Labor 2/2: a manually constructed aqueduct still interesting…

Labor, as argued in the previous blog, is a often neglected energy factor. [1]Which might seem not that important , given the immense quantities of energy that we require for our society. Nevertheless, its interesting to give it a try to quantify this. And when I did that, some years ago for the students in a Master course, it had a surprising outcome.

The motivation came when I saw again one of the aqueducts from the Roman period. In this case the one in Segovia, Spain,which had been in function no less then 1900 years… Amazing. In 1995 it was still supplying water to the city. So there might be a gigantic amount of work and stone involved in such a waterway, they also last very long, you don’t need them to replace often, and maybe, it could be worth the effort to build one? Well, and that s what I started to calculate.

Happily Roman aqueduct building is well documented, especially the ones around Rome. [2] Good data are available for a stretch of 11 km, part of the aqueduct Claudia Anionovus Rome. It has 1200 arches, with a 9 mtr span, and about 3 meters wide, the water channel on top is about one by one meter. The bricks used are 0,9×0,9×1 meter, each weighing around 2 tonnes. Giving a total of 1,5 x10*5 stones and a total weight of 300.000 tons for the 11 km stretch , or 27.500 kg per m1 !

That’s a lot of stone, and work!

So we do a bit of math. Quarrying requires about 2 men for 5 days to free the stone, giving a total of 1,5 10*6 man-days quarrying effort .

The quarry in this case was around 8 km from the construction site, and for transport oxen driven wheel carts were used, which took a team of 6 people going 1 km per hour. So 1 stone per team per day, or a total of 0,9 10*6 man-days are involved.

Next step is construction. As the literature reveals, per pillar construction 15 people were involved, another 4 for the lift that took 10 minutes per 4 meter lift , adds up to 3,3 10*5 man-days for the construction . giving a total construction input of 2,7 million man-days . Or around 7.400 Man-years

To make a interesting case I calculated a benchmark in the form of the most basic way of obtaining drinking water: walking to a pond up and down is the most basic mode ( as it is still now is in some developing countries) and compare that to this “new technology” : building aqueducts.

Rome consumes (today) yearly around 600.000.000.000 ltr. of water. Suppose everyone has to walk 11 kilometers to a pond to get the water. One person can walk twice a day up and down the pond , and carry say 20 liters of water each time: 40 liters a day per person, and times 365 days is around 14000 litres per year pp.

To supply Rome with water this way, we would need 42 million people walking continuously. And Rome has only 2,75 million inhabitants…. The workforce comes down to 42×10*6 man-years.

To compare that to the aqueduct, we have to find out how many aqueducts are needed for the water supply in Rome. The Claudia aqueduct provided Rome with around 200.000 m3 water a day, which is about 12% of the (current) Rome demand. We need to build 8 equal aqueducts for Rome, which adds up to 60.000 man-years in total. Now its clear that its much more smart to build an aqueduct, in stead of walking.

But hold on, were not there yet: The walking option, is man-years per year, that is, they have to be provided every year, continuously. The aqueduct lasts for longer time: Suppose the aqueduct is functioning for 100 years, then the service has required only about a 600 man-year/per year. Add 80 for the maintenance each year permanently , makes 680. Compare this to the 42 million manyears by walking( every year continuously) , makes the aqueduct system 60.000 times more effective. The investment in aqueduct building is huge, but spread over the time of use its neglectful compared to direct labor. It pays of.

On the other side, the aqueduct of Segovia, near Madrid has been in function for nearly 1900 years , which would further reduce the man-years to 30 plus 80 is 110 per year average….

Nice to know, but now at this point in data gathering everyone wonders how we do today, with our modern way of water transport, by piping and pumping? As indicators show in the Netherlands it requires about 0,5 kWh average per m3 of water in pumping energy.[3] For Rome this would add up to 300 million kWh a year . Suppose we provide this with manpower again, each person providing 1 kWh a day, the need would be for 820.000 manyears continuous… Therefore much better then walking, however still much worse as the good old Aqueduct.!

Suppose we will not put men to work for manual pumping, we provide the energy with modern style solar power . To provide 300 million kWh per year requires a solar park of 2,5 km2 permanently . (at 120 kWh/m2 for a PV panel) Mind that the piping solution might function also for a 100 years, but requires yearly energy input.

Now it is getting very interesting, when comparing man-years with km2: This can be done by re-calculating the man-years from the walking and gravity options into ‘ solar powered’ land needed to produce food for these people, which in effect is the ultimate energy source for all three options, and develop a land based comparison.

There are many different data with a wide bandwidth for the land required to produce a affluent diet ( including meat) , I used 2000 m2 per person a year, of open land agriculture, which is somewhere in the middle of data available. That leads to 84.000 km2-year agricultural land for the walking option ( permanent) , and 1,36 km2-year for the ‘gravity’ option , (with 100 years of operational lifetime for the aqueduct. In the case of Segovia , functioning until in the 20th century, its even reduced to 0,22km2-year). For modern pumping with Labor power, this is 1640 km2-year.

Ok, we did not add the food for the oxen in the aqueduct building: 1 stone/day can be transported by 1 oxen driven carriage to the construction site, with 1,5 x10*5 stones makes 3×10*5 oxen days (including return day) or 810 oxen-years. Suppose one ox eats 60 kg grain a day (average of Dutch cows) , he eats 20 tons a year . With a yield of 8 tons of grains per hectare-year, each ox requires 2,5 ha of land . Times 810 oxen years requires 20 km2-year for the food. Spread over the lifetime of the aqueduct of 100 years, adds 0,2 km2 to the gravity option: 1,56 km2-year.

Surprisingly, the aqueduct option turns out to be the most effective way of transporting the water, even much less than the land needed to install for solar panels for the modern pumping alternative! So even today, the aqueduct system would make sense… The human powered constructed version , at the same time providing a lot of employment.

The only reason we don’t built aqueducts anymore ( besides some exception) is that we have free oil , gas and coal, and can deplete the stock built over millions of years. An interesting observation as well is that our knowledge of better conversion routes , from a resource point of view, is already among us. Technology innovation is not needed in the direction we develop, but in improving a long existing technology: Today we could built the aqueduct even with much less material and effort, even in a labor mode. The problem is, we have developed a decision system, capitalism, that neglects the physical evaluations. And of course this is not only about aqueducts, for many services we are not using the optimal configuration in terms of time- land- energy and materials .

In all 3 cases I did not calculate the material input , like the buckets, bricks, pumps , and piping needed. Which require energy/mass as well, and , if we would include that, , most likely will make the piping solution not much better, since the material for the aqueduct can nowadays be greatly reduced, and the more since that would also imply a material time relation, say 100 years , in which the solar panels will have to be replaced every 25 years or so.

The main point in this example is that this shows a relation between different ways of energy input providing the same service, and in a time and space related comparison. (Which is the Embodied Land approach developed as the Maxergy Methodology)[4]

Essential in evaluating a chain of conversions is not to evaluate a product, but a function, a service , in a whole system exergy optimisation: to improve the chain of conversion so that with the least work/land input you create the most functional output. In order to understand the importance of that, we have to put this in a global perspective, in combination with the role of the one and only source adding potential to that system, solar energy. The source of the sources so to say. Its the only way as a reference, to come to the right decisions when looking at a local system.

* the calculation is meant as indicative, not as full exact calculation: most figures have sources, some are educated guesses. Suggestions for improvement are welcome.


[2] Frontinus’ legacy – Essays on Frontinus’ de aquis urbis Romae D.R. Blackman and A.T. Hodge 2001

[3] Vewin 2009

[4] closing cycles calculation tool, on the basis of Embodied land :