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I watched a video about ancient monuments and mega-structures, found here: https://youtu.be/khjdheYDhiw?t=328

Each of the foundation stones for one of the ancient structures weighs more than 1,000 tons. Another stone shown weighed over 1,600 tons.

It's not clear how they moved such massive stones, but one obvious possibility is that they used human power (perhaps via a long rope system).

Is there a way to calculate how many average, adult males, it would take to pull a 1,000 and a 1,600 ton block 1 foot / 100 feet / 1 mile?

I know there are many factors to consider that could complicate this such as what the incline/decline is, how the rope system distributes the weight, and the friction caused by the type of surface it's being pulled on. But I'd like to simplify this as much as possible. So imagine a perfectly flat plane with a sand or dirt surface.

Image: 1,600 ton block

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  • $\begingroup$ Maybe also,mention how much force an average person can exert. Also i think there would be other factors like how much deep the stone goes into sand or dirt unless we consider it rigid. The velocity at which you have to move it . I think a simple frictional force equation could solve this if your aim was just to move the stone. $\endgroup$ Aug 26 at 14:16
  • $\begingroup$ Is there any chance that it's made of concrete? The Egyptians knew how to make it and I've read that some of their own concrete repairs are still good where as modern concrete from the 1900s has crumbled away. I always reckoned that building the pyramids with shuttering and concrete would explain the perfect fit and be an awful lot easier than mullocking massive blocks across the desert. $\endgroup$
    – Transistor
    Aug 26 at 18:47
  • $\begingroup$ Levers. Pulleys. If you search around a bit, you can find folks who have built multiperson lever+rope rigs which seem to work pretty well to "walk" a stone up a hill. $\endgroup$ Aug 27 at 13:57
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This is not an answer. It is an extended comment on why this calculation is impossible - IMHO - to be accurately answered.


For the calculations, I'll assume that the maximum pull force of a person on a rope is on average his body weight (think about pull ups - although many people can't do them). So a 80 kg person can produce a 800 N push force.


Perfect rolling

I will take the simplest case. I.e. a flat plane, with rigid surface (no dirt), and assuming you have perfectly round (and rigid) logs. In that scenario, the friction between the floor or the logs would not be affecting the rolling (there will be no friction losses because there will be only rolling).

In that case, only one person could actually move the mass - albeit very slowly. He would actually be able to consistently accelerate it, with an acceleration of:

$$a = \frac{F}{m} = \frac{800 [N] }{1600000 [kg]} = 0.0005\frac{m}{s^2}$$

so it would take him about 40 minutes at full force to get this stone to move at 1[m/s].


wheel on granular media

The moment you move away from the above assumption, (perfectly round log, or rigid surface) essentially the following condition occurs

enter image description here

Figure source

In this scenario, you need to have a lot more information (i.e. internal angle of friction for the sand/dirt, thickness etc) in order to determine the forces of resistance.

Friction case

In the worst case scenario (almost) where people would just drag the stone on a flat plane - without any wheels, then the coefficient of friction would play a role. Assuming a value of 0.1, then you'd still need to apply a force of $\mu\cdot W=\mu\cdot m\cdot g= 1600000 [N]$, that would mean that you'd need about 2000 people of average weight of 80 kg.

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The simplest weight-moving mechanism in ancient times is pictorially shown below. The weight was placed on wood logs and rolling ahead. The movement was done by the pulling and pushing of the slaves using ropes, rods/levers, and hands. You can estimate the number of slaves required if you know the following parameters - $W$(weight), $\mu$(rolling friction coefficient), and pulling force/capacity per person.

enter image description here

General Equations:

$W = m*g$, in which, $m =$ mass (kg, lbm), $g =$ specific gravity $(9.81m/s^2, 32.2ft/s^2)$

The frictional force, $F_f = \mu*W$, $\mu =$ rolling friction coefficient

Now, estimate the number of slaves required to initiate the movement:

$n. Slave = \dfrac {F_f}{pulling.force.capacity.per.slave}$

Approximate Data:

  • Rolling Friction coefficient, $\mu$, = 0.2 (Approx.) Note, physicists at the University of Amsterdam investigated the forces needed to pull weighty objects on a giant sled over desert sand, and discovered that dampening the sand in front of the primitive device reduces friction on the sled, making it easier to operate. The findings help answer one of the most enduring historical mysteries: how the Egyptians were able to accomplish the seemingly impossible task of constructing the famous pyramids.

The rolling coefficient can also be expressed as $\dfrac {\mu}{r}$, in which $r$ is the radius of the log (wheel).

  • Pulling/pushing capacity of a person = 1.5 to 2 times of body weight.

enter image description here enter image description here enter image description here [enter image description here] 5http://www.renegadetribune.com/uncovering-the-impossible-6-of-the-heaviest-ancient-stones-ever-made/

Note: This technic is still in use today when there is a need to move the entire house (less foundation) from one location to the other without tearing it apart.

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  • $\begingroup$ They still have the initial effort to pull the 1,600 ton brick onto the logs in the first place, which would take even more work (not saying they didn't, just noting) $\endgroup$
    – TCooper
    Aug 26 at 23:15
  • $\begingroup$ From what I understand the 'log technique' doesn't have complete support from the archeological community - in part because there is zero evidence of its use in some areas. In other words, this technique may have been used by some cultures, but others (on entirely different continents) have no evidence of its use. Nevertheless, it's fascinating to learn about. I still imagine these blocks were literally dragged across the earth in some cases though too. $\endgroup$ Aug 27 at 17:39
  • $\begingroup$ @MatthewCallegari You are partially correct. The log method was an improvement from dragging from the wood boards (acting as tracks), which in turn was an improvement from dragging directly through the dirt/sandy ground. All these methods are manageable for smaller stones that weighing less than 100 tons, or even less. I couldn't figure out how they manage to move the 160 tons stone yet - the log method alone seems not to work (need too many slaves within a limited space. $\endgroup$
    – r13
    Aug 27 at 18:01

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