessing.
I do know that there have been thermal (i.e. hot air) balloons that have attempted to exploit the same principle; I don't know with what success. It looks like getting something for nothing, but of course a hot air (or steam) craft is using fuel to heat the air or steam, and a hydrogen version like Andrews's is using hydrogen that has to be synthesized at some trouble and expense, and casting these resources literally to the winds.
I think that designing a craft to use it to advantage at opportunity would on one hand be better than no powered propellors at all (or, given 19th century limits on power/weight ratios, practically none), and on the other help out a craft that has marginally adequate prop/engine systems.
Once the latter were available, serious inventors tended to focus on them and the Aereon approach was pretty much relegated to a stunt.
One reason I've been thinking of Andrews, and the relation of thrust to dynamic lift in general, is that this thread has revived a sleeping monster in my brain, the cargo airship that uses a significant amount of steam for variable lift. The steam volume can be used much more efficiently if it is not necessary to vent the steam, but rather it could be condensed and converted to ballast.(Here, my concept is, an airship whose fixed weight is borne by helium, nearly as efficient as hydrogen and much safer, and hopefully we never have to vent any helium, while the cargo and perhaps fuel weight is borne--partially, I'm hoping--by steam). Then, if that were practical, a much smaller steam volume suffices to leverage a given payload.
At sea level for instance, if we have steam kept at just boiling temperature (as would happen if there were any liquid water in the cell, because it would stabilize the temperature of both phases at the transition temperature) of 373 degrees Kelvin, in air of a nominal standard temperature of 288 K, then the steam, whose molecules already mass significantly less than air--18 AMU versus air's average around 28.8--is further lowered in density by being hot, so a cubic meter of steam would mass 48 percent what air does, or 590 grams versus air's 1225 grams, and thus that 590 grams of water vapor lifts 634 grams of load. So one kilogram of steam by mass lifts 1.07 kg of payload--if we plan on simply venting it.
But if we can take the time to condense that steam, then--there are several ways of looking at it--condensing a cubic meter of steam draws in 1.225 kg of air that wasn't in the system before. Or, if we condense a kilogram of water and keep it aboard we need to lift it with helium, and meanwhile we've lost another 1.07 kg of static lift--since that kg of steam formerly occupied 1.7 cubic meters and the air that fills it masses 2.07 kg we see the numbers come out the same. Bottom line, if you have any substance that you can shift between a gaseous and condensed state, you change the lift by 1.225 kg for every cubic meter you fill or vacate. So to lift say 1000 tons of cargo with steam you plan to vent, you need to vaporize 933,000 kg of water--then dump it overboard, and at sea level that steam occupies 1,577,666 cubic meters approximately. (If you want to do this at greater altitudes, actually steam becomes somewhat more effective there, so you need somewhat less water, but still the volume you need to set aside is much greater due to the lower pressure). But if we can expect to conserve the steam and store it as liquid ballast, then we only need 816,326 cubic meters at sea level, massing 482,573 kg. That steam itself only lifts a bit over half the cargo's weight, the rest of the cargo is lifted by the fixed lift of helium--but the weight of the water ballasts that helium when we condense it, so the ship can be brought into balance without venting anything but heat. (And we only need to design in half the volume for steam we would otherwise need!)
The trouble is, it takes a remarkably long time to condense steam!
One might wonder, why I am even talking about such extravagantly huge cargo masses as 1000 tons! Well, there was a grandiose project, or conceptual contest, put out by the Department of Defense and called "Walrus" in the early 2000s, when I was participating in a listserv devoted to airships. The challenge was to come up with a way to deliver IIRC 1000 tons of cargo to an unprepared forward site (presumably in a combat, or at any rate only barely and recently controlled, zone) without imposing on the recipients in any way. Taking on water or sand ballast (or any sort of ballast the ship could not provide itself directly, in any environment) was ruled out explicitly. This is the context in which I was thinking of how to create 1000 tons variable lift! I'm once again trying to work out, if say 150 tons can reasonably be borne on an airships propellors (turned mostly upward, with a reserve of thrust forward to maintain a modest airspeed until arriving at the destination), can the ship afford to retain 850 tons of lift until there is time to condense the steam? I figure such a static-lift steam Walrus might be designed to cruise at say 5 kilometers, at which altitude air density is about 60 percent surface densities (and temperatures about 40 Celsius lower than on the surface!) and its all-up mass might be in the ballpark of say 3000 tons (with payload, 2000 once that is dropped off) so the question is, how low a rate of climb can the ship parley 800+ tons of lift into, can it buy itself time to condense the steam before exceeding that pressure height? Bearing in mind that as it condenses the excess lift will be dropping off, I think maybe it can be done.
But Tom Goodey and others could not figure out why I couldn't just reconcile myself to simply venting 1000 tons worth of steam lift upon cargo drop, problem solved. Elegance, that's why! I liked the idea of the more compact ship you could get with recondensing the steam, and the idea that it stands ready to once again boil the steam and lift another cargo, and so on--truly variable lift.
The other sticking point is, while Tom Goodey empirically learned that a square meter of his small steam balloon in a workshop condensed about 1.4 kilograms of water per meter of its surface area per hour, nobody really knows how that rate will respond to radically different ambient temperatures (desert conditions, or arctic) nor to substantially different air densities, nor to forced drafts. Trying to solve these problems is a brick wall I've battered my head on a lot!
But for now, I'd be happy to work out just how low a rate of climb 800 tons of lift or so could be limited to in such a big airship (I'm thinking, 840 meters long, 140 wide); whether one needs to add some wings on the sides to tip the odds in its favor (rather not if they can be avoided, but last time my mind went down this track I was figuring on quarter-circle wings about the same radius as the hull itself, thus doubling the greatest width--they can also provide a lot of area in a cool slipstream for faster steam condensation for what that's worth), how much lift helicopter-type rotors that can be swiveled forward to serve as big props can reasonably be expected to offer, and so on. As I say, if we can take a huge unbalanced lift and lower it by condensation before hitting the upper limit of pressure height, then we never need to actually vent and thus lose the steam, and a significant portion of the payload would actually be lifted by helium instead, helium later ballasted by the condensed steam.
So I'm looking at the other side of Andrews's problem--he wanted to get forward motion from unbalanced lift, I want to mitigate the unwanted consequences of unbalanced lift to buy time to balance it.