Some of the most important things one learns in a physics degree are:
- Dimensional Analysis (have I stuffed up anything obvious?)
- Scale Analysis (what terms in this equation actually matter for this problem?), and
- Start with an Envelope (know what your answer is roughly, before further calculation).
The last is pretty fundamental. I used to teach a course called “Nursing Mathematics” at my local polytechnic, for, you’ll not be surprised to know, nurses. The entire point of the course was to give nurses the mental arithmetic tools (supplemented on occasion by an envelope and a pen) to know what the answers to most of their day-to-day calculations are, before using a calculator to get things right. You may or may not be surprised to know how important this is, folk have died because of incorrect factors of ten in IV flow rates … Scale problems happen often with calculators, but less often when individuals have a grip on the scale of answers before attempting the “real” calculation (either from experience, or explicit “pre-calculation”).
Which is a long winded way of introducing a post which both validates my original decision to buy an electric lawn mower instead of a petrol mower, and removes my guilt over not buying a push-mower.
I spend a lot of time thinking about this sort of issue, but never get down to writing it out. Well done “King of the Road”. My current suspicion is that it would be a good thing to get an electric garden shredder, rather than pile the stuff on a regular basis in a car and drive to the dump … one day, I will do that calculation …
Meanwhile, along David MacKay’s fabulous book, I feel I now have two “back to basics” places to go to find some numbers about practical ways of dealing with our energy futures.
To shred or not to shred? (from “Bryan’s Blog” on (on Sunday 18 April, 2010)
For a long time my wife has been suggesting we should get a garden waste shredder …
Chris Rusbridge (on Wednesday 16 December, 2009)
Bryan, I used to call your 3rd bullet the “engineer’s wet finger in the air” calculation. And I have to say that, looking at the post by “King of the Road”, I’m bringing it into play very strongly. My wet finger is really itching at the suggestion that the petrol-powered mower uses 120 times the primary energy as the hand-pushed mower. This is especially when the previous post that KoR refers to on going to the supermarket only shows a factor of two difference between walking and driving a small car, or factor 4 between walking and a 4*4.
In fact, looking at the small car case in the earlier article, he uses 1/33*6= 0.182 (US) gallons of fuel and claims that as 28.9 megajoules. But in the mower case he uses 0.186 gallons and claims that as 2800 megajoules. So I suspect that KoR has made a simple transcription error and that is the source of this huge discrepancy!