Thursday, June 7, 2012

The Economics of a Roman Suez Canal

Guest post by Christopher Brielman.

Many conversations about an alternate classical history involve a discussion of a possible canal connecting the Red Sea and Mediterranean, similar to the modern Suez Canal.  The idea is often dismissed as infeasible for the technology of the time.  The evidence for this is usually little more than that the actual Suez Canal was not constructed until the 19th century.

This dismissal is often met with discussion of the Canal of the Pharaohs, a supposed structure built by the Pharaoh Necho II, Persian Emperor Darius, or Ptolemy II  (accounts vary as to who actually managed to finish it) that connected the Nile delta to the Red Sea.  This canal is supposed to have run from the eastern-most branch of the Nile Delta (the Pelusiac, named because it emptied in the Mediterranean at the port of Pelusium) eastward to lake Timsah, and then south through the Bitter Lakes, and then to Clysma, on the Gulf of Suez.  This route is estimated to be 140 km long, and Herodotus tells us that it would take 4 days to traverse the canal.

The ancient sources dispute whether or not the canal was finished properly until the Ptolemaic period, due to the concerns of salt water from the Red Sea contaminating the Nile Delta.  Ptolemaic Egypt is said to have been able to overcome this concern with the invention and implementation of the canal lock, allowing them to regulate the flow of water between the Red Sea and Nile.  However, this canal was still prone to the whims of the Nile, and frequently silted up, due to the regular flooding.  The Roman Emperors Trajan and Hadrian had to re-dig the canal, as did the Abbasid Caliphs.

The Canal of the Pharaohs would ultimately be of limited use for a variety of reasons, including the silting and the constraints imposed by the lock (basically, that no ship larger than the lock could be used).  In addition, the canal was only part of a longer river network; any cargo going to Alexandria had another 300 km to travel before reaching the Mediterranean.  Further, sea-going craft were not generally used for Nile traffic (even if the lock were not an issue).  This necessitated unloading of cargo at Clysma, loading it onto riverboats, transporting the cargo along the canal and Nile, and then unloading at Alexandria, before being loaded onto another sea-going ship.  This added additional time (a modest sea-going ship would take at least 2 days to load or unload) and expense.

However, the Canal of the Pharaohs is important for another reason:  It showed that the Persian, Hellenistic, Roman, and Arab civilizations had the necessary technical skill to build a canal of considerable length, and operate it under difficult circumstances.  Given that the main challenge of the Suez is its length, the question  becomes whether or not it would be economically feasible for any of those civilizations to build such a canal.

We have some of the information to answer that question due to the economic policies of Diocletian, Emperor of Rome at the turn of the 4th century.  Diocletian attempted to institute price controls on virtually every good and service within the Roman Empire (listed in what is known as Denarii Communes; basically just a bookkeeping invention from which the value in the contemporary Roman currency actually in use could be calculated. This enabled the price controls to fluctuate with the changes in currency.  Unless otherwise specified, all costs will be in these).  The results are still debated, but most consider this to be a 'bad idea.'  However, it did have an upside:  The Edict of Maximum Prices has proven a treasure trove to Historians, provided a fairly comprehensive catalogue of  Roman micro-economic conditions in AD 301.  This will enable us - along with liberal use of algebra, Google, and guesswork - to calculate the cost of building such a canal.  The ORBIS project from Stanford (a free online resource to calculate travel expenses and times between various points in the Roman Empire, based, in part, on the Edict) enables us to determine much of the economic value of the canal (along with, again, the Edict to determine the value of cargoes).

Here, we shall review the costs and benefits of the construction of a direct canal from the Red Sea, at the Roman port of Clysma, to the Mediterranean Sea, at the Roman port of Pelusium,  This cost-benefit estimate will not be precise or exhaustive; there will be many factors not considered, due to lack of information or ease of calculation.  Much estimation will be used, generally rounding up on costs and down on benefits, to maintain some sense of conservatism about results.  However, the results should show that, unless the numbers are wildly wrong, the general idea is sound.

