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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).
Mathematical analysis of spark production and energy efficiency in an ignition coil system.

Identifier  ExFiles\Box 52\3\  Scan295
Date  11th December 1917
  
Contd.
-7-
EFE/T11.12.17.

value C, with as little expenditure of electrical energy as possible and in some cases in as short a time as possible. If L be the inductance of the primary winding, the stored energy of the magnetic field is then ½ L C² and represents the energy available for secondary spark production.
We shall consider the amount of this energy to be fixed.
The mathematical results are as follows.
(a) Assuming L and therefore C to be fixed, the energy supplied by the battery per spark (or the efficiency of magnetic field production) is a function of C₀ only, where C₀ is what we choose to call the final current, being the quotient E {Mr Elliott - Chief Engineer} /R, where E is the battery voltage and R the working value of the total primary resistance. So long as we keep C₀ the same, then for an assumed fixed value of C the energy supplied per spark is the same. We can double R and double E at the same time, and we do not alter C₀ or the energy supplied by the battery. The rise of current to the value C takes place however twice as quickly. The quantity of electricity supplied is thereby halved, which fact, taken with the doubled voltage, means the same amount of energy supplied. In order, therefore, to make a coil give twice the number of sparks per second of the same intensity as normally, we may double the voltage and double the total primary working resistance, and the efficiency of spark production is unaltered. This would seem to be the other advantage of the addition of ballast resistance. It is
  
  


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