Re: Case Displacement

Posted by RAB on July 24, 2007 at 23:26:02 from (195.93.21.134):

In Reply to: Re: Case Displacement posted by Owen Aaland on July 24, 2007 at 17:22:22:

Ha, that is what they teach you at school. I know, I do it too. But an engineer knows it is really difficult to measure R so most just measure the diameter. It then makes much more sense to substitute D for R (so R squared is now D squared over four) for the calculation.
Makes no practical sense using a formula containing a derived measurement.
The reason it has been taught that way at school is because the proof of the area of a circle is from 'the limit of the area of a rectangle of R times half the circumference'.
Only the sharpest can absorb circumference, area, area proof AND that D2/4 is just the same as R2. That is the way the exam boards set the Q's for this topic and the formula given is always in terms of the radius and not the diameter.
They keep it simple at the learning stage whereas I keep it simple in the practical real world.
When did you last measure a radius directly? None of the engine specs refer to the radius of the bore, do they? The circumference of a circle is Pi*D. Why divide D by two just to multiply it again in the formula, like they teach at school.
As you said it does make it easier for calculating the displacement of an engine. Real world practicality.
Only the sharper sets realise the value of cancelling when doing practical maths. So much for the advent of the cheap calculator! They just don't use their brain at school anymore, unless they have too. In my school days we used log tables to multiply sets of numbers (two, three or four at a time) so any cancelling first made things so much easier for the final calculation.
Most Q's in exams fall apart if done this way (cancelling), but the majority of students just make life hard and calculate unecessary parts on the calculator. OK at school but not in the real world when the calc battery expires!
Regards, RAB

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