Construction Costs
The most important factor to determine is how long the canal will be.  This is because we know that there is no need for locks or any other advanced technical work, beyond the digging of the canal and the removal of the soil.  When we run the distance between Clysma and Pelusium on ORBIS, we arrive at 155 km.  Meanwhile, the Modern Suez Canal was 164 km long at completion.  We shall thus use 160 km as the length of our canal, and chalk the difference up to sedimentation and the growth of the Nile Delta.  We can subtract 13 km from the length needed to be dug, to account for the length of the Bitter Lakes (which will be dry until the canal is dug).  Thus, the total length needed to be dug is 147 km.

Now that we know the length of the canal, we need to know the other dimensions.  For this purpose, we can use the Canal of the Pharaohs as our starting point.  Estimates vary as to its width, between roughly 30 meters to 50 meters.  Meanwhile, the likely depth seems to be agreed upon: 9 meters.  Of course, in the case of that canal, subjected to sedimentation, those values wouldn't last very long at all.  Regardless, we are able to calculate the total volume of the canal.  Assuming it is 30 meters wide, we arrive at a value of 39,690,000 cubic meters, which we will round up to 40 million cubic meters.

The next question is how much can one man dig in a day?  This is a harder question to google than one would think (thanks to it being a popular algebra problem, there is no shortage of useless hits on the Internet), so we have to think outside of the box to determine that figure.  The most useful figure that is easy to find is the time it takes to dig a grave.  We can estimate that a grown man can dig a typical grave in 3 hours.  We know that a grave has a volume of 2.71 cubic meters.  We know that the typical Roman workday was 6 hours long.  Thus, we arrive at a figure of 5.42 cubic meters, per day, per worker.  We'll round this down to 5 cubic meters.

According to Diocletian's Edict, the maximum a laborer can charge for his work is 25 Dn per day.  While it is very likely that any Roman Emperor building such a project would use slave labor, the labor costs will be calculated as though it were constructed by freemen for two reasons.  First, because its easier to calculate; we don't have to worry about the cost of feeding or housing the workforce (or guarding them to prevent revolts).  Second, because we can assume that slave labor would be cheaper than freemen, we maintain the principle of estimating up on costs.

Now that we know the amount of work to be done and how much each worker can do, its a simple task to determine how much needs to be done.  Dividing 40 million cubic meters by 5 cubic meters gives us 8 million man-days of work.  Multiplying that cost by 25 Dn gives 200,000,000 Dn as our base construction cost.

However, that would leave the entire mass of earth removed from the canal right next to it on either side, ready to be blown back in during the next windstorm.  The removed material must be transported somewhere else.  That somewhere is, of course, the ocean.  To transport the material, it is likely that the Romans would use river barges, towed by teams of donkeys.  This allows us to run our next calculations.

Assume a barge, 5 meters wide, 30 meters long, with a 3 meter draft, providing it a capacity of 450 cubic meters.  Sail-driven barges of similar dimensions have been found at a archaeological site in Zwammerdam.  Using barges of these dimensions, not only could construction be carried out continuously, with craft passing each other easily in a 30 meter wide canal; they could also pass each other are the head of the canal, where the width might be narrower.  Dividing the total amount of material (40 million cubic meters) among the barges (450 cubic meters) results in 88,889 trips needed to transport the entirety of the canal.  We shall round this up to 100,000 trips, out of sympathy for the donkeys who will be towing the barges.

Armed with this information, we shall now calculate the cost of these trips.  We shall use Herodotus' figure of 4 days to travel the Canal of the Pharaohs as our starting point, and assume that, when this Canal is finished, it would take a draft team the same amount of time to tow a barge the entire length.  Even though the distance is 20 km longer, this Canal would be of uniform dimensions, direction, elevation, and with no current (at least, until completion).  With a travel time of 4 days to travel 160 km, we then divide the construction into 2 groups; one digging from the Mediterranean, and one from the Red Sea (we'll ignore the possibility of teams in the middle of the route, as that would only complicate our calculations).  That means the furthest any barge would have to travel from the dig site to the sea is 80 km.  With the shortest distance possible being 0 km, we can calculate an average distance of 40 km.  That would require 1 day of travel in each direction for the average barge trip.  We'll add another day to account for towing the barge away from the mouth of the canal and unloading into the ocean (its possible that the material could be used to expand the ports on either end).

