Excavating a City/Moving tons of sand (Brainteaser: Lots of Math/Physics needed)

[Neijin]

Pyrex- You certainly think "outside the box" I like it. I see a couple issues with raising the city with water. First is, why do you assume the city will float in water? For the sake of example let's assume that I build a box out of six permanent walls of force and fill the box full of stone. I then throw the box in water. Does the box float? I would think not. Weight calculations of a Wall of Force aside (assuming even zero), the box has mass to it and would sink.

Let's assume that by some stroke of luck you found a sunken city like the one I want to raise, but sunk in water instead of sand. What is the minimum about to air that would have to be in the city to counteract the weight of the city and raise it to the surface? Perhaps I am underestimating the power of buoyancy here. I know such a calcuation is dependent on area, perhaps someone can estimate and ballpark it.

Also, sand absorbs water quite readily, and from my limited research increases in weight by ~35%. I do not know how much water a pound of sand can absorb before it becomes saturated, however.

 

[Machiavelli]

Actually, I should think that a city will readily float on sand, going only by the densities involved, because the city will most likely be made of local-ish materials that will only be a bit denser after being processed for construction. The city's "box" will also contain very much of air.

The only reason the city wouldn't "float" is that the sand is not a liquid. Adding water to it until it becomes saturated, however, turns the mixture into a thick liquid. With enough time, and perhaps some agitation (an earthquake spell would help), the city should rise to the surface until it displaces just enough sand slurry to equal the city's own weight. The walls of force just act like the hull of a submarine.

Nice thinking, Pyrex.



Regardless, it seems that a problem of this scale, even in D&D, requires a large number of participants to adequately tackle.

 

[Pyrex]

Pyrex- You certainly think "outside the box" I like it. I see a couple issues with raising the city with water. First is, why do you assume the city will float in water? For the sake of example let's assume that I build a box out of six permanent walls of force and fill the box full of stone.

Because in the case of the city, the box isn't full. The inhabitants have to breathe.

Assuming the city is 2 mi^2 in area, roughly circular, And that the Walls of Force surrounding/covering the city are roughly* dome-shaped, the volume of the enclosed area contains massive amounts of air**. Since saturated wet sand has a density approaching that of stone, the dome of force only needs to extend, say 15' above any building in the city to lower the average density of the city enough (unless they did something odd like build the foundation of the city out of lead) to float it to the surface.

Granted, the whole city isn't going to be floating at the surface unless you place hundreds of tons of low-density material under the foundation, but once the top 20' or so is exposed to air that's good enough to get started.

*With a diameter of over a mile, the dome obviously isn't a perfect hemisphere; if it was you could hardly consider the city "buried"

**Maintaining air quality in an airtight large city is a whole 'nother thread...

What is the minimum about to air that would have to be in the city to counteract the weight of the city and raise it to the surface? Perhaps I am underestimating the power of buoyancy here. I know such a calcuation is dependent on area, perhaps someone can estimate and ballpark it.

It's not about area, it's about density. If the average density of the city is less than the average density of the surrounding medium, it'll float. The greater the difference the faster it'll float.

Solid Granite is 2691 times as dense as water, so you'd need 3 10x10x10' cubes of force enclosing 1ft^3 of granite to float it; meaning you'd need a massive dome of force to float a city mostly constructed of stone.

Wet Sand has a density 1922 times that of water, which is well over half the density of solid granite. Which means that even if the Wall of Force is skimming the rooftops, the air in and around the buildings is more than enough to float the city in wet sand.

Machiavelli is probably right though. Once you've got the sand good and saturated you'd probably need some Earthquake spells to shake it up enough to act like a liquid.

 

[tomBitonti]

Drain away the sand through a portal or gate ...

How about creating a gate or portal (or several) just above the surface of the walls of force?
(Assuming that dimensional travel works *outside* of the walls of force.)

Let the sand drain out to your favorite destination ... a nearby canyon, or the elemental plain of air. (Or, outside of a city that needs a new breakwater.)

Or, above a not-too deep body of water ... you'll get a new island out of the deal.

I'm not sure if the sand would flow freely enough to drain through the gate, but if it did,
that should eventually clear a large cone of sand from above the city.

Hmm, question of how long it would take, parameterized on the radius of the gate.

Thx,

Tom Bitonti

 

[tomBitonti]

Solid Granite is 2691 times as dense as water, so you'd need 3 10x10x10' cubes of force enclosing 1ft^3 of granite to float it; meaning you'd need a massive dome of force to float a city mostly constructed of stone.

Wet Sand has a density 1922 times that of water, which is well over half the density of solid granite. Which means that even if the Wall of Force is skimming the rooftops, the air in and around the buildings is more than enough to float the city in wet sand.

Those numbers are off ... solid granite in a 1 meter cube has a mass of 2691 kilograms. Water in the same volume has a mass of 1000 kilograms (by definition!)

You need to throw a decimal point in there, so solid granite is 2.691 times as dense as water, and wet sand is 1.922 times as dense as water.

Thx!

Tom Bitonti

 

[Hypersmurf]

So, lets assume that with the front door closed, the city is airtight; and, ecological damage be darned, we're going to float the city to the surface.

Have you ever tried to push over a Wall of Force?

The average density of the city enclosed by the walls might be less than that of wet sand, but that's irrelevant:

A wall of force spell creates an invisible wall of force. The wall cannot move...

The city can't float if the wall surrounding it is immobile; neither can it sink. It will always remain in the same place.

-Hyp.

 

[Pyrex]

How about creating a gate or portal (or several) just above the surface of the walls of force?
(Assuming that dimensional travel works *outside* of the walls of force.)

Let the sand drain out to your favorite destination ... a nearby canyon, or the elemental plain of air. (Or, outside of a city that needs a new breakwater.)

That could possibly work, assuming you tunnel down and create a clear space in which to open the gate in the first place. (having your caster buried in sand kind of limits Line of Sight and Line of Effect)

 

[Pyrex]

Have you ever tried to push over a Wall of Force?

The average density of the city enclosed by the walls might be less than that of wet sand, but that's irrelevant:

A wall of force spell creates an invisible wall of force. The wall cannot move...

The city can't float if the wall surrounding it is immobile; neither can it sink. It will always remain in the same place.

-Hyp.

Excellent point.

Which then begs the question: How'd the city get buried under 500' of sand in the first place?

 

[Pyrex]

Those numbers are off ... solid granite in a 1 meter cube has a mass of 2691 kilograms. Water in the same volume has a mass of 1000 kilograms (by definition!)

You need to throw a decimal point in there, so solid granite is 2.691 times as dense as water, and wet sand is 1.922 times as dense as water.

Thx!

Tom Bitonti

Gah! Teach me for posting before I've had any caffiene. I know those numbers sounded large, guess I just can't read in the morning.

So to float stone in water your container needs to be approximate 1/3 stone and 2/3 air.

However, a domed city with at least 1/3 total volume of air will still float in a suspension of wet sand.

 

[Hypersmurf]

Excellent point.

Which then begs the question: How'd the city get buried under 500' of sand in the first place?

Take a box, and bolt it to the floor.

Now dump 500 feet of sand on it.

Has the box moved? Is it buried under 500 feet of sand?

-Hyp.