B Energy Requirement to Levitate 550 lb Mass at Sea Level

[stevmg]

To maintain a 550 lb mass in the air not touching the ground at sea level (radius of Earth is 4000 miles), what is the expenditure of energy required given perfect efficiency of the process?

 

[Dr.D]

No work is done if the mass does not move, so there is no energy expended.

Now, if you are thinking of a man holding this weight up, using his muscles to do so, then energy is required to maintain the tension in his muscles. But this goes into his muscles, not into the mass itself.

 

[Nugatory]

To maintain a 550 lb mass in the air not touching the ground at sea level (radius of Earth is 4000 miles), what is the expenditure of energy required given perfect efficiency of the process?

You're describing a mass sitting on a table or hanging by a chain. It doesn't require any more energy than if the object were sitting on the ground, which is to say none at all.

Even if you're doing something more exciting, like using an enormously powerful fan to produce an upwards-flowing column of air to support the weight, none of the energy is going into holding the weight up; it's all going into moving air around. One of way of seeing this is to imagine that the weight is sitting in a vertical pipe so that none of the air underneath it can escape. Once we get the pressure up to where it will support the weight, as long as there are no air leaks the pressure will be maintained forever without us having to spend more energy pumping more air in.

 

[stevmg]

Still, no answers posted. Only vague generalities.

 

[nasu]

The answer was given in all his specificity: with perfect efficiency, the energy is zero.

 

[berkeman]

Still, no answers posted. Only vague generalities.

Why do you say that? Because you don't like the answer, or because you think it is wrong?

 

[Ibix]

Still, no answers posted. Only vague generalities.

Your question is too vague to be answered except in the case where the object is suspended from a rigid object (tree, crane, etc). In that case the answer is zero, as stated in every response so far. If you mean any other case then you need to provide details of the support mechanism.

 

[stevmg]

Aware that work done on the mass is zero. BUT it won't stay up on its own.

Where does the force come from? How is it generated?

 

[stevmg]

Your question is too vague to be answered except in the case where the object is suspended from a rigid object (tree, crane, etc). In that case the answer is zero, as stated in every response so far. If you mean any other case then you need to provide details of the support mechanism.

Don't want to start a "fight."

 

[stevmg]

Don't want to start a "fight."

Is there any way to convert horsepower into pounds thrust?

 

[Ibix]

BUT it won't stay up on its own.

It will if it's hanging from a bridge. What are you hanging it from? Rocket? Helicopter? Hot air balloon?

 

[Nugatory]

Is there any way to convert horsepower into pounds thrust?

No, because they are measuring different things. Pounds of thrust is a measure of the force being applied to something, while horsepower is a measure of how much energy is being expended per unit time. If I hang a 100lb weight from a chain, the chain is applying 100 pounds thrust to the weight to balance out the force of gravity while burning no energy and producing zero horsepower as it just sits there. On the other hand, if I try supporting the weight using a rocket engine that generates 100 pounds of upwards force, then much energy will be spent pushing hot exhaust gases around. But the pounds of force is the same either way.

No matter how much or how little force I apply to something, no horsepower at all is required if it's not moving. That's why the answer to your original question, supplied by many posters already, is "zero".

 

[russ_watters]

Is there any way to convert horsepower into pounds thrust?

Not in a general way, but for certain dynamic propulsion devices such as fans, you can calculate the input power required to get a certain thrust. What you find if you plug in different specs, is that the input power for a fan does indeed drop asymptotically to zero as the rotor diameter increases.

 

[stevmg]

No, because they are measuring different things. Pounds of thrust is a measure of the force being applied to something, while horsepower is a measure of how much energy is being expended per unit time. If I hang a 100lb weight from a chain, the chain is applying 100 pounds thrust to the weight to balance out the force of gravity while burning no energy and producing zero horsepower as it just sits there. On the other hand, if I try supporting the weight using a rocket engine that generates 100 pounds of upwards force, then much energy will be spent pushing hot exhaust gases around. But the pounds of force is the same either way.

No matter how much or how little force I apply to something, no horsepower at all is required if it's not moving. That's why the answer to your original question, supplied by many posters already, is "zero".

Thank you, Nugatory

I think "I've got it."

If the "mass" were kept aloft by an airfoil (vertical lift generated by horizontal motion), i.e., translating induced drag to vertical lift by the airfoil, is theoretically possible with a super large airfoil of no weight itself to generate large lift with relatively small induced drag which would require little power. Akin to a glider. A little push, or pull by a truck or a small airplane gets the glider aloft and it stays there with very little input from upward air currents or dropping the nose a small bit to get "God's g" on your side. In effect no power is being applied to the "mass" (the glider) to keep it aloft.

Note that this super large airfoil described above is akin to a first class lever with its multiplicative effect on input force onto output (lift) force (of course at the expense of distance.)

It has taken me forty years to figure this out. Sorry for wasting everybody's time.

Russ Watters also states above that input power drops symptomatically to zero as the rotor (fan) gets larger. Hence the long blades on a helicopter.

 

[stevmg]

Just to note that the F-4 (Phantom Jet) of the 1950s and later, which looked like a brick could fly because it was given enough power.

 

[russ_watters]

Thank you, Nugatory

I think "I've got it."

It has taken me forty years to figure this out. Sorry for wasting everybody's time.

Not a waste of time, it's just that your approach was a little off-putting in how short your first response was. But we're glad you figured it out.