Best electricity generation from a magical conveyor

Question

The setup

I have a conveyor that is 10m long and 2m wide. The belt moves at 15,6m/s (56,16km/h).this is a magical belt that when placed, will never move from it's spot. If you remove the foundations, it'll just float there. Disregard things like Earth rotation or flying through space. If it is placed a meter from my house, it'll stay a meter from my house. It is also indestructible. The return part on the bottom of the conveyor is accessible as well, giving 10m extra to work with. There is 10cm between the conveyor top and bottom.

The conveyor is made of indestructable rubber, relatively smooth but designed so items do not slide on it.

The speed of the belt is constant. It is unable to lose or increase speed, nor can be stopped.

Electricity generation

We have a great opportunity here to make a free energy source. Theoretically it it is infinite. If you have further indestructible materials, you can just keep increasing the size or amount of dynamos to create more and more energy. However, the world does not consist of indestructible materials [citation needed].

What would be the best method to generate electricity in a day? Keep in mind that breaking real world stuff during power generation is allowed, but the contraption should pay for itself. If you generate 1kW with a wheel or 2kW but use something expensive that breaks, the 1kW is preferred. Side effects not part of the contraption can be disregarded. If the surrounding countryside burns down because of heat, this is not part of the contraption and allowed.

The best method would:

• create the most electricity from this conveyor in any way possible.
• have the best contraption cost to energy generated in a day.
• has the best scientific explanation why this is the best method.

I've made this science based, as the details aren't 100% covering every detail, which gives some agency to the people answering the question.

Answer 1

Okay, I spent way too long thinking about this, trying to come up with a way to extract nuclear power or using some crazy relativistic effects, which may be possible, but I ended up going with straight mechanical force output.

Item 1 - Friction is not an issue for the top conveyor, you can simply stack more weight on the interface for the top conveyor to increase the normal force pushing down until the infinite conveyor will move whatever you put there. Normally this wouldn't be possible but the magic conveyor magic and will not stop, which leads to item 2.

Item 2 - The issue with engaging the conveyor is breaking your interface, so it's a strength of materials issue. So some rough numbers for super strong titanium alloys or high strength steel alloys puts you in the realm of 500 MPa shear strength as the max strength possible for an interfacing material.

Item 3 - How much force can the conveyor exert before exceeding this strength. Your interface can cover 500 Mpa without breaking so over a surface area of 2m x 10m you can get a force of 10^10 Newtons of force.

Item 4 - How much power is this. Force x velocity is power. So... 10^10 Newtons x 15.6 m/s = 156 GW of power.

Now theoretically you could do the same for the bottom, but you would have some real issues engaging as it's not as simple as making it heavier to prevent slippage, while relying on the strength of the conveyor to hold it, but I'm going for a theoretical maximum here so assume it works and you get twice as much by using the top and bottom surfaces. So you're looking at max power out as 312 GW.

Now you asked for electric power. Mechanical to electrical conversion can be pretty efficient, the highest conversion efficiencies get up to around 98%. So I'm going with around 306 GW of electrical output. We're going to ignore how you dissipate the 6 GW of waste heat from conversion inefficiency as well as many other practical limitations which would likely lead to you getting much less, but if you want the max theoretically possible: 306 GW

Answer 2

The limiting factor on your magical conveyor belt is that it will always move at precisely the same speed. On the other hand, the thing that makes the conveyor potentially great is that it will always move at precisely the same speed. No matter how much load you add, it will keep trundling along.

In theory, you could make great use of this. Simply press an axle (small wheel on the contact surface optional) against the belt and hook the other end up to a humongous gear, which in turn drives a much smaller gear connected to the driveshaft of a large dynamo (think the ones in hydroelectric dams or nuclear power stations).

In practice, however, this is not workable. As you pointed out in your question, while the conveyor belt can take infinite load, the materials of the gears cannot. There is another problem too, although less obvious: friction.

As you describe it, the magic conveyor belt does not have any convenient points to mount a gear. Therefore, in order to extract energy from it, you have to use a wheel pressed against its surface (as I described earlier). Even if the belt surface has infinite friction, whatever material you use for the contact surface does not. Once you put enough load on it, the contact surface will begin to slip or erode* away.

While the conveyor has (theoretically) infinite energy, the amount of actual usefulness you can get from it is pretty limited. At best, I imagine that you could power a neighborhood using the setup I described above.

^{* This brings us back to what I mentioned about the load limits of gears. In the end, a gear is just a way of artificially increasing the friction between two wheels so that the limiting factor becomes erosion (teeth snapping) instead of slipping.}

Answer 3

First idea: make heat from friction. Cover the belt with a deep layer of sand or gravel (or other material?) whose weight pushes it down onto the belt. Friction creates huge amounts of heat as it drags sand through sand and grinds it to dust, and friction between the belt and any material touching it. Immerse in water (or other working fluid) which boils, driving steam turbines. We're not limited by materials strength, we just keep feeding gravel into the crusher. But this relies on consistent forces pushing gravel into the belt, no jams in the gravel.

