# Floating Pumice Road. Slab Size

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)?

• With Lava People do you mean "people made of molten rock"? – L.Dutch - Reinstate Monica Jul 5 '19 at 5:57
• @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 5 '19 at 6:06
• 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 5 '19 at 6:28
• @LiJun -- Magic doesn't preclude science, and thus the 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 5 '19 at 6:30
• how long does the bridge need to be? long floating bridges suffer from drag due to ocean currents. – John Jul 5 '19 at 18:44

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)

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.

• I haven't seen 'parallelepiped' used in anger in 20 years. – Separatrix Jul 5 '19 at 7:41
• @Separatrix, I don't want to be remembered here only for the potatoid ;) – L.Dutch - Reinstate Monica Jul 5 '19 at 7:45
• You can use normal enamel or even resin as a sealant, instead of trying to melt the pumice itself. – John Jul 5 '19 at 18:36
• Just FYI, the density of pumice averages around 0.25 g/cm^3. seawater is 1.024 g/cm^3 to make solving the equation easier. – John Jul 5 '19 at 18:42