Power = thrust x time
Those 3 arguments are perfectly clear.
I argue they are not...
thrust x time =
impulse, and probably not relevant to this discussion
thrust is a
force created by the propulsion system
work = force x distance = energy delivered by the propulsion system
power = energy rate = energy / time
power generated = thrust x distance / time = thrust x velocity
power consumed = fuel flow x specific energy
efficiency = power generated / power consumed
Now consider an aircraft in climb.
Climbing, in energy terms means increasing potential energy.
potential energy = weight x height
climb speed = change of height / time
The
highest climb speed occurs when you have the highest excess power, i.e. the highest rate of adding energy.
When looking at the climb angle, we abandon the energy model and look at forces only.
Along path there are three forces acting on the aircraft.
1. Thrust
2. Drag
3. Weight x sin(climb angle)
For constant groundspeed climb, the forces are in equilibrium.
Thrust acts opposite to Drag and the along path Weight component
The higher the difference between thrust and drag, the great we can make the climb angle.
The maximum climb angle is achieved at the speed where maximum thrust - drag is maximal.
Note that typically you will fly a constant CAS or constant Mach climb which requires change of groundspeed during the climb and therefore the forces will not be in equilibrium.