How many slaves do I need to keep my mountain palace supplied?

Question

As the (reputedly) Mad Wizard-King of Jagatap, I would like to move my court to the remote fastness I recently finished building in the be-jungled hills of Nam.

(Image from DudQuitter at DeviantArt)

The altitude and fresh breeze makes it quite pleasant, and the roof under the open stars is a great place for summoning Eldritch Horrors from the Beyond. Also, I like the view.

There are some practical problems with this setup, however. I like to keep a large court. A 600 man regiment, my harem, generous guest quarters, not so generous incarceration quarters, various apprentice wizards, advisers, flunkies, etc. You can see that it quite adds up. There is a reasonably good road, and a water source at the foot of the peak; but that is all about 300 meters below the main level of my palace.

I'm going to be moving in soon, but I need to know this: How many slaves do I need to bring with me to move food, water, and various other luxuries from the road below up 300 meters of steps to my palace?

Considerations

• Pack animals are more trouble than they are worth in this climate. They die within the year from disease, and I just don't want to spend the money. Slaves will last 5 years easily, as long as you feed them once in a while. And let me tell you, as a Wizard-King, you just seem to acquire slaves by the thousand.

• I suppose I could summon a Terror from the Beyond to do the work for me, but they have to be bargained with or magically subjugated or whatnot. If I keep my palace running for a few centuries, there are going to be a lot of pissed off Abominations in the Beyond. I don't want to deal with that.

• Assume that I keep 1500 people in the palace. Do remember to count the slaves in your calculations, I want them to last the full 5 years, remember?

• The goods and supplies I need only have to be brought up 300 meters. Transportation of goods from nearby settlements is already handled.

• Mechanical solutions reek of 'progress.' Generally, people who reek of progress find themselves in my throne room. Or at least, their skull does after the vultures have had their fill.

Answer 1

Actually, fewer than you think.

Suppose the 1500 "nobles" in your court, in addition to 3kg of food and 1 kg of water just for consumption, also use on average 11kg more water to wash (I mean who needs to wash daily when you're an evil lord? You can just keep a water reserve in the palace and wash on sundays. And if anyone mentions your smell, you'll have a nice new skull in your skull throne.)

That's 15kg per person in the palace, so that makes it 22,500 kg in total. Let's round it up to 25,000 kg, to have more "wiggle room".

This article speculates on how the Egyptians could have moved so many enormous stone blocks on top of the pyramids, using only manual labor and primitive technology.

In particular, this rolling stone carrier is interesting for our purpose:

This is perfectly capable of letting slaves move a 2.5 metric ton stone block up a slope, so you can easily stock it up with 2500 kg of food and water, packed in a way to keep it still when rotating.

The article also explains how many workers would be needed to move this thing uphill.

(You can also remove the hill-brake to have a little fun with your slaves. 5 year duration may not be guaranteed in that case. YMMV)

That's 16 slaves to pull it up a 5% slope. If you can't or don't want to build a ramp too long, you can up that to 10%.

Assume 12 kgf of pulling force per slave. The carrier on a plain surface requires a pulling force of 0.025 * 2500 = 63 kgf.

With a 10% slope, it would need 63 + (2500 * 0.1) = 313 kgf, so a total of 26 slaves per trip.

This way, you would only need ten trips per day. This means that the total number of slaves you need has a maximum of 10 * 26 = 260, if you want every team to only have to make one trip per day.

But I assume that's not what you want, so you can change this accordingly. I would say that they would be able to make 5 trips a day and last at least 5 years, so that means 52 slaves in total.

You could keep only 26 slaves and have them make 10 trips per day, but I'm not sure how long they could keep going.

You could always go "trial and error": first time, have only a single 26-slave team make the 10 daily trips. If they die after only 1-2 years, too bad; now you know you need 52 slaves. ;)

Also, all the food and water the slaves need are already accounted for in the whopping 2500 kg extra we put in at the beginning.

That means that, whenever you have extraordinary needs (like, one day you invite the Army of Oversexualized Witches™ over, and you need double the food and more water to wash beforehand), you can easily add a few more daily trips and just need 26 more slaves each. Or, what the hell, just have the same slaves make an extra daily trip. They're there to work, after all.

Answer 2

Let's see...

On level ground, the US Army assumes one soldier averages 20 miles (32,000m) per day carrying 50 lbs on their back. A 45-deg angle for the steps (100% slope) is much too steep, so let's back that down to 9 degrees (16%).

At 9 degrees, your steps are 1875m (horizontal, one way) and your average slave's reliable per-day average is around 24,000m (since it's not level). Each slave will do a round trip 6-7 times per day. Shallower steps mean longer distance, steeper steps slow progress; either way it winds up around 6.5 trips per day. Maybe some do 7 trips on some days.

