So if I have a 1 lb ball and a 10 lb ball and I want to give them equal acceleration do I apply the same amount of force to both or does the 10 lb ball require more force given it's greater inertia?
That's the thing about gravity; it acts upon objects equally regardless of size or mass (unless you get into astronomical sizes). So the 1 lb ball and the 10 lb ball will both accelerate at exactly the same rate, however you would have to apply a 10 lb force to counteract the gravity of the 10 lb ball, while the 1 lb ball only requires 1 lb.
There are four forces acting upon an aircraft in a vertical climb:
Gravity: A constant 1G applies a force towards the ground that equals the weight of the aircraft.
Drag: A variable that depends on speed and the aerodynamic properties of the ariceaft.
Thrust: A variable that depends on engine power, prop efficiency and other factors.
Kinetic energy: The stored energy (inertia) of the aircraft; speed.
If the thrust is insufficient to overcome gravity and drag, the aircraft will lose kinetic energy until it is stationary and starts to fall. Gravity is constant, but drag is reduced by the square of speed. In other words when you reduce speed by half, drag is reduced to one-quarter.
The reason why kinetic energy/inertia is important is because WWII fighters have so little thrust that inertia becomes the main source of energy to overcome drag. Gravity is equal no matter the size of the aircraft so the only factors that
will make a major difference between two aircraft is inertia and drag. The aircraft with the best weight to drag ratio is the better zoomer unless there is a
major difference in thrust to weight ratio.
Throw a 1 lb steel ball and a 1 lb cotton ball into the air at the same speed. The steel ball will go higher due to its better aerodynamic properties; weight to drag ratio. Glue on a rubber band powered prop on both... Steel ball will still go higher.