Very large can of worms
(But far better than an oil thread - at least this can be interesting )

I will use simple terms here to explain it

To move the plane vertically requires the engine to overcome a few things.
1 - the weight of the plane
2 - the Acceleration force to actually make the plane climb (even a steady rate climb is an acceleration)
3 - the Drag of the plane -
That Drag includes
A - The induced drag caused by the prop wash
B - The drag from the control surfaces being used
C - The "effective drag" caused by things such as engine thrust angles

To make it really simple to work out?
Use a Thrust to weight Ratio of at least 1.5:1 and you will have "unlimited vertical" for practical purposes.