From Robert Perrin and Thomas Charnley, Loughborough University of Technology
As physicists who have worked for over 25 years as consultants with John Taylor & Company, Bellfounders of Loughborough, we were surprised by the article “When the Great Bell Broke” (17 December).
Modern bell metal contains approximately 23 per cent tin and 77 per cent copper. The 30 per cent tin mentioned would be an alloy close to speculum, which is very brittle. The metal used for Great Paul was not assayed but was certainly of roughly the modern composition.
It is true, as claimed, that blow holes can occur in badly cast bells (which ought to be scrapped). However blow holes would only influence Young’s modulus locally, not globally as the author implies. If they were of much significance the bell would exhibit appalling “warble”, which it does not.
The author is correct in stating that Great Paul was not tuned and that the Quint is about a semitone sharp. However, when he quotes 233 Hz for B flat he is forgetting that the International Convention fixing that frequency was not adopted until 1939. Although the frequencies of Great Paul’s partials do not conform well with modern tuning practice, they are in general agreement with Old Standard Tuning which was in use when it was cast in 1881. Thus the Hum is only a minor 7th below the Fundamental rather than the octave in a modern bell.
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Finite-element methods have been in common use in bell research since at least 1980 in Britain, the Netherlands, Canada and New Zealand. They are a routine tool in bell design. In particular they were used by the Royal Dutch Bell Foundry to produce major-third carillon bells. We suggest that Shippen re-runs his finite-element programme using the values of 103 gigapascals for Young’s modulus and 8.85 × 103 kg m−3 for density. The results should be insensitive to Poisson’s ratio, which is about 0.38.
