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

[Neijin]

More formulas for those willing to take a crack on the wind idea:
http://www.usace.army.mil/publications/eng-manuals/em1110-2-1100/PartIII/Part-III-Chap_4entire.pdf
You would really have to go to the link; posting is not kind to the formulas.
q=BBagnold times (pa/g) times (the square root of [D/d] times u cubed

in which q = the mass transport rate in gm/cm-s, BBagnold = a coefficient, ρa = the mass density of the air =
0.001226 gm/cm3, d = a standard grain size = 0.25 mm, D = grain size in mm, and u* = the shear velocity in
cm/sec;

q=Zzing times (pa/g) times [D/d] to the 3/4 power times u cubed

in which ZZingg = a coefficient, and q, D, d, ρa, and u* are as in the previous expression.
(2) Chapman (1990) provides an evaluation of these and several other equations. The predictive
capability of the seven equations investigated by Chapman (1990), as gauged by the coefficient of
determination, ranged from r2 = 0.63 to r2 = 0.87 (see Table III-4-2).

 

[Pyrex]

For a party of adventurers, the front door is probably still the best option, regardless of how barred it is.

So now we're back to a ruler (doesn't necessarily have to be evil or a despot, but it helps...) with huge amounts of resources to devote to the project.

For a straight excavation, we need to clear down to the city, and space around the city as well. Since we assume the city to be 2 square miles, we'll probably have to plan to excavate a 3 square mile area.

3 square miles * 500' deep ~= 42 Billion cubic feet of sand that needs to be moved.

Which means that with three months available we need to be able to move just short of 465 Million cubic feet of sand every day .


So, moving along, lets assume that our ruler can field 100,000 workers. Working 10 hours a day, each of those 100k workers has to (on average, some workers will be digging, some running supply trains, etc) move(or eliminate or otherwise remove) 465ft^3 of sand.

Given that this is well beyond the bounds of brute labor (each laborer might reasonably to be expected to be responsible for 1ft^3 of sand per hour, leaving us way, way behind schedule); we now have to assume that each of our 100,000 laborers have a significant amount of magical power at their disposal.

Say, 5 Disintegrate spells each. Every hour. For three months.

Hmm, that doesn't work so well either.

So excavating the city clearly isn't going to work...

 

[RainOfSteel]

All readers: I'd love to hear you ideas of how to excavate or raise the entire city in less than three months.

Ok . . .

Sphere of Anihilation.

Gulp, gulp, gulp.

Sand all gone.

 

[Pyrex]

... which brings us to raising the city.

We know that the city is domed with impervious walls of force. Presumably, the walls & floors are also reinforced with walls of force; else the city wouldn't have been able to withstand being buried under 500' of sand.

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.

First we're going to round up as many mages capable of casting Gate as possible.

Or, given that we've got three months, build a gateway capable of holding open a Gate indefinately.

Spaced around the city we'll open as many Gates as we can manage to the elemental plane of water and insert 9' diameter tubes through the horizon of the gate to form massive faucets.

A month or two of this should be sufficient to saturate the sand to the degree that the city will begin to float. If the Wall of Force dome isn't actually enough to make the city float, we'll send teams of creatures with Water Breathing a Swim speed and a Burrow speed to install floats across the bottom of the city.

 

[Michael Silverbane]

Make friends with a beholder... Or better yet, cast simulacrum on a beholder. It will be able to disintegrate away the sand at a pretty good rate, uncovering your city in no time at all... Also, it can get through the wall (or walls) of force once the city is uncovered.

Later
silver

 

[Pyrex]

At best the beholder can clear 1000ft^3/round.

If he does that for 10hrs he clears 6 Million ft^3.

Given 90 days, that gets you 540 Million ft^3.

That means you still need 80 beholders working 10hrs a day for 3months.

 

[javcs]

Sphere of Annihilation should work, assuming that it can be adequately controlled.

Pyrex is probably right that finding a door, any door, not necessarily the front door is good.

Hold up - if it is assumed that one can pass through the door, you can probably get through some of the wards against magical transportion.

Use incorporeality to locate the doors or a good spot to tunnel down to (sewers or other tunnels that pass beneath the city), this reduces the amount of required to get in. To get out, well, if they can ceate a force bubble around a city, they probably have something capable of lifting it 500ft.

Or you could be "cheap" and burn a few wishes/miracles to get the city up.

 

[Felnar]

does anyone know the steepest angle sand will sit still at? (not flow downhill)
i seem to recall ~35 degrees, but maybe someone knows for sure

 

[Sigurd]

Once in the vicinity of this city can you be rid of the sand or does it have to be disintegrated. Where did it come from?

If you need delicate work I'd suggest a lyre of building, but thats a lot of sand.

Turning it into sand golems that dig for you seems elegant.

s

 

[Machiavelli]

How about those Entropomancers, who can direct and control a Sphere of Annihilation? They could get rid of that sand nicely, I'd imagine. Of course, you'll need to have at least one SoA at your disposal, and probably an army to fend off the evil baddies that would attempt to wrest control of it from you. Of course, there may even be those who wish to lock the SoA away where it can do no harm, and will be willing to kill anyone who tries to stop them from doing so.