# B What formula defines the power (i.e. horsepower) of gravity?

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1. Sep 15, 2015

### Cameron234

What is the calculation that shows how much power is required to offset gravity?

Gravity force is defined with units of kg.m.s-2. How to convert that to Joule.s-1?

I am talking in the context of theoretical physics, not practical engineering like using a rocket or helicopter.

But BTW could use the engineering characteristics of a flying machine for checking the solution. e.g. a helicopter weighing 10,000kg uses say 1,000kg/hr of kerosene fuel, (44.8MJ/kg heat of combustion) and has 30% energy efficiency, then that would give an approximation to the theoretical energy being used in opposing the gravitational force.

Does the solution involve knowing the formulas that define space and time?
e.g. If E=m.c2, (kg.m2.s-2),
EdT(J.s-1) = gravity force . c2 ? (units check: J.s-1 = kg.m.s-2 . m.s-1)

2. Sep 15, 2015

### cjl

There is no power required. If I set a book on a table, the table is expending zero energy to suspend the book against gravity.

3. Sep 15, 2015

### Staff: Mentor

Theoretical physics doesn't enter into things here.
The force due to gravity is (obviously) a force, in units of $\frac{ML}{T^2}$, (M - units of mass, L - distance units, T - time units).
The units of Work are F*L = $\frac{ML^2}{T^2}$.
Power is work per unit of time, or $\frac{ML^2}{T^3}$.
No. This formula gives the energy equivalent of a specified amount of matter.

4. Sep 15, 2015

### Staff: Mentor

That depends on what is offsetting gravity. A table of chair requires zero power, as no energy is expended in countering gravity. A helicopter must do work on the air, so it will expend some amount of energy per time but that depends on a great number of variables, including the specific model of helicopter, conditions of the air, etc.

5. Sep 21, 2015

### Cameron234

"Theoretical physics doesn't enter into things here. The force due to gravity is (obviously) a force, in units of MLT2, (M - units of mass, L - distance units, T - time units)."

Is this correct? It means that gravity is time dependant.

Guess I'm not looking at the traditional viewpoint but for a different angle.

" A table expends zero power".

That is because it is now connected to the earth and becomes effectively one body.
If it were to hover using let's call it "anti-gravity", how much power would be required?

6. Sep 21, 2015

### nasu

No, it does not mean that the force is time dependent.
The fact that the unit of force includes time does not mean the force is time dependent.
A constant speed is still measured in m/s.

You can offset gravity with zero power, does not matter how you explain this. Depending on the device you use, the power may not be zero, you can have a range of powers, but there is no theoretical minimum. You could find the power for a specific real device. For imaginary ones you can only imagine. :)

7. Sep 21, 2015

### Staff: Mentor

No, it's because power is force times distance over time. With no distance/time (no motion), there is no power.

As such, different methods for opposing gravity will use different amounts of power or no power at all. Indeed, because no power is applied to the object being held aloft, many methods of support, including helicopters, have a theoretical minimum power requirements of zero. For a helicopter, the longer the rotor span, the lower the power requirement.

8. Sep 21, 2015

### Cameron234

Thanks, I get what you are saying, and I know that's what textbooks say, but it still doesn't sit well.

So let's turn the focus to a theoretical anti-gravity sphere if 1kg mass. No propellers or chairs. If it hovered, how would we define the theoretical power required?

9. Sep 21, 2015

### nasu

You can define it anyway you want it. This is not a real situation. The anti-gravity sphere is not theoretical but imaginary. And I don;t mean that you need complex numbers to model it.
"Theoretical" were the answers you received so far. Based on verified theories of physics, describing the reality as we know it.

10. Sep 21, 2015

### Cameron234

Reality and undeveloped knowledge aside, how would you define or express the power requirement of an anti-gravity device?
(This would be another way of posing my question.)

11. Sep 21, 2015

### nasu

Same as above. Asking several times the same question does not change the answer.

12. Sep 21, 2015

### Staff: Mentor

Zero.

Sorry, but the answer is what it is. The actual power required wI'll depend on the details of the method. The theoretical power required will always be zero because mechanical power requires motion.

13. Sep 21, 2015

### cjl

The minimum power required will always be zero. The actual power required will depend on the specifics of the implementation. Even in the case of something like a helicopter, you can make the power requirements arbitrarily low by increasing the volume of air moved, and decreasing the speed of the downwash. This is why the first human powered helicopter had such large, slow-moving blades - it decreases the power required to hover. If there were no engineering limitations on how large you could make the bladespan, you could decrease the power as low as you want, since there is no theoretical lower bound to the power required to hover. This is because no energy is being added to the object which is hovering, and thus, the rate of energy addition per unit time required is zero.

14. Sep 21, 2015

### Cameron234

Ignore helicopters people, I'm talking theoretical. A helicopter pushes against a cushion of air held against the earth by gravity. A theoretical anti-gravity sphere would work without an atmosphere.

15. Sep 21, 2015

Staff Emeritus

"Two plus two continues to make four, in spite the whine of the amateur for three or the cry of the critic for five." James Abbott McNeill Whistler.

16. Sep 21, 2015

### Cameron234

A bit condescending... Anyone else believe that gravity doesn't require energy?

17. Sep 21, 2015

### Staff: Mentor

Me. As has been said more than once, the amount of power required to counteract gravity varies between zero and a non-zero number that depends on the details of the system used to counteract gravity. Since you don't appear to want to listen to people, and because you're speculating about something which doesn't exist, thread locked.