As recorded in Genesis 11:1-9, the ancients allegedly built a tower to the skies in a valley in Babylon (near present-day Baghdad), and God scattered them across the Earth as a punishment. According to the sources brought in this question and this one, both at Mi Yodeya, measurements of its height are given as 2.6 km, 5 km, 52.5 km, or 138.24 km, with widths being given as "203 bricks wide" for the 2.6 and 52.5 km versions and left unspecified for the others.

Given that the verses in Genesis describe this structure as being built from purely brick and mortar, is there any way that this story could have been plausible, working entirely within the realm of known science? Ignoring the plausibility of all humankind actually working together, or the amount of man-labor required, or anything like that.

Now, the one catch is that most of these sources lack any widths for the tower. Is it possible, given the strength of bricks and mortar at the time (Orthodox Judaism places this incident in 1996 AM, or 1765 BC) for towers of these varying heights to have been a reasonable width? In other words, is it possible to calculate the widths based on the height and strength, assuming that the tower could actually stand?

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    $\begingroup$ Note: a structure of this size is not required by the original sources. The original sources (Bible/Torah) does not give a height for the tower (or that it was practical or completed), only that they intended to build "a tower that reaches to the heavens, so that we may make a name for ourselves". The intent was to build a large tower than can be seen for miles; (I'm fairly sure that the words for sky & heavens are the same; if not, it could be metaphorical). A tall structure to 'make a name' would be very possible, cf. the Great Pyramid. $\endgroup$ – Dan W Apr 23 at 15:18
  • $\begingroup$ @DanW In fact many sources of the myth refer to a "seven-story tower", which is not at all unreasonable. (It should be noted that this story in various forms long predates the biblical records. See: Etemenanki) $\endgroup$ – Darrel Hoffman Apr 24 at 20:21

I guess there are several questions to consider when trying to answer this.

Could Ancient People Have Drawn Straight Lines Tens of Kilometers in Length?

The Nazca lines were up to 370 meters long, and could achieve surprisingly complex patterns. One of the hypotheses for how they did this was by drawing in a valley and having construction managers spotting from higher elevation.

Could a Multi-Kilometer Structure be Kept Level?

Egyptians (almost a contemporary) had sight levels consisting of a plumb line and a triangle on a table. Look here for an example.

Wooden sticks, marked at a common desired height, with string run between them was the technique used to level the pyramid. The sticks were initially sighted with the sight level, and reviewed periodically by construction site managers.

Between the two base lengths given (2.6 km and 52.5 km), the curvature of the Earth would be between 2 and 53 meters. This curvature would foil the plumb lines, as gravity is curving with the Earth. However, the alignment and design of the pyramid also indicates that the curvature of the Earth was not unknown, and near contemporaries had calculated the circumference, and thus radius, of the Earth accurately, so it would be possible for building site managers to pre-calculate the curvature and account for this 2 to 53 meter curvature that would happen at these very large dimensions.

Are There Physical Limitations to Such a Large Height and Width?

There would be some side force, due to the curvature at the very largest dimensions. To calculate angle, get the arctan of the drop (53 meters) and half the base (26 km ~ 26,000 m) = 0.11 degrees. To find the percentage of all force that is transmitted as a side force, use the sine of this angle.

At the largest dimension (52.5 km) you mentioned, this side force would be about 0.19% of the weight is being transmitted as a moment trying to crack the structure apart.

Tensile strength of mud bricks (which is the type of strength that applies here) 1.5 MPa for mud bricks and 15 MPa for fired clay bricks (same as it's compressive strength). The density of mud brick is 1520 kg/m-cubed; for fired clay brick 2000 kg/m-cubed.

Geometery (whether this tower tapers as it gets higher or is straight up) plays a very important part in total load. For a straight up tower, the total pressure on the bottom tier is the density of your brick multiplied by the structure's height (in meters). P = rho * g * height * 0.2% (the amount of load being transferred)

So, at what height would this set-up fail? 390 kilometers for fired clay brick; 52 kilometers for mud brick.

Also, since brick is not a solid piece, some of this pressure would be absorbed by the bricks shifting in the mortar. And the case mentioned was for a vertical tower - the load could be greatly reduced by tapering the structure as it rose to the top.

How About Maximum Height?

The crushing strength of modern bricks are between 3.5 to 50 MPa. Mud bricks are 1.5 MPa and fired clay bricks are about 15 MPa. The equation, for a straight tower is still that the pressure on the bottom tier P = rho * g * h

For mud brick, the highest altitude before mud bricks start crumbling is 100 meters; for fired clay bricks 750 meters; for modern bricks 2.5 kilometers. This does not include a factor of safety - normally you'd cut these values by 4x to 5x for safety. Again, you could taper the structure to reach greater heights.

For comparsion, the ziggurat of Ur stands at 45 meters and the great pyramid stands at 139 meters.

How High is High Enough?

Per here, altitude sickness begins to set in at 2,500 meters height. Also, per the same site, the highest altitude a human can reach without a compressed air supply is only 8,000 meters.

How Much Height Can We Squeeze Out of Tapering?

The advantage of such an impossibly large base is that you can do a LOT of tapering. With the largest base of 52 km, reaching altitude sickness @ 2.5 km an extremely gentle 5 degree slope (an 85 degree taper). To reach the highest possible altitude for humans @ 8km is a not-terrible 17 degree slope (73 degree taper).

At such a shallow angle, you're not really building a structure (I guess you still are), but merely piling up a mountain. If you could effectively keep the pressure distributed, only 9% to 30% of the total force is being communicated down to the bottom layer. That would allow a height of 1,000 meters for mud brick; 4,400 meters for fired brick at a 10 degree incline; and 8 km for modern brick. You would still want a factor of safety for the structure. Then again, maybe not, because this thing is so shallow.

Effects of Wind

Wind adds a small amount of pressure to the stack. The density of wind is 1.225 kg/cubic meter. A 60 mile per hour wind would add 440 Pascals, and this is without including the effects of the shallow slope.

Breakdown Mode

At these very shallow slopes, the tower wouldn't fall down when it breaks. The failure mode would be more like erosion. Failure can be controlled the same way we control erosion with retention walls made of piled-up dirt, wood, or bronze.

So, I'm really surprised by this, but it's possible.

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    $\begingroup$ "I'm surprised by this. but it's possible" - basically science's motto... $\endgroup$ – corsiKa Dec 24 '17 at 20:33
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    $\begingroup$ Coming back to this all this time later, I'm only now noticing this. In your formula $P=\rho gh\sin(\cdots)$, where the sine term is your percentage of load transferred that I'm too lazy to type out, it seems that, since the base is only taken into account in the sine term, the height and base are inversely proportional to each other; in other words, solving for height, $h=\frac{P}{\rho g\sin(\cdots)}$. This doesn't make much sense to me, that the larger the base, the shorter it must be, and the smaller the base, the taller it's able to be; I'd have expected them to be directly proportional. $\endgroup$ – DonielF Oct 12 '18 at 22:07

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