As an aside, we will not add in additional time for loading the barges, but it is worth noting that, with a digging capacity of 5 cubic meters per day, it would take 360 man-days of work to load each barge.  We'll be estimating digging teams vastly larger than 360 men (which could fill each barge in a day), so the time needed to load each barge will be fairly negligible.

Back to the transportation time table, assuming 100,000 trips, and 3 days per trip, that results in 300,000 trip-days to transport the material.  Draft team drivers were paid 25 Dn per day, the same as general laborers.  We'll assume a team of 4 men per barge, in some combination of drivers guiding the animals and polemen (assumed to be general laborers) guiding the barges, for a labor cost of 100 Dn per day.  That provides a labor cost of 30,000,000 Dn.

Next, we should not neglect the cost of feeding the donkeys.  A typical working donkey is fed 0.5 kg of grain and 2.5 kg of chaff per day.  We shall assume that the grain used is oats (a typical food for draft animals), which cost 3 Dn per kg.  Since we don't know the cost of chaff (its a byproduct of milling grain), we have to do some guesswork.  If chaff cost the same as oats (it doesn't, its a byproduct of milling), it would cost 9 Dn to feed a donkey each day.  Since that number is much higher than would be likely for the cost of chaff, we'll round down the cost to 5 Dn per day.  It is unlikely that that will be the exact type of feed the donkeys get, but it'll serve, again, as a useful benchmark.  Thus, if every single barge trip were pulled by 1 incredibly overworked donkey, the feed cost would be 1,500,000 Dn.

Of course, we know that there's no way one donkey could pull all those barges.  We need to figure out how much the donkeys actually could pull.  The average donkey weighs between 80 kg and 480 kg and can pull a cart that weighs twice as much as the donkey (they can carry, on their backs, a load equal to 30% of their weight; not that that is relevant, but its good to know).  Meanwhile, draft animals can pull barges that weight 50 times as much as the largest carts they can pull.  In other words, a donkey can pull 100 times its own weight in barge loads.  That means that each donkey can pull a barge that is between 8,000 kg and 48,000 kg.    We will not, by the way, factor in how much sails would help the draft animals, other than to note that it would reduce the load, so long as the donkeys are pulling with the wind (in this case, south, unless the barges are equipped with lateen sails, which is a whole 'noter can of worms).

Now that we know how much the donkeys can pull, we need to figure out how heavy the barges are.  The density of dry sand, which will serve as a useful benchmark for how dense the loads are likely to be, is 1600 kg per cubic meter (gravel is not too much different).  That will place our typical barge load at 720,000 kg.  If we assume each donkey can pull a barge load weighing 40,000 kg (this assumes that the construction team uses healthy, strong donkeys, a reasonable assumption), then that load would require 18 donkeys.  We'll round up to 20 donkeys, which, conveniently enough, is the largest team of draft animals known to history (the famed 20-mule borax teams).  So, with 100,000 trips, each with 20 donkeys, each consuming 15 Dn worth of feed per trip, we get 30,000,000 Dn in feed costs.

We now have a general estimate on the total cost of construction.  Digging costs are 200,000,000 Dn, and transportation costs are 60,000,000 Dn, for a grand total of 260,000,000 Dn.  We can assume that costs will go over budget with some certainty, for a variety of reasons, not the least of which that our calculation does not incorporate other construction costs, the cost of any laborers beyond the drivers and diggers (such as overseers), as well as corruption and/or any bonuses paid out.  To be very cautious, and to maintain the consistent trend of decimal laziness evident in these calculations, we'll round the total costs up to 300,000,000 Dn, nearly a third of a billion Denarii.