The water could be salt water, doubling as a desalination plant (unless too much salt ends up in the air/vapor and corrodes the turbines), or ore smelter if we omit the water. The belt is presumably indestructible by heat as well as mechanical puncturing / scraping / cutting.

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Or extract mechanical work directly to turn generators. Building on the ideas of others, especially Josh King's upper bound on force from materials strength limits. And the OP's invitation to take liberties with the details of the belt (letting it deform to fit around a shaft).

This could semi-plausibly extract a significant fraction of Josh's theoretical max power, given material strength limits. Like within an order of magnitude of that 306 GW, so perhaps 30 GW. (The world's largest real power plant is the Three Gorges Dam, generating 22.5 GW from 32x 700 MW turbines.)

A large-diameter round metal shaft seems like the best bet to extract work from the belt. Along the length of the shaft, to either side of the belt, cut gears into it so multiple gearboxes can extract reasonable amounts of power, with each one being far from the strength limits of steel so it's possible to build bearings and smaller gears that turn faster.

This also spreads out the waste-heat, although if there's a lot right around the shaft, perhaps capture that for district-level heating and/or boiling water for desalination and/or steam turbines. But we can't let the steel or titanium shaft get red hot, that would weaken it. Fortunately metal conducts heat quite well, and portions with a stainless steel coating could have water poured over it for cooling.

The shaft is heavy and much of its weight is supported by the belt, for large contact friction forces. Far to either side of the belt, there are bearings that keep it stable and gears that it rests on to transfer power into. (I'm picturing the shaft would flex from having its weight supported mostly at the middle, so the metal is constantly bending in different directions as it rotates (tension at the top, compression at the bottom). This might not be viable for a huge driveshaft. So heavy rollers might be necessary to apply force at the belt contact, not the shaft's weight.)

We need a large contact-patch, not like a bike tire that only touches the road over a few cm:

• A very large diameter as suggested by @John, like 51 m, so the bottom of the shaft is close to flat over the 10 meter linear distance of the belt which it sits on top of. (With the belt deforming to wrap around and get a lot of its surface in contact.)

• Or, just under 10 m diameter with the shaft between the belt's top and bottom surfaces so it contacts it on both sides. Total contact should be over more than half of the shaft's circumference, for the full 2m width. This requires the rubber to be able to deform a lot, into a nearly round shape. But if we're lucky, this can apply huge contact forces on both sides of the shaft without it needing to weigh as much as the great pyramid of Giza.

  We can also stack another shaft on top, so the top side of the belt is basically squished between two rollers. But the top shaft would have a tiny contact area. It's still free power, though, and other rollers at angles are possible, especially near the "ends" of the belt where it curves away from our middle shaft to meet the indestructible rollers that are part of the magic belt.

  The contact forces aren't uniform along the contact area: to highest forces are at the top/bottoms, although rollers pressing the belt in could help. If the belt can stretch like this, we're increasing its surface area, which would clearly be "cheating" if we insert many different shafts from the side to stretch it around them. So this might be disqualified.

To contact a perfectly flat belt that won't deform, we could maybe have a segmented metal belt/tread of flat plates, like tank tracks? But that would require huge tensile strength of hinges or chain links, and probably have non-constant friction forces so might slip or make the shaft turn in a jerky way, with surges and dips.

Answer 4

Turning relatively low-speed rotation into electricity is exactly what a wind power plant does. We can use all the same principles, merely replacing the rotation powered by wind with rotation powered by the conveyor belt. Simply add some friction-based drive wheels along the belt surface, and gear up the rotation to drive an alternator. You can add as many assemblies as you have room for - since the belt never slows down, it can drive any number of machines. You're only limited by the number of drive wheels, linkages, and gearboxes you can fit.

Off-the-shelf wind turbine gearboxes will get you into the multiple megawatt range very easily, and you can of course optimize from there. You can pack in more gearboxes by making them smaller (but more likely to break), and you can reduce frictional losses inside the machine with more precise machining. There are too many economic and engineering factors to put a number on whether building a particular gear to a tighter tolerance is going to make the machine more profitable or not, or where you hit the exact limit of extra gearboxes' frictional losses canceling the power they produce.

Answer 5

We are limited by maximal force possible to transfer laterally through 2m x 10m of material which is the maximal surface possible in contact with the conveyor at any moment. This is described by shear yield strength. With high end steel that might be around 1000MPa. Multiplied by area 20m2 gives 20 giganewtons force. Power is force multiplied by speed 15,6 m/s which gives 312 gigawatt.

It is admittedly more like theoretical limit, you will need huge wheel to have the contact area snugly fit to whole 10 meter conveyor. That depends on how stiff the conveyor surface is. You need giganewtons of vertical force anyway that means the wheel should weigh thousands of tons.

Answer 6

It is about 3 gigawatt generator about the same of a large nuclear powerplant.

Your biggest limit is friction, so you what as big a contact surface as possible. Ideally you want gearing but assuming you can't add gear to your belt really big wheels are the next best thing is as big a contact surface on the belt is possible.

