Flight. How can a plane fly when it's thrust to weight ratio is less than one? It's like, if you can produce 10 pounds of thrust, who would look at that and say "ah ha, we can use this to keep a 100 pound machine miles in the air indefinitely"?
I understand flight from a mathematical point of view. I've actually read a few books on the subject, and I could explain how flight works to someone. However, I'm still fishing for an explanation that "feels" more satisfying though. Per the question, I still want it explained better.
Consider the vectors of the four forces (thrust, drag, lift, weight). The thrust only needs to equal the drag at a given airspeed, not the weight of the vehicle. (Unless it's climbing vertically.) The weight is countered by the lift generated by the wings, which, given the efficiency of airfoils, is very more or less why it all works: they produce a positive lift-to-drag ratio.
Put another way, weight pulls it down, thrust moves it forward, the resultant lift keeps it up, and drag limits its speed. Only rocketeers and fighter/aerobatic pilots need to really worry about the thrust to weight ratio as a constraining factor, because the vertical flight regime matters to them. From your average bugsmasher to your commercial airliner, it's not a factor (to the disappointment of pilots everywhere).
Consider that a Cessna 172 has a glide ratio of about 9:1, so it can go 9 units forward for every 9 of altitude it gives up. If that's hard to intuitively grasp, consider that it's traveling through a fluid. Surfing, even. The interaction with that fluid is why it works.
The 10 pounds trust is used to overcome the airodynamic friction, when the plane is in high speed. Because the "way" around the wing is longer on one side compared to the other this create a lower pressure on one side, and higher on the other. This pressure both lift and push the plane up. If there was zero friction you would hold the plane up with zero thrust ;)
The problem with this description is that you don't need a fancy shaped wing to fly, a flat board will work. Aerofoils provide better efficiency but are not required.
I did, but if I use an extremely thin wing with zero aerofoil (a wing made out of credit-cards or flat balsa wood for example), one "way" around the wing is not longer. Why would pressure be different on the top vs. bottom of this flat wing?
Think of it like a wedge. 10 pounds force on the back of a wedge can easily cause 100 pounds force perpendicular to it.
But there is a tradeoff between force and displacement. Larger force = smaller displacement.
Same with a wing. The thrust force is lower than the lift force, but the horizontal displacement (velocity) of the wing is much greater than the vertical displacement (velocity) of the deflected air.
i.e. small force x large velocity = large force x small velocity
Many descriptions of flight focus on pressure differentials. I think it's much easier to think about in terms of Newton's 3rd law. The plane simply needs to redirect enough air downward to compensate for its weight. The energy cost change the direction of the air (via the wing) is very low (similar to how a train does not lose much speed when the tracks curve).
I understand flight from a mathematical point of view. I've actually read a few books on the subject, and I could explain how flight works to someone. However, I'm still fishing for an explanation that "feels" more satisfying though. Per the question, I still want it explained better.
EDIT: There's already a thread about flight. I asked the same question there, but phrased a bit differently: https://news.ycombinator.com/item?id=22993460