How steep a road could a horse/horse-and-cart travel?

Question

I'm in the early stages of designing a city, and would like some advice about to structure its roads realistically for transport.

The city is circular, with large roads entering the city at north/south/east/west. It should also be on higher ground - doesn't have to crown a mountain, but should be higher than the rest of the immediate countryside.

Given that:

(a) the world uses medieval technology;

(b) horses/horse-and-cart are the most sensible long distance transport;

(c) the roads are straight;

and (d) there is no magic,

HOW STEEP CAN THESE MAIN ROADS BE?

If I can't sensibly have straight roads and an impressive-enough gradient, then I'll redesign the city with a different design. Still, it'd be nice to go along with my current mental image!

Further contextual information:

The city is divided into concentric rings, with the palace at the centre and the poorest at the outskirts. A significant slope would therefore make the palace even more impressive to viewers.

The city evolved from a simple trading town at a set of crossroads, but developed in importance and resources. The straight roads are a remnant of that past - while they're not the best defensively, internal walls divide class districts, and are each equipped with defences. (Being on higher ground also helps for defence).

The area may have once been volcanic - the city is fed by natural springs, and may explain a hilly/mountainous terrain.

I've also had a look here for info about road-building, but it didn't seem to cover this.

Answer 1

The story about the development of cable cars in San Francisco involved an accident with a horse drawn car on an 8.3% grade.

from http://www.sfchronicle.com/bayarea/article/Steep-S-F-hills-overcome-with-Hallidie-s-cable-6295164.php

As a team of horses pulling a streetcar up the 8.3 percent grade approached the intersection, one of the horses slipped on the wet cobblestones. The driver applied the brake so hard the chain was ripped out and the car slid downhill, dragging the horses over the pavement. The car came to a rest at the bottom of the grade, and the horses were mutilated and killed.

The fact that the driver was trying it meant that it was part of the normal route. I could not find how much the car weighed but I did find that passengers would routinely disembark and walk along side the car on the steep parts of the line, which were barely within the capability of the horses.

I found this fine math on https://www.reddit.com/r/rpg/comments/12xtqs/what_is_the_gradeability_of_a_horsedrawn_wagon/

[–]Azza_bamboo 1 point 4 years ago* I might be wrong on the following, so I'd urge any physicists to look at what I'm saying and see if there's any mistakes. A horse has a mass of about 400kg and pulls about 801N. Let's say a laden carriage has a mass of about 1000kg. So a carriage pulled by four horses has 3200N pulling it, and has a mass of 2600kg. The force of this vehicle under gravity (which is the technical meaning of weight) would be 25506N. Put simply, the horses could not pull their own weight, plus that of the carriage, straight upwards (ignoring that it'd be impossible for their hooves to gain traction on a vertical face). An incline allows them to pull only a fraction of the total weight rather than the whole lot. 25506 multiplied by the sine of the maximum theoretical incline = 3200. This is because 3200 is the force the horses can give, and 25506 is the weight of the whole vehicle. The angle that would make the force that the horses have to pull be equal to 3200 is the variable we're trying to work out. The arcsine of (3204 divided by 25506) is roughly seven degrees. In other words, the incline had better be less than 7 degrees else these horses won't be able to pull this wagon. Sources The mass of a horse: http://en.wikipedia.org/wiki/Horse#Size_and_measurement The force a horse exerts: http://en.wikipedia.org/wiki/Horsepower#History_of_the_unit (Google calculated that 180lbs of force translates to roughly 800N) I will admit that I simply made a judgement on the mass of a loaded carriage, putting it at a metric ton. I have calculated that the incline needed for the same horses pulling a 500kg carriage is roughly 9 degrees. Of course, you're trying to maximise the proportion of force to mass. That is, you want more force and less mass to be able to make greater inclines. Also, humans don't really get to dictate the landscape. So if you're trying to get big loads up a steep hill, you might use lots of horses to carry less mass. In reality, rather than asking what incline is reasonable for this carriage, you ask what setup is reasonable for this incline.

So maximum grade for a horse with a wagon would be between 7 and 9%, which jibes with the story about the accident on the 8.3% grade. Like your city, San Francisco was laid out without any concern about grade and there are many streets which were (and are) much steeper. You would just not be able to take a cart on those streets - you would have to walk or ride horseback.

