Gravity battery question

[MarcusThatsMe]

TL;DR Summary

The accumulated energy vs. rotations of a motor generator

I'm not a mechanical engineer, I'm just a curious mind that needs some help understanding the logic here.

I understand that a weight, say 120t granite cube elevated 50 meters has the stored energy of 16 kWh. Thus a gravity battery (Ep = m * h * g).

I'd imagine this has something to do with the conservation of energy. BUT, I'm going to ask anyway because to me these are two separate pieces.

So the granite cube falls to the ground hooked to a rope that spins some gears that in turn turns a motor generator. I get that the cube has a stored energy of 16 kWh, but how does that translate into the spinning of a shaft through a gear system to generate energy via a motor generator.

I have a mini 24v brush-less motor generator and just spinning the shaft with my finger is SUPER easy. I couldn't image that a larger scaled system would be that much different, to think that some 120t object would not be able to turn the shaft to generate more energy then 16 kWh is crazy to me.

It just doesn't compute in my head.

Is there some math or something that could put some sense to it?

 

[renormalize]

I have a mini 24v brush-less motor generator and just spinning the shaft with my finger is SUPER easy. I couldn't image that a larger scaled system would be that much different, to think that some 120t object would not be able to turn the shaft to generate more energy then 16 kWh is crazy to me.

Try attaching a large load (that is, a low-$\Omega$ resistor), or even a dead short, to the output of the generator and see how hard it is to turn. Scale that system up and imagine how hard it is to turn a much larger generator connected to a huge load.

 

[MarcusThatsMe]

Try attaching a large load (that is, a low-$\Omega$ resistor), or even a dead short, to the output of the generator and see how hard it is to turn. Scale that system up and imagine how hard it is to turn a much larger generator connected to a huge load.

Interesting, not something I've heard of, so that was a learning experience, I appreciate that.

But for this example, lets say that the output from the motor is optimized to allow the motor to function at its ideal RPM constantly. Whether through capacitors or flywheels to stabilize fluctuations, balanced charging if it's connected to a battery pack as an interim system between being used and other methods.

If the the power generation is optimized for ideal RPMs, just like my little mini 24v motor (which I forgot I had), I still can't see how 120 ton object with 16kw of potential energy couldn't turn something more then the shaft of just a 16kw generator which itself is just a little bigger then twice the size of my computer. I mean, we're talking about an almost 10 by 10 sq ft block of solid granite weighing 120 tons, and that can't turn efficiently a shaft that is probably the size of a christmas paper roll of a motor twice the size of my computer. It still doesn't compute.

Edit: I mean I guess I could potentially see issues when you use gears to increase the RPMS to 300 as the weight is falling.

 

[renormalize]

It still doesn't compute.

It does if you do the math. Here's a link to a calculator that computes the generator torque required to deliver a given power at a given rate of rotation:
https://binsfeld.com/power-torque-speed-conversion-calculator/
For example, in the US, a large portable generator rotates at 1800 rpm. If such a generator drives a 10 kW load, the torque required is about 53 N-m (assuming 100% efficiency), which is about half the peak torque of a gasoline motorcycle engine. You certainly can't provide that torque at 1800 rpm by hand! But your 120 (metric) ton block falling through 50 m certainly can if it's connected to the generator through a gear-train that slows it's rate of descent such that the block takes 96 minutes to complete its fall.

 

[Baluncore]

I mean, we're talking about an almost 10 by 10 sq ft block of solid granite weighing 120 tons, and that can't turn efficiently a shaft that is probably the size of a Christmas paper roll of a motor twice the size of my computer. It still doesn't compute.

Think of, and analyse the system, as "flows of energy", not as a mechanical collection of mismatched parts, that would probably be impossible to operate efficiently in practice.

Consider converting the granite mass into a mass of water that can be pumped up a hill into a reservoir, then operated as a hydroelectric generator to recover the energy.