Its also noteworthy to consider how long it will take to construct the canal.  We know that we have 8 million man-days of digging to do.  If we have teams smaller than 360 diggers on each end of the canal, the time to load the barges, and the number that can be run simultaneously, becomes the constraining figure of how quickly work can proceed.  Herodotus states that 120,000 workers died building Necho's version of the Canal of the Pharaohs, so the labor force would likely be of comparable size.  Emperor Nero attempted to build a canal across the Isthmus of Corinth with a force of 6,000 slaves.  Meanwhile, the greatest engineering project undertaken by the Romans, Hadrian's Wall, was constructed by the three Legions stationed along the border within 6 years, a total of 15,000 men (aside: Hadrian's Wall is an excellent comparison in terms of scale to this project).

These numbers give us a general impression of the scale of the labor forces that could be marshaled in antiquity.  With our figure of 360 diggers needed to fill each barge, we shall use that as our base grouping of construction teams.  It would seem that a reasonable number would be 20 to 40 such teams, or 7200 to 14,400 men, which would put the construction force of a size comparable to the Corinth Canal or Hadrian's Wall.  Both of these teams would be able to quickly dig the canal and fill the barges as they arrived.

With 8 million man-days of digging, a 7200-man team would take 1,112 days to complete the canal.  A 14,400-man team would take 556 days.  Although this would seem to indicate that the canal could be completed in less than 3 years, it is unlikely that construction would continue year-round or, even if it was, it is unlikely that all workers would be working at all times.  We need to take into account weather and holidays.  Given that the Egyptians worked on the Pyramids for 3 months out of the year, we shall assume a 100 day working year for the Canal.  This is a very conservative estimate, as the Egyptians took the majority of the year off, in part, to tend to their farms; a concern that is irrelevant to a specialized work force.  Regardless, it provides an easy time table:  5-11 years.

So, to build a canal across the Sinai Peninsula to directly link the Red Sea and Mediterranean, it could cost the Romans 300 million Denarii and take them about a decade.  This means that annual costs would be in the range of 30 million Denarii.  The easiest way to determine if that would be a surmountable cost is to look that the Roman economy.  During the reign of the Emperor Marcian, who ruled only the eastern half of the Empire, which lasted 7 years, the Imperial government was able to fill the treasury with 100,000 pounds of gold.  To convert that into the Denarii Communes we have been using for our calculations, we convert it into its equivalent in aurei, 1/50 of a pound of gold and worth 1200 Dn in AD 301.  This give us a value of 6,000,000,000 Dn (if we use Diocletian's solidi instead, we get the same value).  This means that the Imperial surplus of an able Emperor and administration could reach a billion Denarii per year.  More than enough to pay for the construction costs of the canal.  The question remains, is it worth it?

Revenue Potential of the Canal
To determine the potential of this canal, we must determine how must it cost to travel.  This cost varied greatly depending on the mode of travel.  The three most important factors for our considerations are caravan travel (where cargo is carried by donkeys or camels), river travel (cargo is carried by riverboats), and (coastal) sea travel (cargo is carried by true ships).  The ORBIS system allows us to run a variety of routes to determine how much it would cost to travel the 160 km route by these various means.  Costs are the cost to transport a given quantity of wheat, a fairly low value, but very commonly traded, bulk good.

Cargo carried by caravan would take 5.33 days, at a cost of 4.49 Dn/kg, to travel 160 km.  Cargo carried by riverboat vary greatly, depending on the river, direction of travel, and season, but we can estimate an average trip would take 3.5 days and cost 0.81 Dn/kg. Cargo carried by ship would take 1.25 days and cost 0.12 Dn/kg.  It clear that land travel is, in general, prohibitively expensive.  This is seen by simply looking at a map: the Roman Empire (and its major cities), in general, was built along the coastlines and navigable rivers.

Now that we know how much it costs per kilogram to transport cargo, we must examine the capacity of Roman ships.  The Roman merchant ships were measured in terms of how many amphorae (26.2 liters) they could carry.  The smallest grain ships in common use were 1,400-amphorae ships, capable of carrying 70,000 kg of grain.  Larger ships in common use had a capacity of 3,000 amphorae, or 150,000 kg.  As an extreme for a large ship in common use might be similar to the Madrague de Giens shipwreck; a capacity of 8,000 amphorae, or 400,000 kg of grain.  In theory, such a ship would likely be narrow enough to traverse the canal, but would likely have a draft too deep.

