Calculating kWh for Lifting 2 Tons to 5m with a Gravity Accumulator Design

Can anyone provide a mathematical formula that I will be able to use to calculate how many kWh is needed to haul a load of, for example, 2 tons to a height of 5 m?

I am thinking of building a "gravity accumulator" (my working name), which would be charged / lifted by a fan, while falling down would generate electricity. I intend to use it on the plot where I usually stay on weekends - the battery could be charged for 4.5 days.

What do you think about such a solution?

The formula is in the gymnasium physics book (I don't know if you walked?): E = m * g * h, where m = mass in kg, g = acceleration due to gravity (9.81 m * s ^ -2), ah = height in m, the result is in watt seconds (joules).
Thus, lifting 2,000 kg to a height of 5 m stores the energy of 2,000 * 5 * 9.81 = 98,100 Ws, or 0.02725 kWh (kilowatt-hour = 3,600,000 watt seconds).
"Competitive" idea: a car battery with a weight of 20 kg and parameters of 12 V / 50 Ah accumulates the energy of 600 Wh = 0.6 kWh, which is over 22 times more.
I think your construction, even in terms of material only - no labor - at the price of scrap metal, will cost more than a car battery.

And I think the idea is very good. A car battery is consumable quickly and has a low energy conversion efficiency. The gravitational one is better because if it is well built, it will be able to work for decades and release a lot of energy in a short time.
But an even better idea is to accumulate energy in rotational motion. If you spin a 200 kg flywheel to 50 rpm, for example, then a lot of energy is already stored. And such energy can be easily recovered and processed - it is enough to use a highly efficient generator with permanent magnets, which also works as a drive motor. Additionally, the generator with a wheel can be closed in a sealed tank and the air can be pumped out of it. You can also use magnetic bearings (they are available) instead of ball bearings. We then have a real mechanical battery.

All you need is an inverter with energy recovery, preferably 3-phase. The only problem is that the inverter should work so that it constantly recharges mechanical energy, increasing the rotational speed of the flywheel. Most inverters, after unscrewing the engine from revolutions, can go into "coasting" or idle mode, but when turned on, they will start to brake such a system. So it must be well resolved.

Nardis wrote:

And I think the idea is very good. A car battery is consumable quickly and has a low energy conversion efficiency. The gravitational one is better because if it is well built, it will be able to work for decades and release a lot of energy in a short time.
But an even better idea is to accumulate energy in rotational motion. If you spin a 200 kg flywheel to 50 rpm, for example, then a lot of energy is already stored. And such energy can be easily recovered and processed - it is enough to use a highly efficient generator with permanent magnets, which also works as a drive motor. Additionally, the generator with a wheel can be closed in a sealed tank and the air can be pumped out of it. You can also use magnetic bearings (they are available) instead of ball bearings. We then have a real mechanical battery.

All you need is an inverter with energy recovery, preferably 3-phase. The only problem is that the inverter should work so that it constantly recharges mechanical energy, increasing the rotational speed of the flywheel. Most inverters, after unscrewing the engine from revolutions, can go into "coasting" or idle mode, but when turned on, they will start to brake such a system. So it must be well resolved.

Buddy - The amount of energy stored in such a mass (2 t per 5 m) - as my colleague @Rzuuf mentioned - is ridiculously small. And that's 100% of the energy you have. Does the term "perpetual motion machine" tell you something?
So you won't get all that energy back, but just a fraction of it.
The operating time of the machinery is unlikely to be "tens of years". Something has to pick up the falling mass. Do you know a system that will lift heavy loads every day for decades without maintenance and replacement of consumables? No rope can stand it. Will the windmill, which is supposed to act as a lifting force (which is supposed to last a few days), also last for decades without any maintenance?
Assuming you can get such a system.
What about the costs? Inverter? The price of a dozen or so batteries, a generator (and a highly efficient one, which is a damn expensive one), the price of the next x-ten / ten batteries.
And ... and I would forget - you still need an ordinary, impaired, expensive and non-durable - battery to keep this recovered energy somewhere.
Flywheel - nice, but to speed it up, you have to first supply it with this energy, and then constantly supply as much energy and as much waste to keep it running. You will only recover a part of the stored energy from it due to the losses. The total energy balance is ... unfortunately negative.
And the wind energy is rather modest. The force of the wind is high considering the surface it is operating on. So a few kilometers wide and 2-3 kilometers high. Will you build a windmill that will use at least 50% of the air stream?
And the power of the wind that will lift 2 tons up in a short time is a Category 5 hurricane.

