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So based on the question can pumice stone be use as castle material on water? I wanted to take pumice and use it to construct a floating road, so my Lava People can safely travel from one volcanic island to the next.

To make the road, I plan on taking slabs of pumice and joining them together using a sharp needle and the fibers from a heat proof tree (its a bit magical, but I want to string all the pumice together into a long floating bridge).

What sort of dimensions would the pumice slab need to be so that a 100KG person walking across it won't sink into the water or tip over the slab (it is joined to other pumice slabs)?

Cyn
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Shadowzee
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    With Lava People do you mean "people made of molten rock"? – L.Dutch Jul 05 '19 at 05:57
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    @L.Dutch Yes. But they have a thin black skin caused by the lava hardening. But if it hardens too much they can't move properly. – Shadowzee Jul 05 '19 at 06:06
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    You might want to rethink sewing the pumice blocks together. Pumice can float for many years, but eventually it will become waterlogged and sink. – elemtilas Jul 05 '19 at 06:28
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    @LiJun -- Magic doesn't preclude science, and thus the [tag:science-based] tag. Shadowzee should clarify the nature of magic in this world and how the magic works in order for us to consider how an in-world scientific approach is to be made. – elemtilas Jul 05 '19 at 06:30
  • @elmtilas but isnt the tag say for question based on hard science, not magic or pseudo scince ? it also dont have science tag too, since science based also require that tag. – Li Jun Jul 05 '19 at 06:33
  • Are strict on a slab (parallelepiped) shape? – L.Dutch Jul 05 '19 at 06:34
  • @L.Dutch No set requirements on the shape. I just don't know how to describe it any better. – Shadowzee Jul 05 '19 at 06:35
  • @LiJun The [science-based] tag just means the answer needs to be based on science, not magic. The pumice bridge will need to obey the laws of this world. – Shadowzee Jul 05 '19 at 06:42
  • In addition to @L.Dutch excellent answer, as well as using a coating of glass to protect the pumice from water, you could use glass-fibre rope, a real product you can buy today. – Ben Jul 05 '19 at 18:09
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    how long does the bridge need to be? long floating bridges suffer from drag due to ocean currents. – John Jul 05 '19 at 18:44

1 Answers1

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Let's assume you take a parallelepiped of pumice with vertical dimension h, width a and length c, and put it into water. To which extent will it sink? If we call the sinking s and indicate the density with $\rho$, it's easy to show that

$s \over h$$=$$\rho_{pumice}\over \rho_{water}$.

In order to prevent sinking when having a load of 1000 N, you need to have that the additional sinking due to the load shall be less than $h-s$. Or, you need to displace enough water to compensate for the added weight.

In other words,

$(\rho_{water} - \rho_{pumice})\cdot a \cdot c \cdot (h-s)=$

$(\rho_{water} - \rho_{pumice})\cdot a \cdot c \cdot h(1-$$\rho_{pumice}\over \rho_{water}$$)=100$

Therefore, if you set two among a, c or h, you can determine the other using the above formula.

The tipping moment for a slab can be also calculated and give you other constrains on the dimensions. However, a slab is not the best shape if you want to stay practical: if it is not large enough, it will tip as soon as you approach its edges (try standing on a paddleboard and you will see what happens if you move toward the edges along the shorter dimension).

To improve tipping stability while keeping the dimension reasonable, it would be better to adopt a catamaran-like hull cross section (image adapted from here)

catamaran hull

And, since pumice over the years tend to soak in water and then sink, flame the outer surface so that it turns to glassy enamel and is better sealed against water.

L.Dutch
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