# How can I generate electricity inside a cave network?

After a particularly large bombing raid during a war, a mountainous rural region is left mostly destroyed. Villages are in ruins, bands of survivors look everywhere for food and shelter, and all hope seems lost. The government of the small country has collapsed, and anarchy reins.

Then one inquisitive young boy finds a network of caves in one of the mountains. It seems like it can hold a large number of people rather comfortably. Some villagers set out to explore it, and over a period of a few weeks, people start using the caves as places to live, safe from the continued bombing runs. There's a river there, complete with fish for food.

One day, a bomb causes an avalanche, which causes the only entrance to the cave network to cave in. People frantically try to find ways out, but to no avail. Eventually, it is decided to "keep calm and carry on" while a few explorers try to see if somewhere in the depths lies a previously unknown way out.

Everyone staying behind need a few necessities, such as heat and light. They can make fire easily, and they have raw materials (e.g. enough wood to make about fifty homes, which is what the wood is currently being used for), but they need electricity to properly work the lighting system, previously powered by solar cells outside.

How can the villagers generate electricity?

• Don't forget a source of oxygen. – GrandmasterB Mar 22 '15 at 4:24
• If you only need light, it would be simple to have natural (small, too small for bombs) light-wells through the roof of your caverns. It's also useful for oxygen. – Petit Lama Oct 26 '15 at 13:23

If they have a few strong magnets available, using some of the wood, and wire salvaged from the lighting circuits, villagers could feasibly construct a crude dynamo which would not be very efficient, but would convert circular motion to electricity. The link takes you to examples of early dynamos, which are in essence very simple - multiple loops of wire moving through a magnetic field is all you need to convert mechanical movement to electric potential. With a simple dynamo, you can even feel the effort required to move the device increasing as power is drawn from the device.

The villagers could either take turns keeping the dynamo working, or could perhaps find a way to link the device to the water flowing in river using a simple water-wheel constructed from the wood they have.

The solar system for the lights would of had battery storage. If the batteries survived, they could be placed into the circuit to help smooth out power through any short downtime, allowing even hand-cranked power to keep lights on while whoever was working it could take a rest. Otherwise you will get some problems with maintaining the right levels of power.

With this hand-made setup I would expect voltage and power levels to be relatively low. Realistically you'd want to have LED lighting throughout and probably need to be very sparing with which sections of cave you kept lit or what else you used power for.

Here's a modern example where a whole house's power supply was run by people on exercise bikes (stepping up the power and voltage in your caves to this level would be far more of a challenge though, you'd need some decent tools and an electrical engineer or two to set this up in your caves).

If hand-building a dynamo seems far-fetched for your group of villagers, then many electric motors can be used as dynamos when they are hand-cranked - motors and dynamos are very similar internally. So if the villagers could perhaps salvage an electric winch or mobility scooter for tourists/visitors to the caves, then there could be a motor inside just suitable for the task. For believability you want a motor with high torque and low revolutions, and that was in a device run from a battery.

Update: I stumbled across this video "how to" where the presenter converts an old washing machine into a generator. Proof-of-concept for the idea.

• Hydropower is an excellent suggestion indeed -- no fumes to ventilate, and capable of "black starting" a grid. – Shalvenay Mar 21 '15 at 17:31
• If by motors and dynamos are very similar internally you mean identical... ;) There might be some differences in the construction of modern motors and dynamos, but in principle, they're the same object, the only difference being which ends you call the "input" and "output." I even asked Google for the difference between them and every link was basically "duh, a dynamo converts motion into power, whereas a motor converts power into motion!" and couldn't find any technical details about how they're made. – Draco18s Jul 13 '17 at 15:04
• @Draco18s: Yes I think the main thing to look out for is AC vs DC motor. AC motors from a brief search seem to be more fiddly to get to work right (e.g. may have preferred rotation speeds in order to generate anything at all). DC motors seem more forgiving. However, if any of the villagers in the story was an electrician, they'd have a pretty good shot at getting a range of things working in my opinion. – Neil Slater Jul 13 '17 at 15:20
• IIRC an AC motor will happy generate power, but to turn a motor, that motor would also have to be an AC motor. Been a while since I futzed around with such things, I just remember being Super Impressed by the notion of a slip ring. Other AC devices would probably have a fit if the frequency wasn't stable, I'm not an electrician. But yes, if the story features an electrician, the story can just say "and the electrician electricianed with the parts on hand and made a contraption that generated power when turned." That said, given the initial solar panels, everything's likely already DC. – Draco18s Jul 13 '17 at 15:30