 

[256bits]

TL;DR Summary: The accumulated energy vs. rotations of a motor generator

I couldn't image that a larger scaled system would be that much different, to think that some 120t object would not be able to turn the shaft to generate more energy then 16 kWh is crazy to me.

If the 120t object is connected over a pulley by a rope to another 120t object, would you think that the first 120t object could raise the second to a height greater than what the first was?

Mechanical-electrical systems perform the same energy conservation, where energy is converted from one form to another. With the first 120t turning a generator as it falls, the generator supplying electricity to a motor lifting the second 120t, the second 120t can be lifted only to a height as what the first 120t was at.

Maybe this is what's troubling you, unless a typo.

I still can't see how 120 ton object with 16kw of potential energy couldn't turn something more then the shaft of just a 16kw generator

 

[MarcusThatsMe]

It does if you do the math. Here's a link to a calculator that computes the generator torque required to deliver a given power at a given rate of rotation:
https://binsfeld.com/power-torque-speed-conversion-calculator/
For example, in the US, a large portable generator rotates at 1800 rpm. If such a generator drives a 10 kW load, the torque required is about 53 N-m (assuming 100% efficiency), which is about half the peak torque of a gasoline motorcycle engine. You certainly can't provide that torque at 1800 rpm by hand! But your 120 (metric) ton block falling through 50 m certainly can if it's connected to the generator through a gear-train that slows it's rate of descent such that the block takes 96 minutes to complete its fall.

That's what I was looking for, thank you!

 

[MarcusThatsMe]

Consider converting the granite mass into a mass of water that can be pumped up a hill into a reservoir, then operated as a hydroelectric generator to recover the energy.

That's an interesting thought experiment.

So with a granite weight we're looking at 16 kWh with 102 tons of granite dropped from 50 meters.

With 102 tons of water (76301 gallons), that would be releasing roughly 1271 gpm to stretch the hour, or 0.08 m3/s, which is sad. But... P = 0.9 (turbine eff) * 1000 (water den) * 9.81 (gravity) * 0.08 (m3/s) * 50 (head) = approx 35.31 kWh

So you'd generate twice the amount of energy basically utilizing water then the same amount of weight... Which is interesting.

 

[renormalize]

So you'd generate twice the amount of energy basically utilizing water then the same amount of weight... Which is interesting.

No, that's wrong because you're confusing power in watts = joules-per-second ($\text{kg-m}^2/\text{s}^3$) with energy in joules ($\text{kg-m}^2/\text{s}^2$). Your gravity-battery stores about 16 kWh of energy, which can, for a limited time, provide any amount of instantaneous power (large or small), depending upon how quickly or slowly you can release that stored energy.

 

[MarcusThatsMe]

No, that's wrong because you're confusing power in watts = joules-per-second ($\text{kg-m}^2/\text{s}^3$) with energy in joules ($\text{kg-m}^2/\text{s}^2$). Your gravity-battery stores about 16 kWh of energy, which can, for a limited time, provide any amount of instantaneous power (large or small), depending upon how quickly you release that stored energy.

I have to admit, reading that hurt my brain, but I like a challenge. Both those formulas look the same.

So you're saying the 16 kWh available in the gravity-battery is stored as energy (energy in joules), while the 16 kWh available with the turbine is power (power in watts).

I think that makes sense, since one is "generating" power and the other is "potential" energy for the most part. But what I thought I heard from others is that that 16 kWh of "potential" energy can ONLY be converted, regardless of method, into just 16kWh of power. I'm taking my assumption in that is incorrect.

So if that isn't the case, is there some formula or method to determine how to convert the 16 kWh of energy into what it "could" translate into as power? I'd imagine it would take in a number of variables... Maybe a basic example I could dive deeper into?

edit: Energy is such an odd thing. So I have my barrings kW = rate of energy produced, kWh total produced over time, in this case an hour. If the turbine produces 34.95 kWh that's 34.95kJ per second, thus your mention of joules-per-second. But the turbine is still producing 34.95kW of instantaneous power, and over an hour that's comes out to 34.95kWh, which hurts my head, you'd think if you'd consumed 34.95kW per second that over an hour it would be considered a lot more. But okay, I'll accept that since apparently that is how it is.