Answer 2

Most of these questions are the wrong questions. If you were to ask 'when should I use a 10% grade' the answer would be never unless you could absolutly not avoid it. Roads are a means of commerce in the real world. Roman roads are a poor example of roads because they were not built to move goods or services but to move armies. A marching soldier has zero rolling resistance. Traversing inclines on foot is rather easy. A man might even traverse a grade of 100% using a ladder.

All of this changes dramaticly when a wagon becomes involved. A draft horse can reasonably pull a wagonload of aproximatly 1 ton over a level good road for a day at around 2.5 miles an hour. This is basicly one calculated horsepower. Now lets say you increase the grade to 2%. Now you have added 40lbs of energy pulling in opposite direction. This essentialy doubles the energy requirements in terms of horsepower. At a 6% grade you have doubled the requirment again and at under 15% you have doubled it a third time.

Could you have a horse pull a one ton load up a 15% grade? Yes, maybe. A horse can generate up to 15Hp in pulling force for a short time. But after an hour you would have to change horses. This means that a 2% grade road 10 miles long and level road 20 miles long are about equivelant in roads you could travel in a single day.

This why roads tend to wind. The economic return on a level road that winds is far greater than a straigt road with a steep grade.

Answer 3

I've ridden a horse up a 20%-25% gradient many times. Horse riding is not going to be your limiting factor.

Answer 4

There is a long distance pack horse trail through our region. Short sections are between 20 and 30%. The climbs and descents are quite manageable for the horses. But at those gradients drainage and erosion become big factors and both horses and people will only be able to move slowly up and down.

Answer 5

From wikipedia on Roman Roads

Roman construction took a directional straightness. Many long sections are ruler-straight, but it should not be thought that all of them were. Some links in the network were as long as 55 miles (89 km). Gradients of 10%–12% are known in ordinary terrain, 15%–20% in mountainous country. The Roman emphasis on constructing straight roads often resulted in steep slopes relatively impractical for most commercial traffic; over the years the Romans themselves realized this and built longer, but more manageable, alternatives to existing roads. Roman roads generally went straight up and down hills, rather than in a serpentine pattern.

https://en.wikipedia.org/wiki/Roman_roads#Construction_and_engineering

So, if the road builders are stubborn the roads could be 15%–20%, but more sensibly they would be 10%–12% with some switchbacks.

Answer 6

This may seem obvious but it depends on whether you're going up or down and how heavy the loads are, you could have much steeper exit roads for empty wagons going down away from the city than you can entry roads bringing heavy loads up into the city.

Answer 7

Where I live, horses are used to pull timber in areas where machinery can't reach. They seldom pull the logs up the slope, but they do work with considerable loads in quite treacherous terrain.

These horses are bred and trained for this purpose, and they use special horseshoes designed to grip the dirt.

Since your question specifically pertains to a city environment, I presume you want paved roads. However, this can be very dangerous for horses pulling anything uphill or downhill, as such roads offer very little traction for hooves. The use of horseshoes actually makes it even more perilous. (Yet many traders coming to your city would have their horses shoed specifically for better off-road performance.)

The best way to make the slope accessible for horses is to rebuild parts of the roads into an Equestrian staircase (combined with ramps for the wagon's wheels). This way, horses can pull their cargo without the danger of slipping and can "force-pull" heavy loads step by step, taking pauses between pulls. Ridging in steps will help to get traction for shoed horses.

If you wanted to maximize the slope, you can use counterweighted pulleys at strategic points to assist the horses up the hill. These could also serve as convenient tolling points. (Perhaps the toll amount could be calculated based on the amount of ballast used for counterweight.)

The grade wouldn't necessarily need to be uniform, but you could aim for a bit steeper than the 9% suggested in the accepted answer on average.

As for getting the loaded wagons down from the city, this video shows how logs are pushed down the hill.

First, a horse is used to position the log with the "thin" side downhill. Then, the log is hooked to the harness, and the horse, going diagonally down and across the slope (rather than directly down), gives it a push downhill.

If the roads are wide enough, a similar technique can be used to safely get cargo down from your city. The wagon would be placed on a sledge, which would be pushed down the slope. When traction inevitably stops it, the horse would give it an additional push until the sledge is safely down.