# Minimum force to keep a mass floating in the air

1. Apr 7, 2010

### guest1

This is bugging me and maybe someon can help me find the obvious mistake:

I want to calculate the minimum power needed to keep a mass of 1 kg floating in mid air.

The naive approach is this:

The mass falls 5 meters in one second so to get to the original position I have to invest an energy of 50J (m*g*h with g = 10 m/s^2) per second

So for the one second case I get a power need of 50W.

If I do the calculation for 2 seconds I need 100W.

Actually what I would have to do is get the limit for t->0 ...but of course that gives me 0W (which is not very helpful since stuff like airplanes and helicopters do require constant lift/power to keep falling out of the sky)

2. Apr 7, 2010

### mgb_phys

No power is required to keep something in the air.
A shelf manages to do it for years without any power source.

Energy is force * distance, (and power is just energy/time) if you don't move anything against a force you don't need any energy.

The reason heavier than air craft need power is that they are pushing an aerofoil (ie. wing) against the force of aerodynamic drag (the rate of pushing is power) - even helicopters hovering are pushing a rotor blade around.

3. Apr 7, 2010

### Staff: Mentor

Use a table: power = 0

4. Apr 7, 2010

### guest1

Zero is what I get, too - but that's not a real useful answer.

The question came about like this: Let's say I want to build some sort of flying contraption that is able to lift the mass of 1kg into the air. What would be the lowest power energy source I would need for this (in the absence of some sort of passive buoyancy aid) .

If you take a 1kg mass and hold it up in the air you are expending energy/power (mathematically it's zero, but you really are using calories to accomplish the feat otherwise you could do it indefinitely/effortlessly. You need to counteract the force downwards constantly. This should be similar to the drag issue, shouldn't it? (there you are constantly counteracting a force also))

5. Apr 7, 2010

### Staff: Mentor

How far do you want to lift it? How fast? As has been pointed out, no work is required to support the mass once you've lifted it into position. (And put it on the table.)

Sure it will require energy for you to support it with an outstretched hand. But that's because you chose a biological system to support the mass. All of that energy expended to create tension in your arm to support the mass is wasted. Use a table.

6. Apr 7, 2010

### guest1

I know that one could lift the mass (theoretically) infinitely slowly using a 0.0001W source. But in reality that just doesn't work (if you attach it to a string and pull it upwards with such a power source it would lift off the floor but I'm talking about flying contraptions here)

You can rig a system that will generate a lifting force to the mass (e.g. a very slowly turning helicopter rotor with a 0.0001W motor) and it will never get off the ground even though you are constantly enacting a force upwards.

Obviously this is because the force needs to be greater than the gravitational attraction.
The point is: You need to generate that force somehow so some sort of energy is involved (and hence some sort of power) otherwise we could scale down flying machines indefinitely (which seems absurd).

7. Apr 7, 2010

### Staff: Mentor

This is the first time you've mentioned 'flying contraptions'.

You want to know what kind of efficiencies are available for helicopter-like systems? What is the minimum power required to generate a certain thrust?

8. Apr 7, 2010

### stewartcs

The minimum force required to keep an object "floating" on earth is equal to the object's weight. This can be accomplished with buoyancy or some other means.

One can build many different machines to achieve the "other means" such as helicopters. However, it becomes a matter of which has the best efficiency. The one with the best efficiency will use the least power to keep the object floating.

CS

9. Apr 7, 2010

### guest1

Sort of. I was simply wondering whether there is a lower limit for the power needed to generate the kind of thrust which would allow a certain mass to remain stationary in the air (or lift off infinitely slowly).
I'm specifically talking about thrust here not any sort of buoyancy or lift generated by wings and airspeed. Just plain thrust downwards from a standing start.

Whether this is by helicopter or other means (e.g. particle acceleration via electromagnetic thrusters or whatnot) is immaterial.

I realize now that the term 'floating' was a bit ambiguous in the OP, sorry

10. Apr 7, 2010

### Staff: Mentor

There is no theoretical lower limit to the power. For a helicopter, the larger the rotor, the lower the power.

11. Apr 7, 2010

### mgb_phys

Not really, you just have to fly slower with a larger wing.
eg http://en.wikipedia.org/wiki/Solar_Impulse_Project

12. Apr 8, 2010

### guest1

The point was: pure vertical thrust. no wings. no horizontal component. no balloon.

There has to be some way to calculate the minimum impulse I need to impart on air (or the amount and speed of reactive mass) in order to keep station?

13. Apr 8, 2010

### Staff: Mentor

Again, there is no minimum.

14. Apr 8, 2010

### guest1

Somehow I can't really believe that. If you make the rotorblades on a helicopter wider then you can turn it slower but the amount of air you need to shove downwards remains the same. You need to continually shove some air downwards or your object will fall. You can't reduce that to zero. Moving air downward means imparting an impulse to it (i.e. accelerating it) which means imparting energy to it which means that there is some power involved.

Likewise with something that uses a reactive mass (rockets). In order to at least keep their height you need to continually expel a certain amount of mass downwards. Gravity wants to impart in impulse downwards on your object so you need to counteract that in some way.

15. Apr 8, 2010

### TurtleMeister

I think guest1 wants to know how much power (watts or horsepower) is required to accelerate a 1kg mass at 9.8 meters per second per second.

16. Apr 8, 2010

### Staff: Mentor

You need to generate a force equal to the weight, which means that you need to accelerate some mass of air downwards. The question is how much air mass you accelerate. The more air you accelerate the less you have to accelerate it and therefore the less power is needed. There is no theoretical limit to this. The larger mass of air you push down the less you need to accelerate it and therefore the less power you require.

Essentially, your error is in the assumption that the amount of air you need to shove downwards remains the same. This is not correct. You can shove more or less air downwards depending on how much you accelerate the air. A small-mass high-velocity air movement will be much more energetic than a large-mass low-velocity air movement.

17. Apr 8, 2010

### TurtleMeister

I'm sure that it gets complicated when considering real world application such as helicopters. Just google "power required to hover". However, the question that I am considering is: What is the power required to accelerate a 1kg mass at 9.8 ms-2? (disregarding exactly how we're going to do it)

Here is my attempt. I'm not sure that it's correct so please check my work.

Converting weight to force:
acceleration = 9.8ms-2
mass = 1kg
Force = mass * acceleration = 9.8 Newtons

Work done in moving 9.8 meters:
Work = Force * distance = 96 joules

Power required:
Power = Work / 1sec = 96 watts

Please note that the distance moved is the distance that the object would move if it were not canceled by the earths gravitational acceleration 9.8 ms-2.

18. Apr 8, 2010

### Staff: Mentor

You are not moving, you are hovering.

19. Apr 8, 2010

### TurtleMeister

Okay. Just disregard that the object is near the earths surface. How much power would be required to accelerate 1kg at 9.8ms-2 in the absence of any gravitational field? After you've calculated that then place the object near the earths surface with it's direction of acceleration pointing away from the earth. What will happen?

20. Apr 8, 2010

### Staff: Mentor

To accelerate 1 kg at 9.8 m/sÂ˛ requires 9.8 N of force, not any specific power. In fact, when v=0 m/s the power required is 0 J.