You're underground? And you need to generate electricity?

Sounds like you want Geothermal energy.

The idea is to take heat sources from underground, and use those to generate steam. Those then drive your turbines and generate electricity.

It's generally very clean, non-polluting and 100% renewable, all very large bonuses for your cave system. All you need is a source - maybe an underground hot spring? And then you can tap into that.

• And geothermals also general warmth and hot water as a very nice bonus. – MichaelK Jun 18 '16 at 8:38

Wikipedia says that wood contains $14.9\text{ MJkg}^{-1}$, or $10.4\text{ MJkg}^{-1}$ at 70% efficiency. If you're burning your wood as a fuel source, then it'll burn at significantly less than 100% efficiency; 70% seems around right to me so we'll say 10 megajoules per kilo.

Enough wood to build 50 homes? You have a lot of wood there. About 30,000 board feet of wood goes into a house, which is about 262.5 tons[1]. Multiply by 50 and you get 13,125 tons. (Where are you even storing all of this??) However, that measurement is for all hardwood timber, which 14,000 board feet of the house is not, so we'll drop the measurement to 10,000 tons. So:

$$10,000\text{ tons} = 10,000,000\text{ kg}$$ $$10,000,000 \times 10\text{ MJkg}^{-1} = 100,000,000\text{ MJ}$$ $$= 1 \times 10^{11} \text{ J}$$

That's equal to 27,778 kWh. One kWh can run a heater for half an hour - thus, these 27,778 kWh can heat 50 rooms for 278 hours.

However, you have now run out of fuel. You might now be able to look at hydroelectric power, since there's an underground river conveniently in your caves.

The formula to calculate power output of a hydroelectric turbine is this:

$$P = \eta\rho Qgh$$

where

• $\eta$ is the turbine efficiency (average is 85%);
• $\rho$ is the density of water (1000kgm-3 for fresh water);
• $Q$ is the flow rate;
• $g$ is the acceleration due to gravity (9.81ms-1 on Earth); and
• $h$ is the height difference between inlet and outlet.

The only two there we don't know are flow rate and height difference, but these can be estimated: a subterranean river is not usually that big, so a flow rate of 50 cubic metres per second seems reasonable; and the height is unlikely to change a huge amount - we'll say 20 metres. This gives a consistent output (as long as the river keeps flowing) of:

$$P = 0.85 \times 1000 \times 50 \times 9.81 \times 20$$ $$= 8,338,500\text{ W}$$

Watts are joules per second, so this gives you a huge output - enough to power all your needs and store plenty - you might want to consider giving these people access to capacitors.

Perhaps what you do here is you burn some wood while you're working on getting the turbine running. Then you can still build some houses. Once the turbine is up and running you're not going to have any problems with energy.