My colleague Madrik, it seems to me that your technical thinking is totally limited, and I will not mention the practice ... At the beginning I have to tell you that here the topic of the energy accumulator, not the perpetual motion machine is discussed!
Of course, I do not question the fact that the amount of stored energy in the lifted mass of 2 tons at a height of 5 m is ridiculously small. True, it is small, but I disagree that it is impossible to construct a reliable system that can do this for decades. You just need to think a little and design the right hydraulic jack ...
This lift does not have to carry a weight of 2 tons so high, as high as 5 m - it can lift 100 tons to a height of 0.1 m and it will come out the same. And the windmill can work lightly, giving a small kinetic energy of water, e.g. to a hydraulic ram, and this will create a pressure impulse that will start the hydraulic cylinder and raise the weight by 1 micron upwards. Energy recovery can be achieved in an extremely simple way using, for example, the famous METOZ system, which performs work from the energy of water pressure.

When it comes to systems with flywheels, they occupy a high place in the ranking of accumulation systems - today on a par with acid batteries due to the low resistance to movement of the magnetically mounted wheel in a vacuum.

I would like to add that in my opinion you are all slightly wrong in assuming that these 2 tons must be one weight, why not break it down into 10, 200 kg each? Each line will withstand this, the size of the system will slightly change (the system will grow a bit), but we can be sure that such a system will survive us and our grandchildren.

And the material, as someone mentioned above, does not have to be scrap metal, but e.g. earth, because why not place it 5 meters underground? I think that the excavated material will weigh more than two tons, besides, the material may also be water, which is probably not a problem for people who have their plots and draw water from under the ground.

Yes, @ Pietro54 - water is it!
Here is a simple example of how this can be done:



Reliability guaranteed for decades (after using appropriate valves and a pump, e.g. a gear pump).

How it's working? The windmill drives a simple gear pump, which forces the water to circulate through the hydraulic ram. In the tare, we close and open the valve cyclically, which causes huge pressure jumps and pumping water into the tank at the height of H. In fact, apart from the fan and valves, there is no need to service. :)

greetings,
Peter

Added after 6 [minutes]:

Of course, the ram also needs to be supplied with water to replenish the defect that is transferred to the reservoir.

And why not just use a mains-powered electric motor instead of building these wonders on a stick? This amount of energy will cost less than PLN 6 ANNUALLY. 0.03 kWh × 365 days × PLN 0.5 / kWh = PLN 5.47.

But what are you talking about? What engine?
Besides, you've been hitting the calculus, multiply the result by 24 and you'll be okay.

A 2-ton "weight" (whether whole or in parts) hanging at a height of 5 m has a potential energy:

E = mgh = 2000 kg * 9.81 m / s2 * 5 m = 98 100 J

1 kWh = 3,600,000 J

So the potential energy of the hanging "sinker" is:

E [kWh] = E [J] / 3,600,000 = 98,100 / 3,600,000 = 0.02725 kWh

This energy would have to be converted into electricity. You should take into account the conversion efficiency of e.g. an alternator (max. 0.5) and mechanical losses (say 20%), so you will get an energy impulse at the output:

Ewy = E [kwh] *? A *? M = 0.02725 kWh * 0.5 * 0.8 = 0.0109 kWh = 10.9 Wh

The above assumed efficiencies are very optimistic, the actual ones will be much lower due to the non-constant rotational speed of the electrical energy into mechanical converter.

Weight drops from a height of 5 m with time (free fall) =

$$t=\sqrt{\frac{2*h}{g}}=\sqrt{\frac{2*5m}{9.81 m/s2}} \approx 1.01s$$

But there is no electricity generation. A generator system with gear ratios (losses) will slow down the decline.

I suppose dragging this weight to a height of 5 meters will take a lot longer than 1 second, so the efficiency of the system will be negligible and the processing efficiency even more negligible. :(

And for this you have to take into account:

- securing the system against access by children (the baby pancake has a larger surface to hug, but there are problems with transport, because you have to roll it up each time before loading it into the car and this is troublesome in the long run )

- noise problem - 2 tones falling to the ground every few seconds can piss off the quietest (+ scare the surrounding fauna -> environmentalists are waiting) and you may have problems with the local peasants, and the anti-irregularity T-shirt is uncomfortable to wear, especially in hot weather.

- the problem of vibrations and durability of the structure (and surrounding structures too -> e.g. cracking walls)

Generally pointless, because in this "battery" you lose most of the introduced energy (on processing).

