Hmm. Sorry Ozexpat, but you are way off base in several areas in your post.
Your Para 3:
The additional thrust creates the change in AofA...
[Whilst accepting that local AOA changes can be caused by thrust changes for prop aircraft, both of us have elected to ignore prop effects for the time being. Certainly a Jet discussion should suffice for considering climbing - the mechanics are not going to be fundementally different by powerplant.]
Changing thrust will not directly influence AOA. Granted, it may do indirectly by causing a pitching moment, but we are assuming a Piloted aircraft, i.e. the pilot controls that attitude of the aircraft.
The flight path has not yet changed, and the attitude is unchanged. Therefore the AOA is constant. there must be some other mechanism for commencing the climb. That mechanism is either a speed increase leading to more lift, or a pitch increase leading to more lift, in order to generate an upwards force to initiate the climb.
Your para 4:
The actual physical length of the lift vector line is still the same ...
No it isn't. We're talking steady state climb here, and both you, I , and Kermode agree that lift is less than weight at that point. The length of the line represents the magnitude of the force, so if it were the same, lift would be the same.
Look at the Kermode excerpt. He specifically states that he is resolving forces parallel and at right angles to the flight path. He is not talking about just the vertical component of lift, he is talking lift, all of it.
Your Para 5:
You are adding vectors here. No problems with that - vectors can always be added. But the Total Reaction is the addition of Lift and Drag. What you describe however is the addition of Lift and Thrust, and hence is not the 'Total Reaction'.
Incidentally, I think maybe you ment to make that an 'Excess' Thrust line, because then at least your diagram would have accounted for all the forces, even if the 'total reaction' was misidentifed.
What your diagram basically shows is that excess thrusy must be present in order for a climb to be maintained. Thats fine, correct, and I'm not arguing with it.
But it does not show how the aircraft gets into the climb!
To show that once an aircraft
is climbing, a vertical component of thrust exists, is not an arguement to show how that condition came to be.
I reiterate: During the cruise, thrust and drag are horizontal, and lift and weight are vertical. If the aircraft is displaced vertically upwards in can only be because lift has increased, or weight has decreased. If something has not been dropped, fired, kicked or fallen off of the aircraft, then the only remaining possibility is that Lift has been increased. [note 1]
Let me show it another way. If you enter a climb, you feel G. Maybe not much, perhaps sub-threshold, but we all know it is there.
What is G? Answer = Load Factor (N)
What is Load Factor? Answer = Lift / Weight.
Therefore, if you are feeling G, Lift exceeds weight.
[G relative to aircraft Normal Axis. For progressively steeper climb angles, although you still feel your own weight, more and more of it will be on your back rather than the seat of your pants. In a sustained vertical climb, you'd have zero lift, and zero load factor, although you obviously would still feel your weight by virtue of the seat back pushing you up]
Note 1: Or our model is wrong. Which it is, in fact. Both Kermode and I have so far assumed that Thrust acts along the aircrafts flight path. This is not true, but rarely much of a real issue. But when you see highly agile aircraft performing high AOA manoeuvres with a large excess thrust, it becomes significant. Consider a slow fly past by a modern fighter. It will have a big AOA - maybe very big. Hence its thrust line would already be pointing up. If it then applies max burner you can easily see that a climb will result without lift necessaraly having been increased. But that isn't really the kind of thing we are talking about here. As I said earlier - mundane aircraft, routine manoeuvres.
Also, to reiterate, I agree totally that this is way deeper than most pilots need. Nevertheless, people have expressed an interest, and in mechanics terms it is not that deep - just a free body diagram and a few forces.
Cheers.
CPB