• Yeah -- 8MW of hydropower is enough that once they get their own house in order, they can poke a couple copper wires out the door and start selling power to the neighbors! – Shalvenay Mar 22 '15 at 22:27
• Off by a few decimals on tons of wood by these source:1000 board feet weigh 8.75 tons, time 30=262.5 tons – user2448131 Mar 23 '15 at 0:46
• @user2448131 Ah that's where the mistake is. Thanks, I'll correct this later – ArtOfCode Mar 23 '15 at 8:41
• I love an answer that says the wood for a house weighs about 262,500 tons and doesn't blink. – NPSF3000 Oct 26 '15 at 9:05
• @NPSF3000 correction was required. Done now. – ArtOfCode Oct 26 '15 at 9:21

For you to explore energy from wood, or geothermal energy, or any energy based on heat, you need a heat machine. There are lots of machines that are called heat machines (or motors, or engines): Stirling engine, Rankine engine, etc.¹

In general terms, the larger the difference in temperature between the hot source and the cold sink, the larger is the potential thermal efficiency of the cycle. On Earth, the cold side of any heat engine is limited to being close to the ambient temperature of the environment, or not much lower than 300 Kelvin, so most efforts to improve the thermodynamic efficiencies of various heat engines focus on increasing the temperature of the source, within material limits. The maximum theoretical efficiency of a heat engine (which no engine ever attains) is equal to the temperature difference between the hot and cold ends divided by the temperature at the hot end, all expressed in absolute temperature or Kelvin.¹

For a heat engine to work, you need heat, but not only heat. You need a thermal sink. And that lies the problem of exploring energy inside caves while inhabiting it at the same time.

In the absence of a thermal sink, the ambient air temperature will raise. While the machine capacity to do work (or generate energy) will fall. The efficiency of a heat engine is given by : $$\eta = 1 - \frac{T_c}{T_h}$$

Where $T_c$ is the temperature of the cold, heat sink, while $T_h$ is the temperature of the heat source.

This means that if the rocks around the cave have low heat transmission and capacity, the temperature of the air will raise slowly, killing everybody, while losing efficiency at the same time.

In other words, you need to find a heat sink. If by luck your cave has access to a underground river, this might be a perfect thermal sink. Circulating water from the underground river to the heat engine and back, should provide enough capacity to drain heat and keep the engine running.

Now you face a problem with oxygen. If you burn all that wood to provide energy, your fire will drain oxygen from the ambient until it is not able to sustain life anymore. So, in that event, a geothermal source of heat would be much more usefull. Unless your geothermal source produces sulfurous gases. In that case, even a small concentration of such gases can be fatal.

To sum it up:

Your cave system needs a source of heat that does not burn oxygen neither produces sulfuric gases. There are certain formations where lava is not directly exposed but can render nearby rocks hotter than usual - without direct contact to the lava. While at the same time your cave network needs a source of water to be used as heat sink. Satisfying both conditions is hard but as this is a fantasy setting this might be done. In no event you should burn anything. Air inside the cave, if closed, is limited and would be drained by burning wood. You need metals and people able to produce engines. A crude dynamo etc. One of the simplest heat machines to build would be a stirling engine. Those are pretty efficient and simple if kept on atmospheric pressure levels.

The total heat rejected by a heat engine is the reciprocal of its efficiency. Lets suppose a heat engine working with a thermal source at 900K and a thermal sink at 323K. Efficience of the engine would be : $$\eta = 1 - \frac{323}{900}=1-03588888888888889=0.64111111111$$

This means that for each joule of thermal energy that is inputted into the engine, a maximum (not counting other loses) of 0.64 joules of mechanical energy would be generated into the machine output axis, while 0.36 joules would be directly rejected into the ambient. If you produce, say, 1kw of energy (sufficient for a bunch of lamps and a pump to bring water to the heat engine), this would need 1562 Watts of input energy and reject to the ambient 546 Watts of energy.

• Why my math does not work ? – Jorge Aldo Mar 22 '15 at 18:22
• Dollar signs, I think. – HDE 226868 Mar 22 '15 at 19:03

Well, They need a source of water if they are to live for more than a couple of days, and many caves systems have streams flowing through (often that is how they were formed).

So putting in a water turbine in a decently flowing underground stream would be a good start. You'd want to avoid burning things as much as possible until you know you have a source of oxygen and a good airflow through the caves or you will all suffocate from carbon monoxide/carbon dioxide poisoning.