Another Take on this Question
Let me take a different approach to the questions asked.
Let's assume that the L/D involved is 20 and that the airplane is flying at Mach 0.8 at 30K feet such that its true airspeed is about 800 ft/sec.
Now the question of the thrust increase needed for a level turn:
Lift must increase by 1/cos(phi). Assuming L/D remains about the same below are the percentage increases in thrust required as a function of bank angle (thrust increase proportional to lift increase):
Bank Angle Thrust Factor (1 = trim for level flight)
----------------------------------------------------
0 (level) 1.000
10 deg 1.015
20 deg 1.064
30 deg 1.155
Now the question of thrust increase needed for 100ft/min climb:
- 100 ft/min when flying at 800 ft/sec represents a flight path angle of 0.002 radians (100ft/min) / [(800ft/sec)*(60sec/min)] that is equal to 0.12 degrees.
- This requires an increase in thrust of 0.2% of the airplane weight.
- With an L/D of 20, the level flight thrust required is 5% of weight.
- The increased thrust for the climb is 4% (0.2% / 5%) compared to the thrust required for level flight.
Comparing these results, the thrust required to be able to climb at 100 ft/min is the same as the thrust required to fly a 16 degree bank turn at the same speed. The assumption here is that you are thrust limited and not CL limited so that you are able to increase AoA enough to get the needed additional lift for the turn while maintaining the current speed.
It seems to me that limiting bank angle to 10 degrees when in a thrust limited condition is prudent.
Hope this helps.