Potential Energy Storage: Investigating the Mechanics of a Heavy Weight Drop

[Danimal]

I read about a proposal for storing potential energy by hoisting heavy weights that can be dropped when needed to generate electric power. So using the numbers from a hydraulic turbine from Hoover dam, how heavy would a hanging weight have to be to generate 178,000 horsepower as it descended? What's the optimum height / weight / drop speed for such a mechanism? How much would be lost in friction when hoisting it? How practical is this concept?

 

[Bystander]

Calling the WTC one Mt, and dropping it in 10 seconds, my estimate 20 years ago for the HP of the collapse was between one and two hundred thousand; this accounted for the lack of identifiable remains.

 

[anorlunda]

Calling the WTC one Mt, and dropping it in 10 seconds, my estimate 20 years ago for the HP of the collapse was between one and two hundred thousand; this accounted for the lack of identifiable remains.

Ouch. Technically correct but in terms of humanity a very cruel example.

 

[Danimal]

Ignoring the insensitivity of the chosen example and substituting a block of concrete as the model, assuming you could increase the weight and decrease the drop length, so a 500,000 ton block of concrete (without any human beings inside) could you drop 1,800 feet in ten seconds for the same HP? (I know it didn't drop all at once but just as an example) Could I have a million ton block of concrete drop 900 feet in ten seconds? How about a two million ton block of concrete drop 900 feet in 20 seconds? Eight million ton block of concrete drop 450 feet in 40 seconds?

 

[Drakkith]

Let's hope my math is correct here.
1 horsepower = 745.7 watts, so 178,000 hp = 132,734,577 watts, or just about 133 MW.
1 watt is 1 joule per second, so 133 MW is 133 million joules per second.
Let's assume a 12-hour runtime and a 12-hour downtime to 'recharge'.
Twelve hours is 43,200 seconds, which means we need 5.745 TJ of energy.
Let's use gravitational potential energy and assume a maximum drop of 100 meters.
Near Earth's surface, the equation for GPE is $U=mgh$ where $U$ is the potential energy, $m$ is the mass, $g$ is the acceleration of Earth's gravity near the surface, which is 9.81 m/s², and $h$ is the height. Our rearranged equation to solve for $m$ is $m=\frac{U}{hg}$.
Plugging in our numbers, we get about 5.86x10⁹ kg, or 5.86 million metric tons.

So a mass of 5.86 million tons, falling over a height of 100 meters, will provide 178 MW of power for 12 hours assuming no losses in your generator and that the entire setup is geared correctly to get the correct drop rate.

For comparison, 5.86 million tons is 5.86 billion liters of water. This is a cube of water 180 meters to a side, or nearly two football fields long, wide, and tall.

Luckily, large generators (not turbines) are about 95% efficient, so assuming a small loss in our gearing, our mass wouldn't need to increase drastically over what I've given here to account for inefficiencies. Unfortunately you'd be hard pressed to design and build the equipment to suspend this enormous mass and all the gearing to convert its linear drop into rotational motion for a generator. It's the equivalent of suspending almost 2,000 fully fueled Saturn V rockets, or about 100 Iowa-class battleships.

 

[Baluncore]

178,000 HP = 132.75 MW = 132.75 MJ/sec
PE = m·g·h;
PE / g = mass·height ;
132.75 M / 9.8 = kg·metre/sec
The mass in kg * vertical velocity in metres/sec = 13.55e6
If the mass dropped at 100 m/sec, then the mass would need to be;
mass = 13.55e6 / 100 = 135,500. kg = 135.5 tonne.

 

[anorlunda]

If you're willing to use liquid mass rather than solid, we already have devices that do that at scale. We call them pumped hydro. They are roughly 80% efficient.

 

[The Fez]

There are people working on this concept, with pressurized water lifting a huge weight up and down, and then running through a turbine, similar to pumped hydro, but without the large footprint/ecological concerns:

https://heindl-energy.com/

I think what you guys had calculated is in the ballpark, I remember about 7 million tons or so. Obviously a huge undertaking but as you can see from the link above, people are taking it seriously. There are also some smaller modular technologies using automated cranes.

 

[anorlunda]

There is another proposal to make use of unused railroad locomotives. There are thousands of them in the USA. Drive them up to a mountain top parking area at night, then let them generate while rolling down the next day.

They could be augmented by hopper cars full of dirt.

Right now, they are being stored in huge storage areas, doing nothing useful.

 

[sophiecentaur]

in terms of humanity a very cruel example.

I remember a documentary film about the meat processing plant in Chicago(?) in which the animals walked put to the top storey of the building and their bodies / body parts, after slaughtering, moved down the processing line under gravity. No motors were involved. (Not much refrigeration either, iir)

 

[Dr.D]

Does a hanging weight move? I would have thought not, and if it does not move, it cannot do work. If it cannot do work, it has zero rate of doing work.

Are we perhaps talking about a falling weight? If so, falling subject to what sort of resistance?

 

[russ_watters]

how heavy would a hanging weight have to be to generate 178,000 horsepower as it descended? What's the optimum height / weight / drop speed for such a mechanism?

This example really is fine to keep in IP units: a horsepower is 550 ft-lb/sec. So that's 178,000 X 550 = 97,900,000 ft-lb/sec.

Pick any combination of feet and pounds and divide. E.g., 97,900,000 lb and 1 foot per second.