W8.3 Let There Be Light!

This challenge is all about order-of-magnitude estimation, an important skill to enable you to approach an unfamiliar expression and make sense of the magnitude of the quantity.

When you have an answer, you can ask if it makes sense ( Guideline 0.8).

The question is: Estimate the annual cost of streetlighting Edinburgh.

Solution

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Solution

  • Taking the edge of the city as the City Bypass, Edinburgh is approximately circular, radius 7km. So that’s an area of πr2150km2
  • Assume a streetlight at every corner of a 40×40m square. So there is 1 streetlight every 0.0016 km2
  • So total number of streetlights in the city is 150/0.0015=1×105
  • Streetlights are pretty bright, much like the outdoor spotlights you can get. Let’s say each streetlight is rated at 300W=0.3kW
  • Each light is on, on average, for 8 hours a day, 365 days a year. So each light uses 0.3kWh×8×365=876kWh of electricity
  • A kWh costs me about 7p, the Council probably pay half that (cheap rate ?), so cost to run 1 street light for one year 876×0.035=£30
  • Cost to run all the city’s street lights :
    30×100000=£3M