The Joy of Rough Calculations
This weeks lecture was given by Ben Crave who explained the joys and importance of rough calculations, how they can determine the feasibility of a project early on, quickly and easily. He talked about how staff at GSA were urged to be careful of how much water they put in the kettle when making a cup of tea in order to avoid wasting energy, yet GSA frequently fly staff to their outpost in Singapore, so the question arose, how many cups of tea would you have to make to use the same amount of energy as a flight to Singapore in an airbus A380? You can see my working here. I worked it out works to be around 50 million cups of tea, so really, the additional little bit of water is extremely insignificant compared to just one flight to Singapore. Although this example might not determine the feasibility of a project, the same principles can be used in a more practical manner to show that there isn’t enough rainfall on a roof in the year to be worth harvesting the energy, or it can be used to simply prove a bogus statement wrong.
His train of thought inspired me to question the amount of energy required to dry washing. My flatmate quoted his mother on a number of occasions saying that we should avoid using the tumble dryer because it consumes a lot of power so is expensive to run, however I instinctively ignored his advice. Since then, I’ve moved to a flat without a tumble dryer and miss the convenience it brings. I know they are power hungry machines but they get the job done, fast and easily. My intuition told me it was more effective to dry washing in the tumble dryer than heat the entire house (when the majority of people are out). So, I decided it was time to confirm my theory and did a quick experiment at home. Although the focus of the workshop was on calculations I feel quick experiments are also a powerful tool for evaluating ideas.
After doing some washing and hanging it out on a clothes airer, I turned the heating on and took a meter reading. The washing took a few days to dry so the heating wasn't left constantly on, just for roughly 4 or 5 hours a day. So when the washing was finally dry, I took a second meter reading and worked out the number of cubic feet of gas used then converted it into kilo-watt-hours.
It worked out to 85 kWh, this is slightly larger than it aught to have been because I probably used the hob a little bit over the few days but it aught to be pretty close. If I’d left the heating on constantly instead of turning it off from day to day it would also have used less energy (because the boiler becomes more efficient the longer you leave it running) but this would simply not be practical. I worked it out to cost £2.85 using the gas central heating.
I then compared this result to two tumble dryers: one modern, efficient tumble dryer which uses a heat pump to recycle the waste heat and another older, less efficient tumble dryer. The more modern tumble dryer uses only 2.7 kWh per cycle costing just 40p! The second, less efficient model uses 4.38 kWh per cycle costing 64p. So the tumble dryers both use less energy than heating the house for a couple of days, sufficiently less for them to cost a fraction of the price even though the price of electricity is about five times as much as gas.
Obviously it makes sense to heat the house when you are home and dry the washing this way instead of using additional energy and adding 40p to your bill (though it’s pretty insignificant compared to heating the whole house), however, in cases where you are out for most of the day, it really doesn't cost so much to make use of a tumble dryer and is so much better for the environment.
You can check my working here.
I’m glad I could confirm my suspicions that my old flat mate’s mother’s erroneous statement was indeed incorrect. I enjoy being able to quantify the world we live in, enhancing my understanding of it. It would be nice to work on a project in the future using a concept derived from mathematics like the way Carwardine did with the Anglepoise. His understanding of mechanics allowed him to examine a spring and lever mechanism and derive an expression for the stiffness of the spring, which he found, under certain conditions, depends only on the geometry of the system and not on the angular position. Read about it on my Great Design blog here.
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