Is it feasible for a Dune-style sand worm to have silica scales?

Question

This question (and the links I found for my answer)

Can a "dune" worm actually swim in sand?

got me thinking about how a sandworm might reduce friction while "swimming." One idea I hit on would be natural glass scales, lubricated with some kind of oil. There's only one species that forms silica shells, and while we're not entirely sure how diatoms do it, we have identified the proteins that are probably involved in the process.

https://en.wikipedia.org/wiki/Diatom#Silica_uptake_mechanism

This is kind of similar to this question,

How would or could a creature with a crystalline sail evolve?

but I'm not looking for evolutionary reasons for the scales. I know from experience that glass can be heavy. I'm wondering how thick the scales would have to be (maybe it's even a silica coating on a substrate?), and if something the size of a blue whale could support that much weight.

(Now, if you'll excuse me, I'm off to listen to this soundtrack... https://www.youtube.com/watch?v=yNY0D4z5FJ4&list=PLB066CAAD43DD2047&index=19&t=0s

You're welcome.)

Edit: When I first wrote this question, I used "blue whale" as a shorthand for "as big as the books make it sound." It's led to Frostfyre's excellent answer, but I can also see that I need to be more specific about physical dimensions. So instead of whales, let's try scaling up a green anaconda, since it already has the body shape we're after.

Assumptions for the average, real world anaconda, a cylinder with:

Length = 4 meters

radius = 0.1524 meters

Volume = 0.39 meters^3

surface Area = 3.98 meters^2

Mass = 50 kilogams

density (p) = 128.205 kg/m^3

weight (N) = 490 N

resting pressure (Pa) = 490 / 3.98 = 123.116 Pa

To stay in the ballpark size I was thinking of, we'll round the average blue whale's length up to 28 meters, making our multiplier 7. As per the Square-Cube Law...

This makes the assumptions for an imaginary giant sand worm, a cylinder with:

L = 4 * 7 = 28m

r = 0.1524 * 7 = 1.0668 m (not the widest mouth*)

V = πr2L = π * 1.0668 * 2 * 28 = 100.11 m^3 or 0.39*7^3 = 133.77 m^3

A = 2πrL+2πr^2 = 194.83 m^2 or 3.98*7^2 = 195.02 m^2

assuming density (p) remains the same, = 128.205 kg/m^3

M = pV = 128.205 * 100.11 = 12,834.6 kg or = 128.205 * 133.77 = 17,150 kg

N = 9.8 * 12,834.6 = 125,779.08 N or = 9.8 * 17,150 = 168,070 N

resting Pressure = 125,779.08 N / 194.83 = 645.584 Pa or 125,779.08 N / 195.02 = 644.955 Pa ...or 168,070 / 194.83 = 862.649 Pa or 168,070 / 195.02 = 861.809 Pa

...................................

*Recalculating with a wider radius of 2.1336 gives us:

L = 28m

r = 2.1336 m

V = πr2L = π * 1.0668 * 2 * 28 = 400.44 m^3

A = 2πrL+2πr^2 = 403.97 m^2

assuming density (p) remains the same, = 128.205 kg/m^3

M = pV = 128.205 * 100.11 = 51,338.4 kg

N = 9.8 * 51,338.4 = 503,116.32 N

resting Pressure = 503,116.32 N / 403.97 = 1,245.43 Pa

...............................

So, back from dinner, and the Dune wiki says:

By anyone's standards, Sandworms could grow to an enormous size. Dr. Yueh cited that specimens "up to 450 meters long" were spotted by observers in the deep desert. To make a comparison, the largest animal on earth was believed to be a Blue whale measuring in at only 33 meters, or about 7% of a large sandworm's length.

...Some people believe that worms from 700 to even 1000 meters existed in the southern pole regions. This was neither confirmed nor denied.

However there is some contention regarding these estimates as Harvester Factories were said to be 120 meters long and still ... the sand displaced by its maw) was described as twice that width. Although this particular specimen was stated to be a large example of the species, a Sandworm with jaws 240 meters in diameter would exceed in size even those of myth which could supposedly be sighted in much deeper desert than the typical spice mining region.

http://dune.wikia.com/wiki/Sandworm

So let's try increasing the size even more to make a mythic sandworm.

L = 1000 m

r = 120 m

V = πr2L = π * 120 * 2 * 1000 = 753,982.2 m^3

A = 2πrL+2πr^2 = 844,460.1 m^2

Let's round density (p) up, = 130 kg/m^3

M = pV = 130 * 753,982.2 = 98,017,686 kg

N = 9.8 * 98,017,686 = 960,573,322.8 N

resting Pressure = 960,573,322.8 N / 844,460.1 = 1137.500 Pa

Answer 1

Let's look at some numbers.

The highest recorded weight for a blue whale was 173 tonnes They grow up to 29.9 m in length, but we'll go with some numbers from this archive. So what we have for our specimen is:

• Length: $\text{27.18 m}$
• Girth: $\text{13.90 m}$
• Weight: $\text{1,195,639.2 N}$ (assuming Earth gravity)

We can then use the circumference formula to find the width of our specimen:

$$C=2πr$$

$$\frac{C} {2π} = r$$ $$\frac{13.90} {2π} = r$$

• Radius: $\text{2.21 m}$
• Diameter $\text{4.42 m}$

For estimation purposes, we can now define a block of creature as being a rectangle 4.42 m wide and 27.18 m long. Now we can figure out how much area is covered by our specimen:

$$A=wl$$ $$A=(4.42)(27.18)$$

• Area: $\text{120.14 m}^2$

The pressure our resting specimen exerts on the ground is, thus:

$$P=\frac{W}{A}$$ $$P=\frac{1,195639.20}{120.14}$$

• Pressure: $\text{9,952.05 Pa}$

Glass, however, has a compressive strength of just $\text{1,000 Pascals}$.

As a result, our specimen would shatter its own scales when it was sleeping, let alone while it was moving around or lifting parts of its body off the ground.

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Muuski raises the question of toughened glass, so I'll add a bit more detail.

On first viewing, the numbers for toughened glass look plausible.

• Compression Strength: $\text{69 MPa}$ (minimum)

But we'll need to dig a little deeper to see what it takes to produce toughened glass and whether our specimen can manage it.

There are two ways to produce toughened glass: physically and chemically.

Physical Solution (biologically interesting)

Physically toughened glass is placed on a roller table and sent through a furnace where it is heated to $\text{620 °C}$ then cooled via air flow. This method has the advantage that our specimen can be constantly extruding new glass scales as the old ones chip and break. Unfortunately, we're going to need to employ some magic to have an internal furnace running continuously at that high of a temperature.

Chemical Solution (biologically challenging)

Chemically toughening glass involves immersing glass in a bath containing a potassium salt at $\text{300 °C}$ to let sodium ions in the glass be replaced with potassium ions from the bath. We still have that temperature problem, though, and the animal with the highest internal body temperature seems to be in the $\text{40-46 °C}$ range, depending on which source you want to use.

One fun side note about the chemical solution: You end up with a worm with a juicy, gooey interior. Strip off the glass armor and you have a gummy worm!

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One last note: It might be possible to produce some form of glass compound using lead or another material to strengthen the glass (I'm having trouble finding numbers), but glass production is still prohibitively heat intensive and so requires the use of handwavium regardless.