The costs for transporting a small ship's worth (70,000 kg) of cargo over 160 km would be 314,000 Dn by caravan, 56,700 Dn by riverboat, and 8,400 Dn by ship.  The cost for a larger ship (150,000 kg) would be 673,500 Dn by caravan, 121,500 Dn by riverboat, and 18,000 Dn by ship.  The larger ships mentioned would likely be too rare or too large to factor into consideration for the purposes of the canal.  Therefore, the savings over land travel, for a small ship's worth of cargo, are 257,300 Dn (we'll round down to 250,000 Dn) if the canal is river boat-worthy, and 305,600 Dn (down to 300,000 Dn) if it can handle sea-worthy ships.  For a larger ship, the savings are 552,000 Dn (550,000 Dn) and 655,500 Dn (650,000 Dn), respectively.  The savings would actually be higher for a ship-worthy canal, as it would eliminate the need to unload cargo, an expensive and time consuming process.

With a value of wheat of 10 Dn/kg, a typical small grain ship would be carrying 700,000 Dn worth of grain, and a larger ship would be carrying 1,500,000 Dn worth of grain.  However, the Red Sea trade was not driven by grain trade, but the spice trade.  The most valuable of spices was Indian long pepper, worth 2,400 Dn/kg.  A ship carrying a cargo of nothing but Indian long pepper would be worth 168,000,000 Dn (small ship) to 360,000,000 Dn (larger).  In other words, the total value of a ship loaded with pepper was almost enough to pay for the construction of the canal by our estimates.

The Indian ocean trade drove much of the Roman Empire's tax revenue.  An import tariff (portorium) of 25% was levied on the three main Red Sea ports of Clysma, Myos Hormos, and Berenice.  During a typical year during Augustus' reign, 120-140 ships made the journey from India to the Egyptian ports.  If we make a conservative estimate of 100 ships per year, then the total value of the Indian Ocean trade could be somewhere between 1,680,000,000 Dn to 3,600,000,000 Dn.  This estimate presumes that all the Indian trade is long pepper, the most valuable commodity coming from India.  While this may seem optimistic (it is), we are not factoring in trade from Persia, Arabia, or Africa, all of which were quite important, but for which we don't have as reliable numbers available.

Assuming all those ships were to use the Canal (a reasonable assumption), the total annual savings are 25,000,000 Dn (river boat-capable canal) to 30,000,000 Dn (ship-capable canal), if they're all smaller ships.  If they're larger ships, the savings are 55,000,000 Dn to 65,000,000 Dn, annually.  These figures represent the maximum tolls the Roman Empire could charge; the most the canal could earn in a year.  Anything higher, and the only gain is the savings in travel time.

With the potential savings known and the value of trade known, we also know what the toll rate would be.  Assuming the canal can handle ships, a toll equal to the entire savings represented by the canal would be roughly 1.8% of the value of ships.  Of course, to promote the canal, the tolls would likely be lower; perhaps 1% of value, which would equate to 55% of the savings.  That rate would bring the revenue potential of the canal tolls to 15,000,000 Dn to 35,000,000 Dn, annually (again, rounded down).  This would enable the canal to be paid of within to 8.5 to 20 years.

All this assumes no growth in the Red Sea trade.  We know that the actual Suez Canal carried a trade of 436,000 tons in its first year of operation, and 2,000,000 tons 5 years later, a 4.5 fold increase in trade.  Trade continued to grow drastically in the next 2 decades.  It would be unwise to attempt any sort of comparison in the growth of trade between history and this scenario, but it serves to show that a dramatic increase in trade (and thus, revenues) is very likely.

Historical Implications of the Canal
Now that we have determined the basic economics of the canal itself, we can consider the other effects.  Where Roman merchants went, Roman soldiers often followed.  We know that Augustus made one effort to conquer Arabia, that ended in failure, entirely due to logistical problems.  How might the canal have aided such an operation?

