Coincidentally, the point about saving money/energy by turning off lights came up in conversation a couple weeks ago. Going by the general rule of thumb, I said it wasn’t worth it if the room will be used in the next fifteen minutes or so. I was “one-upped” when a passing customer claimed the energy expended by physically flipping the switch was greater than the energy saved. Of course, the customer was dead wrong, but at just that moment all the phones started ringing and a group of people walked in the front door. Given the situation on the ground we let it go with a “yeah, maybe” and “who knows”.
Reading the column reminded me of that episode. Now I am wondering how wrong the customer was. I will frame the question in the context of Cecil’s column. How much energy is spent by physically flipping a light switch off and on before and after one’s daily shower?
I thought about writing to Cecil/the SDSAB, but then I remembered that the Master has retired and the SDSAB is probably out of commission, too. So here I endeavor to answer my own question.
With my elbows in, my whole arm slack and forming an angle just over 90 degrees, and my hand resting on a scale, the “weight” (mass) reads about 1 kg.
The length from my wrist to elbow is about 33 cm. Using my elbow as the centerpoint, my hand makes an arc of about 90 degrees when I quickly raise it to flip a switch. In practice I use my upper arm but that involves a tiny bit more physics that I don’t feel like doing right now.
With a radius of 33cm the perimeter of the resulting circle is 66pi cm. Therefore the arc of 90 degrees has a length of 16.5pi cm, which I’m rounding to .5 m.
It takes me somewhere between half a second and three-quarters of a second to raise my hand up to the light switch. I will use .5 s for simplicity’s sake.
Moving a distance of .5 m in .5 s (from a state of rest) is equivalent to moving .5 m at constant acceleration of 1 m/s^2 (from a state of rest).
Acceleration of 1 kg at the rate of 1 m/s^2 is equivalent to 1 N of force; 1 N of force acting on an object through a distance of 0.5 m is equal to 0.5 J of work (1 Joule = 1 Newton x 1 metre). Therefore flipping a light switch, by lifting my one kilogram arm a distance of half a metre over half a second, takes half a joule of energy. Considering that the light must be switched twice (once before entering the shower, and once after exiting), this amounts to one extra joule per day.
The ratio between joules and kilowatt hours is 360,000,000 to 1. Therefore, the energy spent moving one’s arm to toggle of the bathroom lights twice a day amounts to 0.00000101389999999… kilowatt hours annually. Put another way, one joule per day is approximately 0.872 Calories per annum, or approximately one celery stick’s worth of energy per eighteen years. You spend about 20 times as much energy after drinking a 16oz glass of ice water (17.5 Calories) than you by flipping the light switch twice a day for a year.
~Max