So the granite block holds 16kWh, does that mean it also holds 16kj. Or is it different because it's technically potential energy, waiting to be used. Which again, I'd have thought that whether its energy or power they'd equal out if you try to convert the energy to power of the same amount of time. If the granite block has 16 kWh and takes an hour to get to the bottom the most you could pull from that with a turbine is 16 kWh. Which would still mean that using water to turn a turbine would generate twice as much energy with the same weight/height, granted the water would I guess have the added water pressure of ALL the water above it pressing down on the turbine.

 

[Baluncore]

That's an interesting thought experiment.

The arithmetic is easier if you use SI units for science and engineering.

The meter on your house is an energy meter, NOT a power meter.
Avoid domestic kilowatt·hours, kW·h. Use the scientific joule, J.

The size of a machine or engine, is rated in watts, which is the flow of energy it can transfer, or convert, per second.
The flow of one joule per second is a power of one watt.

Avoid gallons, use m³. Your gallons are different to mine.
1 gal(us) = 3.785 litre; 1 gal(imp) = 4.546 litre.
https://en.wikipedia.org/wiki/Gallon

Avoid ton(short) = 2000 lbs. Use kg, or the metric "tonne" = 1000 kg.

 

[renormalize]

So the granite block holds 16kWh, does that mean it also holds 16kj.

Nope, 16000 W-h = 16000 W x 3600 seconds = 57.6 kiloJoules megaJoules.

Which would still mean that using water to turn a turbine would generate twice as much energy with the same weight/height, granted the water would I guess have the added water pressure of ALL the water above it pressing down on the turbine.

Nope, if you have 16 kWh of stored potential energy in the elevated water, assuming 100% efficiency the most energy you can extract by letting the water flow down to the low elevation is precisely 16 kWh. If it flows fast, you get high power for a short time; if it flows slowly you get low power for a long time. But both scenarios deliver the same 16 kWh of total energy. Because energy, unlike power, is conserved!

 

[MarcusThatsMe]

The arithmetic is easier if you use SI units for science and engineering.

The meter on your house is an energy meter, NOT a power meter.
Avoid domestic kilowatt·hours, kW·h. Use the scientific joule, J.

The size of a machine or engine, is rated in watts, which is the flow of energy it can transfer, or convert, per second.
The flow of one joule per second is a power of one watt.

Avoid gallons, use m³. Your gallons are different to mine.
1 gal(us) = 3.785; 1 gal(imp) = 4.546 litre.
https://en.wikipedia.org/wiki/Gallon

Avoid ton(short) = 2000 lbs. Use kg, or the metric "tonne" = 1000 kg.

Fair enough, I'll endeavor to utilize SI from now on.

So redoing things in SI...

102 tonnes = 102,000 kg
gravity 9.81 m/s2
height 50 m

PE = 102,000 * 9.81 * 50 = 50,031,000 or 50 MJ

I think that's right. But MJ is a measure of energy, not power, it's basically energy stored. So I'd assume based on how fast the 102 tonne block drops would determine how quickly that 50.00 MJ is released. If it fell within 30 minutes, then would that mean 1,667,700 joules would be released per minute. If that were converted to KW, that would be 27.8 kW. Right?

Then to do the same with the water based system:

1 tonne = 1 m3
102 tonnes = 102 m3 (or a flow rate of 0.056 over 30 minutes [1800 seconds])

[one second]
P = 0.9 (turbine eff) * 1000 (water density) * 9.81 (gravity) * 102 * 50 (head) = 45,027,900 = 45.02 MW

E = 45,027,900 * 1 second
45,027,900 J

[30 minutes]
P = 0.9 (turbine eff) * 1000 (water density) * 9.81 (gravity) * 0.056 * 50 (head) = 24,721.2 = 24 KW

... I think those calculations are right. If so then the weight would be a better then a water "battery" depending on the efficiency I'd imagine of the system to convert the energy from the weight into power.