If each slave carries 50 lbs each trip, one slave day of labor lifts 325 lbs (148 kg) at 6.5 trips per day or 300 lbs (136kg) at 6.0 trips per day.

Now let's look at daily demand per person at the top of the hill: Water is the big one - 40kg for drinking, cooking, washing self/clothes/palace. Pretty much everything else (food, mail, clothes, furniture, treasure) winds up being roughly equal to that daily weight of water, for a total per capita daily demand of 80kg. Remember - the whole point of a palace is being ostentatious. That means gardens and fountains and water-parties and spotlessly-clean ballrooms and lots of rich wastage...for which all supplies must be hauled up the hill.

If one noble or trooper requires 80kg hauled up each day, and one slave can haul 148kg each day, the number of active hauling slaves will be about 55% of the population at the top of the hill...if the slaves live at the bottom of the hill. Add in another 20% for the overseers and cooks and physical therapists for the slaves, and the total slave population works out to roughly 70-80% of the population at the top of the hill...if the slaves live at the bottom of the hill.

We can decrease the hauling slaves by about 35% (down to 40% of the palace population) by using carts on a gentler slope (say, 5% slope instead of steps). The longer distance means each slave makes a slower roundtrip (4/day, even with a shortcut back down for most), but transports much more (50-80 kg/lift, depending upn they type of cart/wagon). Note that it really doesn't matter at this point if we use 2-slave carts or huge 16-slave wagons, the average per-capita lift winds up being roughly the same.

However the question specified 'steps', and the wizard-king obviously doesn't care about economy, and carts smack of a disliked 'mechanical solution' so we'll drop carts and return to slaves plodding up steps.

Since the slaves live at the top of the hill, they and their infrastructure need food and water and a few goods hauled up too. Slaves probably get fewer goods and less mail, so let's assume each slave's daily demand to be about 60kg (most of which is just water). This assumes, of course, that the slaves don't have families with them during their 5-year sissyphan ordeal - spouses and children would really blow up those assumptions! After that it's basically a rocket equation.

So for a court size of 1000, that's about 550 active lifting slaves and 150 non-lifting slaves living at the bottom of the hill, or about 1020 active lifting slaves and 300 non-lifting slaves living at the top of the hill.

Now let's solve it backwards to achieve the Wizard-King's plan for 1500 to live on top of the hill: A court and garrison of 650 supported by 650 lifting slaves and more 200 non-lifting slaves. Note that a 17th-century regiment is about 1000 troopers, so the garrison must be a Regiment in name only.

Maybe we misunderstood, and the boss wants a non-slave population of 1500 - a full regiment plus a court of 500, supplied by 1600 lifting slaves and 320 non-lifting slaves. Considering the King's decrees so far, this might be more likely.

All hail the Mad Wizard-King!

Answer 3

Let's start with Naismith's rule. 5km/h and 30mins for every 300m climbed, that'll give you about 90mins for a round trip. Call it 2 hours because even slaves need to rest. We considered 1/4 to 1/3 of body weight reasonable to carry on long expeditions, these are slaves though and we don't want to get too soft on them, so half body weight is fine. Unfortunately this requires us to know the health and weight of your slaves, so I'll call them an average 60kg and give them a 14 hour working day, allowing each working slave to haul 210kg up the hill per day. It may be reasonable to push that to 16 hours, 8 trips and 240kg per slave, you're only expecting them to last 5 years after all.

Quora tells me that the average person consumes 1.8kg of food and 0.9kg of water per day (that's not enough water, you should be drinking more), total only 2.7kg per person or 4050kg for the whole court.

Some of your court are going to be average, but given that it's a royal court I think it's reasonable to at least double that, call it 6kg per person or 9000kg for the whole court. Of course some of the concubines won't eat that much but many of the senior courtiers will eat more. Meaning that each slave can supply 35-40 people's daily needs.

If you keep your slaves working hard, around 50* slaves are required to supply your court of 1500. This only supplies the daily essentials of course, but it shows that vast numbers are not required for basic supply.

Given the low numbers and the fact that apart from a few household slaves they can all live at the bottom of the hill, it's not necessary to worry about hauling up goods for the slaves themselves.

The real key to this is that you're talking <100 slaves rather than >1000. Or about 18,000 slaves a year if you're using those new disposable single use slaves.

* 42.8, but which bit of the slave do you cut off to make 0.8 of a slave?

