When I read the Hobbit the first time when I was thirteen years old, I assumed the proportions in Tolkien's picture were correct, and measured that Smaug was at least 40 times as long as he was wide across his nostrils.
Since Smaug was unable to fit his head, mouth, and nostrils into the passageway with a doorway five feet tall, assuming that Smaug would twist his neck to fit his head in sidewise if possible, I deduced that Smaug was at least five feet wide through his nostrils and thus at least two hundred feet long.
Remember that even if Samug was as short as the 38 to 44 feet you suggest, he would still probably need a magical anti gravity power to fly anyway.
I have read a Tolkien letter where Tolkien wrote that in the picture he drew Bilbo several times larger than he was relative to Smaug, so that people would be able to see and notice Bilbo. Thus it is quite possible that Tolkien intended that Smaug be five or more times as long as you deduced by comparing Bilbo. So Ancalagon could be 3,600 feet or more long according to your first picture.
‘The hobbit in the picture of the gold-hoard, Chapter XII, is of course (apart from being fat in the wrong places) enormously too large. But (as my children, at any rate, understand) he is really in a separate picture or “plane” – being invisible to the dragon’ (The Letters of J.R.R. Tolkien, no. 27, c. March/April 1938, to Houghton Mifflin, the American publishers of The Hobbit).
Dwarf ladders would have rungs farther apart than Hobbit ladders and closer together than Human ladders. The ladder leaning against a huge jar of gold in the foreground can give a rough estimate of the size of the jar. The jars in the back beside the arch and the stairs should be the same size. Since Smaug is in between the two sets of jars he should be bigger than he looks compared to the closer jars and smaller than he looks compared to the farther jars.
The jars beside the arch, and the height of the steps inside the arch, should give clues to the dimensions of the space that Smaug should be able to get though when he enters and leaves his lair. Smaug's torso looks like it is about four times as wide as the width across his s nostrils, and thus about ten percent of his length. If Smaug can fold his wings really close to his body the space that Smaug should be able to squeeze through would be ten percent or less of Smaug's total length.
If the arch in the background is Smaug's entrance to his lair, estimates of its dimensions should provide an upper limit to Smaug's torso width and size.
How big was Lake town?
There was a South African play about a boxer called “King Kong” who used to boast: “King Kong bigger than Cape Town, King Kong knock any ape down”. If Smaug sometimes sang: “Smaug bigger than Lake Town, Smaug knock any city down” he would be only slightly exaggerating.
About a quarter of the people of Lake Town were killed in Smaug’s attack. Afterwards, a number of fighting men from Lake Town marched to Dale to try to gain some of Smaug’s treasure.
If there were 100 to 1,000 Lake Town warriors in that army and they were 0.05 to 0.15 of the total pre attack population of Lake Town, 666.66 to 20,000 people lived in Lake Town before Smaug’s attack.
If on the average there was 1000 square feet, or 92.9 square meters of Lake Town platform for each person that would be an area of 31.622 by 31.622 feet, or 9.638 meters by 9.638 meters. So 666.666 to 20,000 people would require a total platform area of 666,666 square feet, or 61,935.3 square meters, or 15.3 acres, or 6.193 hectares, to 20,000,000 square feet, or 1,858,060.9 square meters, or 459.136 acres, or 185.8 hectares, or 1.858 square kilometers.
If the Lake Town platform was square each side would be between 816.49 feet, or 248.866 meters, and 4,472 feet, or 1,363.0656 meters, or 1.363 kilometers, long.
Of course Lake Town might have been rectangular with two sides longer than the other two, or might have been irregular with all four sides of different lengths. In Tolkien’s drawing of Lake Town the two visible sides seem to be approximately the same length and quite straight.
On one website there is an argument about Smaug’s attack plan and how would he be “foiled”, as Tolkien wrote, by throwing down the bridge from the shore to Lake Town. Some people deny that there would be any sense in Smaug landing on the shore and walking across the bridge to the platform of Lake Town. They ask how he would squeeze through the narrow spaces between the buildings on Lake Town, since apparently they never watched The Beast from 20,000 fathoms, Godzilla, The Giant Behemoth, or Gorgo.
Tolkien wrote how Smaug destroyed Lake Town: “Full on the town he fell. His last throes splintered it to sparks and gledes. The lake roared in.” He doesn’t write that Smaug writhed around with gigantic convulsions for minutes like a ham actor doing a prolonged death scene, so Smaug’s last throes probably did not destroy a much larger part of Lake Town than what was smashed beneath Smaug when he fell on it.
Since Smaug was nearly as large as Lake Town, as shown when he fell on it and smashed it, and thus hundreds or thousands of feet long, Smaug would move around in Lake Town by simply stepping on and smashing all buildings in his way, or more likely he would avoid breaking through the platform of Lake Town by kicking those buildings to the side with his gigantic feet.
The market place of Lake Town was a circular harbor area perhaps hundreds of feet wide at the center of the Lake Town platform. It was probably Smaug’s plan to reach the harbor and put his front feet on one side and his back feet on the other side, lower his neck and his trail to the level of the platform, and turn in a circle as fast as he could around the market place, sweeping away and smashing hundreds of buildings and thousands of people in seconds.
But Smaug would have to adjust his magical anti gravity power to land on the shore and try walking across the bridge to Lake Town. Smaug would never trust his ability to fine tune his weight closely enough to land on the town and quickly adjust his weight to the correct amount. Smaug’s fear of breaking through the platform and falling into the lake would stop him from landing on Lake Town itself.
If that was Smaug’s original plan of attack, it would have been foiled by cutting the ropes and dropping the bridge from the shore to Lake Town into the water.
Of course, other people may suppose that Lake Town sent fewer than 100 warriors, or more than 1,000, to Dale and eventually the Battle of Five Armies, and some people may suppose that the army from Lake Town was more than 0.15, or less than 0.05, of the original population of Lake Town. And it is possible to estimate that the platform or deck of Lake Town had more, or less, than the 1,000 square feet, or 92.9 square meters, of area for each person that I guessed.
Thus it is possible to estimate that the surface area of Lake Town was much smaller or larger than I estimated. And Smaug, who smashed Lake Town by falling on it and then thrashing around for a short time, probably just a few seconds, could thus be much smaller or larger than implied by my figures, but certainly still gigantic!
Of course various artistic and narrative depictions of Lake Town, such as in the Rankin-Bass production of the Hobbit, or the Hobbit movies, might depict Lake Town as much smaller or larger than Tolkien’s evidence indicates. But those would be the sizes of Lake Town in those depictions, not the size of Lake Town in the book The Hobbit.
The brief accounts of the War of Wrath in various versions of the Silmarillion are the only clues to Ancalagon's appearance and size.
Except that Gandalf implied three different fire temperatures of dragons, which might be linked to their sizes, in The Fellowship of the Ring "The Shadow of the Past".
It has been said that dragon fire could melt and consume the Rings of Power, but there is not now any dragon left on earth in which the old fire is hot enough; nor was there ever any dragon, not even Ancalagon the Black, who could have harmed the One Ring, the ruling ring, for that was made by Sauron himself."
So that gives three temperatures of dragon fire, and perhaps body size ranges to go with temperature: the relatively cold ones then surviving, the hotter ones which could melt Rings of Power, and Ancalagon the Black.
Many people would assume that Smaug could have melted a Ring of Power and thus was one of the middle type, with Ancalagon one step above Smaug, but it is possible that Smaug was unable to melt a Ring of Power and thus was one of the coldest and smallest types, with Ancalagon two steps above him.
And I have always assumed the dimensions of Ancalagon the Black should be given not in feet or meters, but in kilometers and miles.