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From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Analysis of electrostatic principles regarding annular gaps to prevent spark-over, including tests on Lucas electrode sets.

Identifier  WestWitteringFiles\M\2October1924-December1924\  Scan87
Date  20th October 1924
  
Contd.
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EFCS/T20.10.24.

exhibited a coronal discharge preceding the spark-over.
This was definitely visible in the case of the Lucas gap.

On electrostatic principles, in order to obviate this, the ratio b/a of the inside dia. b of the earthed concentric conductor to the dia. a of the H.T. spindle should not exceed the quantity e (2.718), the base of the natural logarithms.
It is considered, however, for certain reasons that this ratio can be exceeded practically and therefore the annular gaps are usually (as in this instance) constructed so that this ratio is somewhat larger. Thus constructed, they give the advantage that the actual gap length is larger, thus reducing the tendency to arc, and that the actual centering of the inner electrode is not so important. In this connection, see attached copy of matter relating to annular gaps.

To investigate the point, however, alternative sets A, B and C of electrodes for the Lucas Elec. Co's annular gap have been made of dimensions according to the table, attached.
Of these three sets, which have been arranged on electrostatic principles to give the same total spark-over voltage,
Set A gives a ratio b/a greater than e.{Mr Elliott - Chief Engineer}
" B " " " slightly greater than e.{Mr Elliott - Chief Engineer}
" C " " " less than e.{Mr Elliott - Chief Engineer}

Their behaviour has been investigated (on the high tension transformer) and the results of the observations are contained in the remarks column of the table.

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