magic9mushroom said:
Of course, the amount of energy required to do that... is scary.
Well, not necessarily.
Suppose the Island has mass M (kg),
the particles each have mass m (kg),
the average total number of particles in the rockets at any point in time is n,
the rockets push particles through at a rate of r (1/s),
and the rockets have length l (m).
The force required to keep the Island afloat would be M*g, and that same total force would have to be exerted on all the particles in the rockets.
The force exerted on each individual particle would be M*g/n.
The energy gain of each particle would be M*g*l/n.
The power used by the rockets (P, measured in W) would be M*g*l*r/n.
We'll call the cross sectional area of the rockets A, so their volume (V) is A*l.
n = V*d = A*l*d
l/n = 1/(A*d)
P = M*g*r/(A*d)
The "flux" of particles in the rocket (f, measured in 1/(s*m^2), the number of particles that pass through one square meter per second) is equal to r/A.
P = M*g*f/d
If you knew the number of neutrinos in a typical cubic meter on earth (d), and how fast neutrinos typically travel (v, measured in m/s), you could calculate the flux of neutrinos (f) by multiplying them:
f = d*v
v = f/d
P = M*g*v
Of course you have no control over M and g, but I was initially thinking you might have control over some other aspect. With neutrinos, this would not be the case, however. Just for fun, I want to try to estimate what the power usage would be if you did use neutrinos
Mass of the Island (M):
The largest known chain of caves on the Island is Labyrinth-Core-Waterway-Artery-Reservoir-Mimiga Village-First Cave. I'm going to guess that they go almost around the perimeter of the Island, and the part that they don't cover would be covered by the Egg Corridor, Plantation, Last Cave, Balcony, and Sacred Grounds. Grasstown and the Sand Zone would be somewhere in the middle, so we'll ignore them. I estimate the circumference of this ring of caves would be about 10-11 times the width of the Mimiga Village (this may seem too small, but remember that many of the caves are stacked vertically (i.e. the Core is probably just above the Artery)). Assuming Quote is about the size of a typical human, the Mimiga Village is probably about 50 meters wide. I'm imagining the Island to be approximately hemisphere shaped, so the circumference of the entire Island would be closer to 20 times the width of the Mimiga Village, or 1000 meters. The volume of the Island would then be (4/3)*pi*(1000/(2*pi))^3 ~=~ 17,000,000 cubic meters. I'm guessing the Island would be about 80% rock and rock typically has a density of around 2.5 g/cm^3 or 2500 kg/m^3, so the mass of the Island would be about
40,000,000,000 kg (4*10^10)
Acceleration of gravity (g):
9.8 m/s^2 ~=~ 10 m/s^2
Speed of neutrinos:
Close to the speed of light, we'll say about
250,000,000 m/s (2.5*10^8)
Multiplying these together, we have 4*10^10 * 10 * 2.5*10^8 = 10^20 Watts =
100,000,000,000,000 Megawatts =
100,000,000 Terawatts =
100 Exawatts
To put that in perspective, according to Wikipedia, the average total worldwide power consumption during the year 2008 was only about 15 Terawatts.
The TL;DR version: I thought magic9mushroom might have been wrong about needing an insane amount of power, but it turns out he/she was absolutely right.