If we have to obey Sir Isaac Newton’s laws of motion, we will use his laws to find the answer.
The drawing shows an object is in free fall. The gravity drag is represented by a dark arrow. At some point, an offset force will intervene. To make the discussion simple, we assume that the anti gravity force is twice stronger than the gravity force, which makes F = 2 Mg.
Here is the condition how anti gravity force will work. As the object falls by T duration, its altitude lost will be L. By this moment, anti gravity force will work against the falling object. When the object falls another T period, the object velocity will be zero. From now on, it will have reversal momentum upwards. When the object climbs back to the position where anti gravity force initially kicking in, we will remove the force. So the object only receives net force from the gravity pull. The object will become zero velocity at the original position A where it will fall back again.
The amount of energy consumed will be:
If the anti gravity force takes earlier action, for example, instead of kicking in at T moment, it happens at ½T. The energy consumption will be ¼ of the first scenario. Why is it? Because the distance to push falling object back to position A will be ¼ of L. But the push-up-action will happen twice. So we can get:
Obviously, you can infinitely divide a unit of time, which reduces energy expense for anti gravity. So we can say:
- Heavier-than-air object cannot float in the air without consuming energy.
- But you can reduce anti gravity energy spending infinitesimally.
This equation is valid for an object being airborne only when energy spending is against another object with relatively larger mass, especially when the mass is regarded as infinitely heavier. When the object mass is finite, say when we use another object within the gravity field as target of reaction by energy, the equation will be different.
First, we set up the environment. Another object 2 is below object 1. They fall together towards gravity centre. At point B object 1 will use energy to act against object 2 with twice the force than the gravitational pull it subjects to. As a result, object 2 will have 3g force instead 1g. The work done by energy should be on object 1 and 2 respectively.
We can simplify the equation as:
This result tells us that when energy is used for object acceleration, it is possible to use less energy when the mass it works against is very big. It makes sense that land transport vehicles use wheels friction against road instead of ejecting gas like aircraft. Aircraft can stay airborne much longer than a rocket because it utilizes external mass and fixed wings for anti gravity purpose. The result also gives us clue why VTOL aircraft will use so much fuel when it takeoffs vertically.
The discussion we have so far allows external mass being used. In a vacuum space, it will be a different story because you cannot access mass in there. We will discuss energy efficiency in vacuum environment in another blog.