Science behind religious things are off topic here. But to clarify certain things you mentioned in the question, I am answering your post.
I can't say about the science behind such an aircraft, but I can say that crafts like those were not completely mechanical. Modern scientists forget to take into account spiritual powers. There are two kinds of science, spiritual which is based upon the existence of spirit, and material, which is based upon the existence of subatomic particles. So such aircrafts must have made use of spiritual power through the usage of mantra, yantra, etc.
Now why no one wrote down the technology behind it could be because such aircrafts were not the norm like we see on airplanes today. Those were used by gods and didn't belong to earth. For example, Ravan got the airplane from Kubera (VRM - 6.121.9), which was made by Viswakarma for Brahma. Similarly, there is another instance in the Bhagavatam where Śālva obtains such a fighter aircraft as a boon from Lord Shiva.
The great Lord Umāpati is known as “he who is quickly
pleased,” yet only at the end of a year did he gratify Śālva, who had
approached him for shelter, by offering him a choice of benedictions. [SB - 10.76.5]
Śālva chose a vehicle that could be destroyed by neither
demigods, demons, humans, Gandharvas, Uragas nor Rākṣasas, that could
travel anywhere he wished to go, and that would terrify the Vṛṣṇis. [SB - 10.76.6]
Lord Śiva said, “So be it.” On his order, Maya Dānava, who conquers his enemies’ cities, constructed a flying iron city named
Saubha and presented it to Śālva. [SB - 10.76.57]
This unassailable vehicle was filled with darkness and could go anywhere. Upon obtaining
it, Śālva went to Dvārakā, remembering the Vṛṣṇis’ enmity toward him. [SB - 10.76.8]
So because those were divine objects and not a norm in the world, nobody probably wrote it down. It is also another fact that retaining knowledge in memory was the norm in the ancient times rather than keeping a written record of it.
However, irrespective of its authenticity we do have a Vaimanika Shastra written down in earlier part of the twentieth century. As per the writer, he obtained the knowledge from sage Bharadwaja. On a side note, it is worth noting that Shri Rama on his way to Ayodhya on the Pushpaka Vimana took a halt at Rishi Bharadwaja's hermitage. To be frank, whatever actual science was behind such crafts was probably known only to the gods and the sages. We modern day people can only speculate it must have been like this, it must have been like that, etc. without taking spiritual power into account.