How fast a current can ancient water way travel overcome?

This question has similarities to this one but concerns canal travel in more ancient times and is aimed at finding an approximate speed of flow not variables.

Background
Assume an Earth-like world but with much less water. Desert conditions prevail over most of the surface and most of the water there is, is locked up in the polar ice caps. The human inhabitants have constructed a large canal network to move the water from the Polar Regions where there’s water but insufficient heat, to the temperate regions (3000km or more) where there’s heat but insufficient water. The original builders are long gone and the canal network is now operated by a more primitive people.

Question
There needs to be a flow of water in the canals for irrigation on a massive scale, but the inhabitants also want to use the canals for trade. How fast can the water flow in the canals before the canals are effectively useless for two-way trade purposes? And what measures can the inhabitants take to avoid this problem?

Assumptions
The primitive people of this world can use any technology available to any human civilization prior to 400CE. Assume winds are similar to those on earth and would blow from different directions from time to time. The trade distances needed would range from tens to thousands of km. The canals can be up to 2km wide.

Out of scope the practicality of the canal construction and no magic.

• The ancients could and did travel routinely up and down the Danube, up and down the Nile, up and down the Rhine etc. Large rivers tend to move slowly, and canal barges can be towed by oxen or other draft animals and were actually towed by horses up to the beginning of the 20th century. See towpath. A much more interesting question would be what is moving the water from the rainy North to the thirsty South? Commented Nov 23, 2017 at 1:42
• Concerning what is moving the water, I have been doing some calculations with this engineering.com/calculators/open_channel_flow.htm And it seems it should be possible with very little gradient. Perhaps a little as 1mm/km. So its gravity Commented Nov 23, 2017 at 9:14
• A gradient of 1mm/km (1:1000000) won't move much water. For example, the Suez Canal is about 200 km long, and the sea level at its eastern (Red Sea) end is (on the average) about 20 cm higher than the sea level at its western (Mediterranean) end, a gradient of about 10 mm/km; but the flow of Read Sea water into the Med is nothing to worry about. Commented Nov 23, 2017 at 11:47
• If your question is about canal transportation, why does its title mention 'ancient sea travel'? Please edit for consistency. Commented Nov 23, 2017 at 12:02

I would suppose that by ancient you mean Ancient Rome, though numbers would be rather alike for other "ancients".

• Rowing: For long journeys speed of trireme would be about 5 knots, short(several minutes) bursts - up to about 10. But those are numbers for military vessel - basically no load. So even 0.5-1 knot current of calm river lessens available load a lot.

• Sail: With very favorable conditions 10-15 knots are possible. In practice for ancient merchant event 4-5 knots in long travel would be good. And using of sail is hard in canal - it is narrow, even on 2 km width tacking is tiresome, a hill/mountain can block wind, canal itself may change direction. If your canal is build strait and placed on the plain and there is good constant wind - then you can manage even 5 knot current. But basically sail-only vessel with load would be challenged even by slow current. It is often estimated that river transport was 5-7 times more expensive per tonn*km than sea transport.

• Horse: On canals I would expect a lot of horse-drawn(or human) boats. One horse would easily pull some 30-50 tons against weak current. And on wide canal current would always be weak near bank, so I am sure it would not mind even 5 knot(in the middle) current, and I would not reasonably expect current so strong.

• If current is strong enough and constant then a very interesting option arises. A water wheel could pull the anchored rope and pull ship against current(anchor is moved by rowing boat). I was not used because on typical canal current is weak and on any natural river there are calm places with weak current - and water wheel power is ^3 of current speed. In this case the stronger the current is, the better.

The main means of locomotion in a canal are a pole pressed against the bottom of a canal, oars, or a tow rope, usually pulled by beasts of burden.

Oars are the worst vis-a-vis a current and any pause in rowing even momentarily means lost ground. Poles only work if the canal is not too deep and materials strong enough for the pole are available. Sails could also be used but require a much larger canal and aren't as steady and reliable, and would be better as a back up source of power when available.

A beast of burden (or crew of people if beasts of burden aren't available) on a towpath is generally going to be the best way to overcome a current and was used, for example, on the Erie Canal. This would provide movement at 1-3 miles per hour. Rowing or poles wouldn't be significantly faster and could often be slower against the current.