Ideally you want a wheel at least 51 meters in diameters so 1/16th of the wheels surface is the same as the belt to maximize contact area. But really the bigger the wheel the better, a solid steel wheel as big as you can make is best, then you cut grooves in it and rubber coat it for a rubber to rubber contact surface. Of course you can put a wheel on both sides of the belt so you really want 2 such wheels, one on each side of the belt. the one on the bottom is more of a pain since you need it to push up but some creative use of leverage can manage that. The idea is to generate as much torque as possible then you gears to step it up to dynamo speeds. This is similar to a wind turbine but you want your own system, wind turbines suffer from limits of material strength due to having to balance weight, but you don't care how big your gear box is, it can be bigger than your wheels even.

Alternatively have your wheel drive something much more robust like a water pump. You then store the water and use as needed, using regular turbines. this has the advantage of getting all the output if you start hitting material limits on your gear box. Of course you should be doing something similar with your dynamo energy since you will not be using all of it all the time. Pumped storage to create load stability. the downside is you need to build a BIG water tank

Your limit is your belt to wheel friction so that also set your maximum theoretical output, one side is rubber and the strongest friction coefficient for that is more rubber. A rubber to rubber contact has a coefficient of friction of 1.15. so lets try a simple bit of math 1.15 times the normal force is your maximum output, the crush strength of steel is 655000000 pascals and really you should be builidng it so this is close as possible to the force on the it. BUT the real issue is the sheer strength of your rubber contact, which is 6205000pascals. So 6205000 times 20 for the surface area times 2 for the second wheel and we have 248200000 newtons.

248200000 newtons times the speed of your belt in meters per second give us the watt output. 248200000 times 15.6 = 3871920000 watts.

Roughly a 3 gigawatt generator or 1/10th the output of the Three Gorges Dam generators, the largest powerplant on earth. Of course this is the theoretical maximum, real issues like axle friction will causes losses but no matter what you have for losses it is still a powerful generator.

Answer 7

The fact is you've designed a perpetual motion machine. Not just any perpetual motion machine, but one that can't be stopped: you've designed an unstoppable force. Such things are highly unphysical, since that implies an infinite reservoir of energy to draw from in order to continually overcome whatever forces are placed against the conveyor belt. Which, of course, doesn't exist.

But what if it did?

The fact that it's a conveyor belt is actually not even that important. A conveyor belt is, fundamentally, two wheels spinning in the same direction with a belt between them. So, you have two unstoppably-spinning wheels, so just hook them up to a huge generator and watch the power pour out. Nuclear reactors, hydroelectric dams, and wind turbines all operate on the principle that, using some applied electromagnetism, rotation can be converted directly into electricity. None of these things actually "extract electricity" or "power" from the source of energy (i.e. nuclear fuel, falling water, or wind turbines). They just convert one form of energy into another: in a nuclear reactor, the heat from the reactor core produces motion in a liquid or gas that flows past a turbine to spin it; in a hydroelectric dam, the falling water hits a turbine and spins it; and in a wind turbine, wind flowing past a turbine causes it to spin.

It's all in the spin: all of these generators operate on the principle (namely, Faraday's law of induction) that motion, usually rotation, can be converted into power. But you already have a source of infinite rotation that under no circumstances will stop; so why not just connect one (or, heck, both) of the conveyor belt's wheels to generators as large as possible? The only restriction on how much power you'll be able to generate is what kind of materials you have on hand; if you make the generator's Faraday's disk-like flywheel too big, the speed at which it rotates will pull it apart. But beyond that, you can attach as many flywheels as you want to a central axle, so you can functionally have as much power as you want (barring adding so many flywheels that the generator collapses into a black hole).

Answer 8

Not sure if I got this right.

If...

What would be the best method to generate electricity in a day?

...means "How to make this conveyor into powerplant that generates the most energy per day" then...

You can literally hook the most powerful generator to this contraption. Unit used in Olkiluoto 3 nuclear plant generates over 1700 MW.

To get to its operational 1500 rpm (it is in Europe, so you need 50hz) you need to affix a wheel with diameter of around 20 centimeter (or around 16 cm for USs 60hz) directly to a generator axle.

The wheel needs to be made of material that can apply enough friction so it won't slip while exerting over 2443 kilograms worth of pressure towards the conveyor.

Theoretically you can fit at least one on every side of the conveyor without need for complicated transmission.

...But if it that means that you need to start generating electricity as quickly as you can, ideally before the next morning.

Then best solution is to buy as many "home wind turbine DIY kits" as you can fit side-by-side next to your conveyor (if we wish to reduce transmission complexity). i.e. newer Automaxx model can generate 1500W (based on advertising) it operates up to 1400rpm which gives 21 centimeter wheels on axles (which I believe is more than generator width). If I did my math right that is 47 units per side x4 means (left upper belt, right upper, left lower,right lower). thats almost 30 KW in very stable setup that is (almost) DIY level of complexity (plus some very deadly amperage)