Am I starting to get on the right track lol, I do appreciate you guys going through this with me, I'm trying really hard to understand how all this works, its fascinating stuff.

 

[Baluncore]

I have not checked your calculations, but if the mass and height are the same, then the stored and recovered energy should be the same, assuming 100% efficient machinery. Any difference is arithmetic, or a misunderstanding.

With a granite mass, the entire weight must be supported on rails, by a long chain and gearbox, even when no energy is being transferred. The mass is constant, while the height of the mass changes, proportional to stored energy.

The advantage of hydro is that the reservoir can have a vast capacity, while the pump and turbine need only be rated for the instantaneous power available or required. The height is constant, while the mass of water stored changes, proportional to energy stored.

A pump or turbine can have a variable geometry to increase the efficiency. For example, a constant speed turbine can drive an alternator, directly connected to the network, while the flow through the turbine varies with demand.

The hydrostatic pressure difference across the pump or turbine (in pascals), multiplied by the flow (in cubic metres per second), is the power (in watts).

 

[jack action]

So the granite cube falls to the ground hooked to a rope that spins some gears that in turn turns a motor generator. I get that the cube has a stored energy of 16 kWh, but how does that translate into the spinning of a shaft through a gear system to generate energy via a motor generator.

As you mentioned, your granite cube is a battery that stores energy, much like the fuel tank in your car. The rate at which your fuel empties depends on the rate at which your car's engine burns it. A bigger engine at full throttle will empty the fuel tank much faster than a small engine idling.

I have a mini 24v brush-less motor generator and just spinning the shaft with my finger is SUPER easy. I couldn't image that a larger scaled system would be that much different, to think that some 120t object would not be able to turn the shaft to generate more energy then 16 kWh is crazy to me.

This is a motor (or generator), thus not comparable with a battery.

16 kW.h (kilowatt-hours) means that this battery has enough energy to run a motor producing 16 kW for 1 hour or 1 kW for 16 hours. Assuming a 1 kW generator charging batteries, it would take 16 hours to charge them such that they hold 16kW.h of stored energy.

Assuming your mini 24v brushless motor would use 10 W to spin a shaft, your granite cube would be able to spin the same shaft continuously for 1600 hours.

This rechargeable AAA lithium-ion battery holds 750 mW.h or 0.75 W.h. You need 21333 of them to hold as much energy as your 16000 W.h granite cube.

An average human being can produce about 75 W over an 8-hour work shift. This means that it would require over 200 hours (over a 1-month period, approx.) for a human to lift your granite cube 50 meters.

In my mind, 16 kW.h is a lot.

 

[russ_watters]

Btw, you can buy or make a cheap hand crank generator to see for yourself how much effort it takes to run a small load and how much the effort changes under load.

 

[berkeman]

Btw, you can buy or make a cheap hand crank generator to see for yourself how much effort it takes to run a small load and how much the effort changes under load.

Yeah, on a visit to the Exploratorium in San Francisco with my kids a number of years ago, they had a great exhibit with a bicycle crank and pedals and various AC Mains loads that you could connect in (like light bulbs of different wattages, etc.). It was a great demonstration of what you can generate with your most efficient human mechanism (bicycling). I did not last long driving the 100W lightbulb, IIRC.

https://www.exploratorium.edu/exhibits/pedal-generator

 

[MarcusThatsMe]

Thanks everyone for your help, I've definitely learned a lot and have a much better understanding, I used to hate this sort of stuff as a kid in school, but I find it fascinating these days the mathematical perfection of it all.

 

[berkeman]

I did not last long driving the 100W lightbulb, IIRC.

And then there's this... (from Facebook today):