SN3
Your first paragraph is correct, but irrelevant. Yes glide ratio is also a function of speed and configuration. However if we considering best glide ratio which is close to how we fly a glide, so that can be assumed constant for a given design, it is also close to best rate of climb speed.
My thrust calculation is not wrong, unless there have been some fairly radical advances in physics since I took my degree.
It was was never meant to be accurate. Read it again and note that I said "the maximum thrust from perfect transmission" of the power. I was not assuming this would be achieved. Of course there are losses along the way, but as you point out these are not quantifiable. All we can do without further information is say that the thrust is less than a certain figure (it is common in physics to work out the constraints of a problem if you can't work out the exact answer, before making some esimates or experimental adjustments). I proved that the thrust is constrained to less than the figure required just to remain level. I never considered climb, as we certainly can't do so unless we can remain level. I am aware that rate of climb depends on excess power. I am also aware that angle of climb depends on excess thrust. I am also aware that to achieve either you need excess power and thrust.
By the way, I have ignored one or two factors. I know enough about the issue to judge that they make less difference than the inefficiencies in power to thrust transfer, and we are only making a ballpark calculation. If you know enough to challenge them, then we can discuss whether they are valid.
I calculated what lift was required to sustain level flight, not the power. For that the only information needed is the mass and 9.81 N/kg.
I was not confused by trying to calculate the limit to thrust (I wasn't trying to calculate actual thrust, we don't have enough information). It is the only way we can consider constraints to available lift. Power can only achieve lift through thrust.
Multiplying by three was correct. It does work that way. If lift:drag ratio is 3:1 then the weight that can be sustained in level flight is 3 times the thrust. Thrust equals drag in sustained flight, and lift is three times drag. That's what lift:drag ratio means.
I never suggested it needed three times the thrust to fly. Multiplying by three I was working from drag to lift, not the other way round.
Drag can indeed be determined from the glide ratio given a known weight. Glide ratio is identical to lift:drag ratio. In steady flight thrust=drag and lift=weight. Divide weight by glide ratio and you have the exact thrust required to sustain level flight. This always used to be taught in the ATPL theory, and I assume it still is.
Before you post again, I suggest you go into the books. Most of this discussion is beyond what a typical pilot would ever bother to learn. However denying that lift:drag and glide ratio are equal you have made an error that no ATPL student would, at least not one who was likely to pass the exams. It is one of the basic facts in the syllabus (I could prove it if you like, but diagrams are a pain here so I suggest you look it up). I don't expect a PPL to know necessarily, but if you're going to discuss aerodynamics at ATPL level then it's really necessary.
Where did you get the figures 6:1 and 3:1 anyway? As I said, they are not the figures I have found. The 14:1 comes directly from the manual of a retractable. The 7:1 was from the manual of an aircraft with lovely short wings, so poor glide performance (in fact I think it was 7.3:1). The rest come from various sources, less reliable but consistent. And anyway, think about a C152 in the glide, about 800 feet per minute at 70 kts as far as I recall from teaching in them. That's a bit less than 9:1 at a bit over ideal glide. The Warrior has a wing optimised for low speed, so it has a better glide ratio.
You now admit that the Katana has 14:1, not surprising from the sleek shape and long wings. Why would you assume that a typical light aircraft is so much worse as to give 6:1, and a poor one 3:1? I don't think you realise how that would affect performance, as you were unaware of the lift:drag ratio's relationship with glide ratio.