Hi all,
As an ancient, I'm enjoying this, so I'll have to do some scribbling and calculating and posting this weekend to compose a proper answer!
Rainboe, welcome!
"total lift balances total mass"
Sure, but you forget again to define "total lift".
Your "total lift" points straight up during a steady climb (or it wouldn't be steady).
So your wing will have to produce an additional force perpendicular to the airstream.... it doesn't "know" it's climbing.
And with the wing providing typically ten times as much lift as the engine thrust (ballpark figure, obviously) it's the wing which will provide the additional force to balance the aircraft, rather than the T*sin(climbangle).
Part of the problem of this discussion is that there is no such thing as "lift" and "drag".
Strictly speaking there are only three forces acting on an aircraft (in the context of this discussion).
Weight (or mass if you like), always pointing down.
Thrust, acting pretty well along the airspeed vector (other effects being second-order).
Aerodynamic forces, acting mostly on the wings, which we like to split out as "lift" and "drag", but which again is not a scalar but a vector tilted backwards from the airspeed vector.
Thanks to all for joining in!
I'll try to come up with something 'clear' this weekend!
CJ