Consider the cost of sending one Roman legion from Rome to Coriosopitum, a town about midway along Hadrian's wall.  At best, it would take 46 days to make the journey of 5936 km, at a cost of 1,160 Dn per person.  With a legion of 5,000 soldiers, it would cost nearly 6 million Denarii just to transport the soldiers, without any consideration of their supplies or equipment.  This represents the the outer limit of Roman ability to project power.

In comparison, with a Suez Canal, it would take about 30 days to sail that same legion from Rome to Arabia Felix, a distance of 5065 km, and a cost of 776 Dn per person, under 4 million Dn for an entire Legion (again, not including equipment or supplies), roughly 2/3 the cost of an expedition to Scotland, enabling a force 50% larger to be supplied.

The end result is this: Rome would be able to project its military power more easily towards the entire west coast of Arabia, as well as Axumite Ethiopia, than it could against the Picts in Scotland.  Somalia and the east coast of Africa, down to Tanzania, would all be within range of the Roman military.  The canal would open up a second front on the eternal wars between Rome and Persia, allowing for Roman legions to attack Mesopotamia from the sea.  Such an expedition would be more expensive than sending a legion to Hadrian's wall, but would be a strategic game changer in the wars.  If Persia were to fall and lose, perhaps, Mesopotamia (to be conservative, in such a scenario), then the entire direction of history changes even further.

And, of course, if the canal is built after the capital is moved to Constantinople (or if the capital is later moved), we can add 900 km to the range of the legions.  However, the canal may also make other cities, such as Alexandria, or even Pelusium or Clysma, (or perhaps along the shore of the Bitter Lake)  more attractive locations for a capital.  Imagine an analogue to Constantine deciding to build his Nova Roma on the foundations of the great trading emporium along the Canal, enabling an efficient administration of the the most valuable provinces of the Empire (Syria and Egypt), as well as close ties to the religious foundations of the newly Christian Empire, and easy supply of armies fighting against Persia.

Perhaps, in a world where the Romans build such a canal, the analogue to the Byzantine Empire would control the southern and eastern Mediterranean, Mesopotamia, the entirety of the Arabian Peninsula, and the African Red Sea coast down to the Horn of Africa, with its capital located near the canal in Egypt.  Such an Empire would have a fantastically secure commercial foundation, having control of the major trade routes of antiquity.  It would control the major agricultural centers of the Nile and the Tigris-Euphrates valleys.  Having incorporated the Arabs into its empire, and with fairly easily defended borders, there would not be too many external threats to its supremacy.  Such an Empire could be as eternal as China's.  Considering how much of China's economy was dependent on its own grand canal, the analogy may be uniquely apt.

4 comments:

  1. Incredible! What an extensive amount of research and a fascinating question. By the way, the ORBIS software used by Christopher Brielman to track distances in the ancient world can be found at: http://orbis.stanford.edu/#

    ReplyDelete
    Replies
    1. A very useful site indeed. And yes this was a great article, I hope more people get to read it.

      Delete
  2. Just getting around to reading this really interesting posting. I do wonder about the width and depth dimensions you stated for the canal. For my book, Confederate Star Rises, I did a lot of research on the Pennsylvania canal system built in the early part of the 1800's. (Called the engineering marvel of the century, it was quickly eclipsed with the advent of the railroad.) The dimensions of this canal system was 40-50 feet wide at the waterline and 4-5 feet deep. Important for my book, it would be fairly easy for troops to wade across the canal. This is quite a bit less than the dimensions stated in your post. I know that the draft of boats using the canal would have to be taken into account for the depth. Maybe the ancient vessels settled more deeply in the water? The 30-50 meter width does seem excessive to me.

    Great post. Enjoyable read.

    ReplyDelete
    Replies
    1. My dimensions were based on contemporary accounts of the historical Canal of the Pharaohs. I imagine that the differences in size are likely due to the conditions; there's no inclines or serious obstacles beyond the earth itself that needs to be moved.

      Delete