Sandworm Anatomy and Basal Caloric Needs

I haven’t read the books so I’m only able to go off of what I found on Wikipedia or the Dune wiki which quotes the books. For example we get the following information about sandworms length and diameter:

“Sandworms grow to hundreds of meters in length, with specimens observed over 400 metres (1,300 ft) long[12][13] and 40 metres (130 ft) in diameter, although Paul becomes a sandrider by summoning a worm that”appeared to be” around half a league (1.5 miles (2.4 km)) or more in length”

Even though it appears that most specimens would be below the quoted 400 meters long and 40 meters in diameter (as those dimensions are specifically called out they are likely not the average) we will take this as our estimate for the average given the absence of additional information.

An additional piece of information from the wiki is as follows:

“Herbert notes in Dune that microscopic creatures called sand plankton feed upon traces of melange scattered by sandworms on the Arrakeen sands.[16] The sand plankton are food for the giant sandworms, but also grow and burrow to become what the Fremen call Little Makers,”the half-plant-half-animal deep-sand vector of the Arrakis sandworm”.[17]“

Sandworms as filter feeders

One source that I found for the plankton biomass in a highly eutrophic lake comes from the following source which finds wet weight of phytoplankton per cubic meter of water. Highly eutrophic means that the oxygen in the body of water has declined to the point that animals begin to die off. This highly eutrophic environment is perfect for algal blooms:

So given that highly eutrophic environments are the perfect breeding ground for phytoplankton we can take our highest estimate for plankton living on Dune from these types of lakes. The wet weight of the phytoplankton found from the lake in question was 680 grams per cubic meter of water, the caloric information for phytoplankton I found is expressed in terms of dry weight so using a deflation factor of 5 source this we can convert wet weight to dry weight and get the calories per cubic meter of water.

\(680 \frac{g}{m^{3}} * \frac{1}{5} * \frac{400\text{Cal}}{100g} = \frac{544\text{Cal}}{m^{3}}\)

So if a Sandworm acted as a baleen whale and was able to convert 100% of the calories in the plankton on Arrakis it would have to process roughly 11,400,000 cubic meters of water per day which turns out to be around 4500 olympic swimming pools of water. Consider

But Sandworms don’t live in the water. And do they even filter feed? The mouth doesn’t look arranged such that they can filter out water in the same way that a whale does – which occurs by forcing water out of the corners of the mouth – based on the movie the Sandworms appear to eat the sand itself without much care? In any case, phytoplankton can exist in the densities they do in bodies of water due to light penetrating the water, otherwise if they were on land they must live on the surface only in order to convert sunlight into usable energy.

Further calculation could illuminate this, lets assume that phytoplankton are only on the surface of the sand or just under it as winds reshape the dunes on top of them. We could expect, perhaps unreasonably, that this phytoplankton is 5mm thick over the surface of Arrakis. If this is the case then in order to get the same number of calories the sandworms must traverse an area 200x larger than before. As we read before, the sandworms have a diameter of 40m given images from the movie and using a tool to count pixels I found that the edges of the mouth are around 110 pixels wide on each side and the mouth itself is about 725 pixels wide. So taking this ratio of 220:725 we can find the diameter of the worms mouth and then the area itself to get an understanding of how many cubic meters could enter the worm’s mouth at once.

\(((40m * (1- \frac{220}{725}))*(\frac{1}{2}))^{2}*\pi = 615m^{2}\)

So as the worm travels along if it keeps its mouth fully open to filter the sand then for each meter it moves along it can fully consume 615 cubic meters of sand. If we were in the highly eutrophic water scenario then it would only take about 18526 meters of travel for the sandworm to sate its basal metabolic needs. Given the previous assumption about 5mm thickness of phytoplankton on the surface then the worm must travel 3700 km per day to get this need met. It’s clear why the worms would be so sensitive to rhythmic motions then, as humans or other biomass with higher calorie counts would be much more appealing sources of calories than long distance travel especially since we haven’t even factored in the calorie requirements of travelling at high speeds with such massive bodies.

Further Limits to Plausibility

And this is by assuming that the energy that the sandplankton is coming from the sun rather than the spice melange as written in the books. Given that the sandplankton feed on spice melange which is a byproduct of the worms themselves and the worms are a later stage of the sandplankton then the energy in the system must be decreasing over time unless there is some outside source of energy.

The offerings of bodies to Shai Hulud at various moments in both Dune 1 and 2 are insufficient to correct this issue unless humans or other animals are brought to Arrakis to be offered en masse (a standard worm would require >49000 humans each day).

All of this to say, in my own meandering way, that if Frank Herbert had written that the sandplankton fed on something other than the spice melange or converted sunlight to energy there could be some maybe-sorta-kinda guise of plausibility, but with the ecology of Dune as it is the sandworms population would only shrink until extinction.

# Parameters for the simplified model
total_biomass <- 1000000  # Total constant biomass in the system (grams)
plankton_biomass <- 800000  # Initial biomass of sand plankton (grams)
worm_biomass <- total_biomass - plankton_biomass  # Initial biomass of sandworms (grams)

# Assuming sandworms need to consume 10% of their biomass daily to sustain their energy needs
daily_worm_consumption_rate <- 0.1
# Assuming 50% efficiency in converting consumed biomass into energy
consumption_efficiency <- 0.9

# Simulation duration
days <- 120

# Vectors to store biomass data for plotting
plankton_biomass_data <- numeric(days)
worm_biomass_data <- numeric(days)

# Loop to simulate each day
for (day in 1:days) {
  # Calculate daily energy needs for the sandworms
  worm_energy_needs <- worm_biomass * daily_worm_consumption_rate
  
  # Calculate how much plankton biomass is consumed
  plankton_consumed <- worm_energy_needs * consumption_efficiency
  
  # Adjust plankton and worm biomass based on consumption
  plankton_biomass <- max(plankton_biomass - plankton_consumed, 0)
  worm_biomass <- worm_biomass + (plankton_consumed * consumption_efficiency) - worm_energy_needs
  
  # Check for cannibalism if plankton is depleted
  if (plankton_biomass == 0) {
    worm_consumed_for_energy <- worm_energy_needs * consumption_efficiency
    worm_biomass <- max(worm_biomass - worm_consumed_for_energy, 0)
  }
  
  # Store the data
  plankton_biomass_data[day] <- plankton_biomass
  worm_biomass_data[day] <- worm_biomass
}

# Plotting the biomass data over time
plot(1:days, plankton_biomass_data, type = "l", col = "blue", ylim = c(0, total_biomass), xlab = "Day", ylab = "Biomass (grams)", main = "Biomass Over Time")
lines(1:days, worm_biomass_data, col = "red")
legend("topright", legend = c("Plankton Biomass", "Worm Biomass"), col = c("blue", "red"), lty = 1)