Paweł Es wrote:

[...]
The weight falls from a height of 5 meters with time ( free fall ) =

$$t=\sqrt{2*h}{g}=\sqrt{2*5m}{9.81 m/s2}\approx 1.01s$$

and this is all the pulse driving the generator lasts, and the generator voltage changes with the revolutions, so the pulse charging the battery will be even shorter (Uprator> Uakumulator to be charged).

But it never will free fall ...
Fundamental error of reasoning, mister Paul Es ... ...by free fall there can only be a loud bummm - to the soil - and no useful energy ...
The equation that solves this problem correctly is much more complicated ...
Of course, the whole idea with this way of "storing" energy is a bad one right from the start ...

Why should it fall, it can turn. In Australia, in the Australian government building there is also an electromechanical "UPS", the energy is stored in the "flywheel" instead of in the battery.

Quarz wrote:

But it never will free fall ...
Fundamental error in reasoning, mister @ Paweł Es

[/ b] ... ...by free fall there can only be a loud bummm - to the soil - and no useful energy ...
The equation that solves this problem correctly is much more complicated ...

I simplified it too much, fact, without knowing the en processing circuit. mechanical to electric (gear ratios, perhaps the rotational speed stabilization system) and forces acting opposite to the driving force, it is impossible to estimate the fall time. In free fall, the energy will not be converted into electricity, but only into the kinetic of the "sinker" itself.

Quote:

Of course, the whole idea with this way of "storing" energy is a bad one right from the start ...

The warehouse itself would eventually get away, but the efficiency (or lack thereof) of the loading and unloading process ...

My calculations show that a 2400 kg weight (1 m ^ 3 of heavy concrete) suspended at a height of 10 m can deliver 653.7 Wh regardless of the power consumed.

It can be at ~ 1.2kW for 30min, 2.4kW for 15min, 4.8kW for 7.5min, 9.6kW for 3.75min and so on.

Misian@ wrote:

My calculations show that a weight of 2400 kg (1 m ^ 3 of heavy concrete) suspended at a height of 10 m can provide 653.7 Wh regardless of the power consumed,
...

After all, for 5 m and 2000 kg the value of potential energy was already calculated here - 27.25 Wh ...
Therefore, for 10 m and 2400 kg it will be only 2.4 times more, that is:
2.4-27.25 Wh = 65.4 Wh ...

It won't pay off, because the mere braking of 2 tons will consume that stored energy, not to mention the accumulation.

R2M wrote:

It won't pay off, because the mere braking of 2 tons will consume that stored energy, not to mention the accumulation.

I don't think that braking would cost anything energy - after all, we would convert all [except for losses] potential energy into electricity.

Colleague SuperMarker I advise you to read about pumped storage power plants and read a high school physics book to realize that it does not pay off. It is different in the case of such pumped storage power plants - but the mass that we can easily store is some millions of tons and the generators and pumps used there are much more efficient than such generally available "motors". Water electrolysis would be a much more efficient energy storage.

Such solutions have been successfully used in technology for hundreds of years. My great-grandfather's old clock, over a hundred years old, has just such a "gravity accumulator" and it still works. Once a week you have to "charge" the battery by lifting the weights hanging on the chains. One of them drives the pendulum and the other the chimes. I don't remember if this mechanism had to be serviced, at least in my lifetime.
In our case there is only the problem of scale and efficiency of energy conversion. Losses must always be reckoned with, but the idea is good, old and proven.
The idea with the flywheel is similar. At one time in Germany, gyrobuses were operated on several lines. These were buses with an electric flywheel mounted on the loop, and the energy was sufficient to reach the other end of the route in an ecological manner. A small detail - the flywheel cannot be called a gravity accumulator, but the principle of operation of pumped storage power plants is. I am convinced that, even taking into account the considerable losses, such an arrangement on the plot makes sense. I have practical experience with lifting heavy loads to considerable heights with a winch powered by car batteries. You can lift several tons to heights of up to 100 meters, but each time 4 batteries of 100 Ah (connected in parallel) are almost completely discharged. The winch heats up so much that it needs to be cooled - waste of energy. But the whole system works and the situation can be reversed - unfortunately with further losses - nothing for free!

It's nice to read this topic, where we have a perspective of 2008-2021.
During this time, for example, kinetic magazines were worked on and it turns out that they can achieve an efficiency of about 90%.
I would like to use such a kinetic energy store, because it probably needs much less space.

On instsani en you can find a brief overview of several gravity technologies - and I already understand what can be done with mine shafts.

This is how you read the pseudo-experts from many years ago, today there are 'gravity' installations that work with an efficiency of 80%.