An alternative to a two path would be to have ropes or chains on each side of a boat that are rolled up in one direction or the other to move the boat (a system illustrated in the anime, Attack of the Titans). This probably wouldn't be much faster but would allow the facilities for maintaining the beasts to be centralized and would eliminate the need for someone to clean up animal manure along the towpath every day. It was also facilitate collecting manure for use as fertilizer or a combustion source.

The amount of work necessary to overcome a current depends upon the weight of the boat and the amount of resistance that the portion of the boat that is underwater presents to the water. A "slippery" design (a function of both the material used and the shape) can overcome current better than a flat barrier perpendicular to the current for a boat/barge that is mostly under water.

It is also possible to have different canal lanes for travel in different directions with different direction of current flow in substantial parts of the system (like a divided highway or boulevard), so that you would always be traveling with the current (the part transporting water from the poles could be a larger canal and the part going against the flow could be only large enough to meet transportation needs). You could have one canal that is high in the north and low in the south, and another that is high in the south and low in the north. This would be the fastest option by far with speed as a function of slope and slope a function of your building capabilities and your pumping systems' capacity.

Then you would have a screw or water wheel or pump to transfer the water at the canal with a low end to the canal with a high end in a two lane system. In a siphon-like system the amount of energy needed to keep the flow going would only have to match the amount of speed lost to friction in the water transfer mechanism and thus could be very efficient.

• This sounds like an interesting idea, but I'm not sure of the details here, how would you arrange a syphon? Wouldn't both the north-south canals you mention just empty out at either end? Commented Nov 23, 2017 at 9:31
• Each one empties from its low end to the other one's high end. You'd need some power to a pump to overcome the friction of a syphon, but it would be pretty modest considering the vast amount of water you would be moving on an continuous basis (and you could simply put actively turning water wheels pretty much anywhere in the loop to accomplish it). Commented Nov 27, 2017 at 2:48

I can see 2 good options here. Since you have man made canals and not natural waterways, these seem almost tailor made to your purposes.

Tow Paths: Other people have pointed these out, but in your canal system they would be ideal. A couple of oxen (or other beasts of burden) could pull, via a long rope, a substantially loaded flat bottom barge simply by walking a path next to the canal. these flat bottom barges are good because they are easy to construct, and don't need to be sleek, and can hold a wide variety fo stuff very easily. Your barges are not going to have to deal with other typical river problems either, like eroding banks, snags, fallen trees, and other hazards that are found in rivers. The path itself might even be paved as a small part of the canal construction in the first place, making movement along the waterway pretty fast, comparatively speaking.

Paddle Boats: This is obviously not about steam powered ones, but their predecessors. Ox Driven paddle boats were described as far back as the Roman empire. Some oxen or horses on a treadmill attached to some gearing and eventually a large paddlewheel(s) like the fanciful Mississippi riverboats. These would be able to move around independent of the banks, especially in your fairly slow moving canals. They could also be fairly fast, depending on how they were geared. Again these would get the benefit of a waterway that was free of unexpected turns, eddies, currents, and debris, especially in canals as wide as the ones you envision.

Sails might also be of use, but I see them as more of an extra thing, to help the beasts along. Reef the sails when the wind is bad, Unfurl them when it's good.

Edit I not I did not answer the question on terms of how fast a current could be overcome. I based things on a loose knowledge of the Mississippi river which flows at anywhere between 1.2 to 3 miles per hour on the surface. Not very swift, but when large amounts of stuff are travelling, it beats walking.

I'm guessing an Ox team on a tow path is not going to go very fast, but the thing is they would be consistent going up or down stream making travel times pretty consistent. Over land, pulling a loaded wagon, they would make about 16 to 24 kilometers a day. I imagine this would go up given that the terrain the canals run through are going to have fewer hills to deal with and a barge isn't going to get stuck in the mud, making journeys take less time overall

If you don't like the flow rate of a river (or water-transport canal), you build a parallel canal for navigation. The navigation canal has basically zero current, the only water movement is to replenish leakage and refill locks.

Your main canal, you say, is 1m/km grade. If that is too steep for the navigation canal, you have locks. A medieval lock could handle 1-2 metres of lift, so every 1-2km.

• The main canal was 1/1000,000 but that's too shallow so I think 1/10,000 or 1m/10km. Should be navigable I think Commented Nov 28, 2017 at 0:29