Answer 4

Given the greenery around the castle and that you're in the jungles of Nam (jungle implying a lot of rain, whether seasonal or year-round), the water issue is likely trivially handled by cisterns within the castle itself that collect and store rainwater. Even though slaves hauling water up might be fine on an egotistical sadistic level, it creates a strategic weakness that's exploitable by a besieging force, or someone who just wants to put the screws to you by interfering with the water supply.

An average modern household in Canada--which leads the world in domestic water usage (and wastage)--will use 200 liters per person per day, and that's with all the conveniences such as flushing toilets, which are the biggest consumers of water. Get rid of wasteful flushing toilets and other wastes, and 50 liters per person per day seems reasonable for comfort, clean, and health.

So let's use that: 50 liters of water per day per person, and that's for all domestic use: drinking, cooking, cleaning, bathing, watering the plants and animals (that aren't feeding on the blood of the enemy, et cetera and so on), and the toilets. For 1500 people, that's 75,000 liters per day, or 75 cubic meters, or (assuming similar year length) 27,375 cubic meters per year.

On Earth, rainforests average between 175 and 200 cm of rain per year. If the total catchment area that drains into your cisterns is equivalent to a square 150 meters across (22,500 square meters), that's about 39,000 to 45,000 cubic meters per year, more than enough to handle domestic water needs.

For reference, 12 of the cisterns on the north side of Masada hold 40,000 cubic meters between them. In a desert. Surely the Mad Wizard-King of Jagatap can do better in a jungle than King Herod.

Answer 5

The picture buries the lede. Sure, you want water and food for guests and your court.

But someone has to supply that waterfall with water.

Have no fear! This is classical tech.

Have a sequence of screw's powered by treadmills that carry water up to the Palace. That is most of the mass you need to lift even if you didn't have a waterfall.

The water can be deposited into decorative water basins on the way up (as ridiculously long screws are unrealistic). Rain that falls can be trapped in these basis as well.

To carry goods and worthy visitors up, you can use a rope lift system. Simply attach two cages to a single rope with a pully on the top.

The cages balance each other's weight. Place an equal amount of stuff (garbage, waste, slaves, even barrels of water) in the "down" cage as the "up" cage, and now the only force needed is to overcome friction (of the pully).

Any slaves that "ride down" then take the stairs back up, along with the lesser visitors.

You'd want to have a "clean" cage and a "dirty" cage so goods or people on the way up don't get soiled.

For a more fun alternative, a huge Archimedes screw can have goods float on rafts or boats. Seal goods and make them float, then screw them up to the next pool.

So the question is, how many slaves do we need? First, what if we only wanted to supply the palace with water.

Human labor produces about 200 W.

If we want 4 kg of water per person per day, 2000 people (8 metric tonnes), and 300 meters of lift, that is 23520000 J.

A single slave working at 200 W can produce that much energy in 1.36 days. And waste down will match food up. So the number of slaves ends up being trivial; more a matter of packing the waste up and loading food than muscle power to lift it up.

But what if we want a waterfall? That looks pretty. Every inch of width of a waterfall is 200 gallons per hour, or about 20 metic tonnes per day. That waterfall looks about 20 feet wide, so we need 4800 metric tonnes of water per day.

4800 tonnes * 9.8 m/s^2 * 300 meters is 14 112 000 000 joules. At 200 W that requires 816 slaves working continuously. Perhaps double that due to system inefficiencies (leaks, inefficient screws, etc).

If we halve the width of the waterfall (so 10' wide), and shut it off half the time (at least during droubts), we are down to 400 slaves working 24/7. If our slaves only produce 150 W and they work for 12 hours/day then we can pull this off with 1000 slaves.

A side effect of this is that supplying your castle with water and food requires only a trivial amount of effort next to keeping the waterfall going. So having 90%+ of the slaves drop dead from a tropical disease just means your waterfall is turned off. You'll suffer, but the parties won't.

The trick to this much higher efficiency than other answers is because the slaves are no longer wasting effort going up and down themselves. Either they aren't going up and down (running the screws on a treadmill of some kind), or they convert their up-work into useful work (being counter weights to carry important stuff up).

This requires classical era mechanical technology: the Archimedes Screw, Ropes and a simple Pully.

The basins and the waterfall will require significant hydrological engineering, but less than the Romans had.

As a significant bonus, the raw splendor and waste of burning a thousand slave's labor on a waterfall should humble your guests.

Answer 6

Historically, the answer has been "as many as you can afford" (with the caveat that you need fewer free laborers than you do enslaved ones to carry out the same task, because it is much more labor intensive to supervise slave labor than free labor).

Levels of luxury and comfort are a product of available resources and are very much on a sliding scale.