Bemx2k wrote:

there are already '' gravity '' installations that work well with an efficiency of 80%.

They work Then give a link to such an installation operating on an industrial scale.
I do not mean pumped storage power plant, but it is also a gravity installation.

Why are you digging up such antiquities? I don't think there are any meaningful topics for discussion anymore. This one does not make sense either, and the author of the last post has not appeared on the forum since then.

Bemx2k wrote:

This is how you read the pseudo-experts from many years ago, today there are 'gravity' installations that work with an efficiency of 80%.

The experts above are pretty good, because they can, based on simple calculations, quickly assess which project will fail in most foreseeable cases, regardless of the design solutions used. The ability to avoid losses - not to get involved in projects that will produce the expected results - is a very valuable skill. Sometimes someone will find a solution to a problem that seemed impossible to solve, but that does not mean that every engineer should now pull out a briefcase with the word "hopeless projects" and devote himself to them completely, abandoning those that are likely to be implemented in a year or two or five.

Q600 wrote:

On instsani.pl you can find a brief overview of several gravity technologies - and I already understand what can be done with mine shafts.

The hoisting machines are going to be scrapped, and the hoisting shafts and mines are buried, so do not count on the fact that there are unused several hundred meters holes in the ground somewhere that can be obtained cheaply - you have to dig one yourself and arrange all the formalities beforehand.

Perhaps this is why the excavation was made, that someone still dreams of such energy storage. Now the Australians want to do it. Link .

LEDówki wrote:

Now the Australians want to do it

Below you have a link to a calculator that allows you to calculate, in any energy units, including kWh, the potential energy of the mass (m) raised to the height (h) https://www.calculatoratoz.com/pl/potential-energy-calculator/Calc-280 FormulaId = 280
If the calculator calculates correctly, the weight of 400 tons, lowered into a shaft with a depth of 1,200 meters, theoretically (assuming lossless energy conversion) will produce about 1,300 kWh, i.e. about 1.3 MWh.
With a sink rate of 1 m / s, the warehouse can work for 20 minutes with a power of approx. 4 MW.
After lowering the mass to the minimum level, it has to be lifted up to load the emptied magazine.

The calculator will also show that all home methods of such energy storage do not make sense, except for a clock powered by weights (post # 18).
For example, a weight of 300 kg lowered from a height of 15 m will theoretically generate 0.01225 kWh of energy. Less than two 3.6V / 2000mAh rechargeable batteries.

vodiczka wrote:

Bemx2k wrote:

already today there are "gravity" installations that work well with an efficiency of 80%.

They work Then give a link to such an installation operating on an industrial scale.
I do not mean a pumped storage power plant, and this is also a gravity installation.

You say, and you have! It happened to me two years ago. I had to bury it, but I found it.

https://www.gramwzielone.pl/magazynowanie-ene...azyny-energii-wchodza-na-rynek-duze-zamowanie

...BROM... wrote:

I had to bury it, but I found it.

I wentogle "gravitational energy storage" and your link appeared in the third position.

Have they fulfilled the order There is only information about obtaining the order and about the operating pilot installation.
Energy Vault has so far built a 5 MW gravity energy storage. A demonstration installation is located in the Swiss region of Ticino.

@vodiczka I suspect that the main activity of Energy Vault is to make a good impression in front of investors and they are not doing very well:

I've read a bit about it. I would like to emphasize that I am a layman, but something does not agree with your calculations. A 2-ton block falling from a height of 5 m is only 0.03 kWh? There is something wrong here, my dear.

Przemyek wrote:

I've read a bit about it. I would like to emphasize that I am a layman, but something does not agree with your calculations. A 2-ton block falling from a height of 5 m is only 0.03 kWh? There is something wrong here, my dear.

If something wrong, present your calculations and we'll show you where the error is. But you are right, buddy, because it comes out even less, which is 0.02725 kWh. Up to 0.03 kWh is even a bit missing.

Przemyek wrote:

I would like to emphasize that I am a layman, but something does not agree with your calculations

Doesn't agree with what? To compare, you have to have something. 1 kWh is a lot - 3600 J, decent electric cars use 0.15 kWh / km, so they can travel 6.7 km per 1 kWh. If you do not use primary school physics (i.e. your school leaving certificate is a fiction), then judge on a peasant's mind how many "kilometers" a car weighing 2 tons should travel down a 5-meter hill - assuming that the slope can be selected so that he didn't stop.

Comparing the calculated over 28 Wh with 0.15 kWh / km, the range is 185 m, which gives a slope of 2.7 cm per 1 m - does it seem realistic to you?