The losing side in any war exagerates the strength of its enemy. It also attributes its successes to the help of traitors from own ranks. If there were no traitors, they are invented.
The "history" of the siege and fall of Constantinople is a good example of it. There were a few written accounts of the surviving eyewitnesses. They not only exagerated the number of the Turkish troops but also invented the legend of the cannon founder Urban that created the bombard that smashed the walls of Constantinople. The legend is this:
There was a Hungarian cannon founder Urban (or Orban) that was seeking to sell his skills of creating enormous guns. (How could he possess such skills if he never created huge guns before is unclear.) He first offered his services to the Byzantine emperor in Constantinople. (Why in Constantinople? It was a poor city by then. Venice and Genoa were already much richer. Besides guns first appeared in Europe and spread to the East and it made more sense to offer his "skills" there. Or maybe the Europeans did not need enormous guns while his aspirations lied in creating specifically such guns? But why would Constantinople need them either? The only country that might needed them was that, which wanted to breach the hitherto unbreachable walls of Constantinople. Still he offered his "skills" to the city, which needed them least.) The Byzantine emperor hired him but paid a little. (Why would he pay him at all if such a gun was useless for Constantinople?) Then in search for a better pay and to fulfill his aspiration of building an enormous gun, Urban turned to the Turkish sultan dreaming of conquering Constantinople. The sultan hired him and Urban created such a gun in 3 month. (Is it not too fast for such a demanding R&D project? There should had been a lot of experimentation as the gun was several times bigger than any gun created before. I estimate that it should had taken years of trials and errors to build such a gun.) So, Urban fulfilled his aspiration and was generously rewarded, I guess, otherwise why did he go to the sultan? And then he got killed (either by explosion of his own gun as some "historians" assert, or was executed by the sultan, as other "historians" claim).
And how did all this become known if Turks had no written literature at the time and left no account of the siege of Constantinople and preparations to it? It became known to the authors of the Europeans' accounts from the Turkish defectors sneaked into Constantinople or from the Turkish prisoners of war taken by Constantinople's defenders!
The "history" of the siege and fall of Constantinople once again raises the question: what is history, a collection of tales or the firmly established facts? It appears to be a mixture of both where facts are in the minority. Regarding Constantinople just one is probably beyond the doubt. Namely, that it was taken on May 29, 1453.