The horse and oat cart challenge

I maintain that this little problem will illustrate how the maximum size of a city is well below that experts currently state. In fact, this problem shows that without fossil fuel the sizes of cities will be severely restricted. This little problem sets a benchmark for how large a city can be, as it is a solution we can apply today, one that is tried and tested.  Designs with electrical railways, sail boats whatever will have to demonstrate they can beat this design.

See the challenge below. A city with boundary at B is surrounded by land that feeds it. The food is taken to town by horse and cart. No fossil-fueled transport is available. Neither is any renewable transport like rail or sailing boats on canals. Boundary A is the outermost limit from which food is brought in. C is the center of the city and the distribution point farthest away from the outer boundary.

Assume for the sake of simplicity that a horse and cart is to come into the town to deliver oats to point C for distribution from point A. And that the horse and cart will return to point A for the next load. Assume as well that the horse needs to eat the oats to be able to pull the load.

Now, the horse cannot eat all the oats on the cart during the journey, or that would make the exercise pointless. As the horse has to return it can neither eat half the oats during the journey. Personally I would think about 10% per direction (20% in all) would be acceptable but you may take your own amounts. (Please show this carefully in your working)

THE TASK

Calculate using this model the maximum size of a city that is independent on fossil fuels. I maintain that the maximum size of a sustainable city is well under one million inhabitants, meaning that the majority of cities in the world today are at a high risk of starvation due to fossil fuel shortages. I would be happy is someone could prove me wrong.

Show all your working and clarify your assumptions.

Helpful data is given below.

  • Although horses eat grass, they need oats.
  • Imagine then a horse carrying food from the area of production to the city where the oats will be consumed.
  • The driver feeds the horse the oats from the cart.
  • Is there a way the answer to this problem could illustrate for us the maximum size of a city? Surely the horse should arrive with its load mainly intact. If the horse has to carry the oats so far that it eats up the load (and has none for the return journey) then sending the oats to the city is pointless.
  • An average horse is about 750kg to 800 kg.
  • It can pull two times its own weight.
  • A draft horse can pull a dead weight along the ground (draft) equal to 1/10 their body weight for 8 hours a day.
  • A wagon weighing 1,8 tons takes four horses to pull it.
  • For simplicity, let us say the wagon weighs 0,8 tons and carries a ton of oats.
  • A grain feeding of only .3% of body weight is all drafts need they can survive on grass they find by the roadside for the rest of their diet.
  • City density ranges from 30,000 per km2 to suburbs of 1200 per km2. Suburbs deemed pleasant to live in have 5-6000 per km2. Dense city centres have around 12,000 per km2.
  • When working in the harness all day, each horse will eat about 4.5 – 7 kg of grain and about 13,5 kg of grass or hay a day. Note – as the distance pulled increases so does the amount of grain I feed.  When pulling  30 km a day, calculate 9 kilos of grain per horse each day
  • For help with calculation the size of the area that will feed the city a rule of thumb is that you need one hectare of agricultural land per family of 4. See more on that aspect in the earlier post here.
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