Today Ben Craven, another Product Design Engineering tutor, came to speak to us for Design and Technology class. He explained and then showed us the importance of approximate calculations and how useful they can be to assess the feasibility of initial concepts. Often it’s incredibly simple to use some basic maths to quickly work out if a design or idea is even possible. Normally, even with approximations, maths will point to one of the extremes, however, the going can get tough when it gives an answer on the fence.
To explain his point, he showed the class a couple of simple examples. Ben explained that a student once consulted him about charging a mobile breathing support system by the kinetic energy of wheeling it behind the user. It required 100W of power to run; that’s equivalent to raising a 10kg weight at one meter per second. For someone with breathing difficulties that’s just not a viable option. Or another idea; let’s catch all the rain that falls onto the Reid building’s roof and use the potential energy to generate power. A quick calculation using rough dimensions for the building and an online search to find the average rainfall in Glasgow shows that actually that would only produce about 11W, enough for one low energy light bulb. The point of an approximate calculation isn’t to be precise, but to better inform an educated guess.
Finally Ben proposed us questions in small groups to test our common sense, arithmetic and, hopefully, help us teach ourselves something. Kasim, Andrew and I attempted to answer; how far could a car drive using the same energy required to make a cup of tea? Similarly, how far could a train travel on expending the same energy? So, using the specific heat capacity of water we worked out that for one cup of tea it would take about 84kJ of energy to bring it the boil. Next, if one litre of diesel stores approximately 10kWh of energy, and our car gets 20mpg, the car can travel around 19m using 84kJ of energy. For the train, we used the Glasgow to Edinburgh route, it would get about 4m with the same energy. However, if we compare these values in people-metres (passengers multiplied by distance) the car gets 76pm and the train gets 2184pm. These latter figures demonstrate the massive gap in energy efficiencies between private and public transport, all with some simple maths. Other groups worked out a range of problems; such as how much land would be required to fuel the aviation industry with wood? It turns out a quarter of a million squared kilometres per day of forests would be needed if that was the case.
I personally found this a really interesting morning. It wasn’t as related to design as other talks have been but a welcome, friendly reminder as to how useful simple maths can be. If you want to know more about Ben Craven and his work, you can find out more here:
Another fun little fact that can be worked out using simple maths; humans are, pound for pound, about 7000 times better at emitting heat energy than the sun. Try answering some questions you don’t know the answer to yourself, you might be surprised.
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