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A city energy budget

Energy and power · level 8, lesson 5 of 6

A question to start

How much power would a city of 1,000 people on Mars need? Nobody knows exactly, but you can still make a good estimate.

The idea

An energy budget lists every use, puts an average power on each, and adds them up. Even rough guesses are useful: they show which uses matter most and how big the power plant must be.

On Mars, people need power for things Earth gives free: air to breathe, water, warmth, and light for crops. Here is one set of guesses, per person, for working with:

Use, per person Average power, assumed
Air, water and waste recycling 1 kW
Heat and light in the habitat 1.5 kW
Growing food under lamps 5 kW
Making oxygen, water, fuel and materials 3 kW
Homes, computers and transport 1.5 kW
Total 12 kW
airheatfood: 5 kW making 3 kWhomes12 kW per person

For comparison, a home in the United States used 10,791 kWh of electricity in 2022:

Average electrical power Mars Earth
Need, as worked out here 12 kW per person (assumed) 1.23 kW per US home (2022)

Worked examples

1. The city. \(1000 \times 12 = 12{,}000\) kW, or 12 MW. In a sol of 24.66 h, that is about 296 MWh.

2. The US home. \(10{,}791 \text{ kWh} \div 8{,}760 \text{ h} = 1.23\) kW on average.

3. On solar. From the level 6 table, a flat panel near the equator gives about 33 W per m² on average. \(12\times10^6/33 \approx 360{,}000\) m², more than a third of a square kilometre, before nights and storms.

4. On reactors. In 10 kW units like Kilopower: \(12{,}000/10 = 1{,}200\) of them. A city would want much bigger reactors.

Try it

  1. If the lamps for food used half as much power, what would the total per person be?
  2. What share of the budget is food?
  3. How many US homes use as much electricity as the city's 12 MW?
  4. Name two uses in the Mars budget that a city on Earth gets free.
Answers
  1. \(12 - 2.5 = 9.5\) kW.
  2. \(5/12 \approx 42\%\).
  3. \(12{,}000/1.23 \approx 9{,}800\) homes.
  4. Air to breathe, and sunlight for crops (also water, and protection from the cold).

Common mistake

Adding kW and kWh. Keep the whole budget in one kind of unit: all average powers in kW, or all energies in kWh per sol. Then convert at the end.

Where it leads