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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 comparison of electrical loss between an S. Smith & Sons dynamo and an ordinary dynamo.

Identifier  ExFiles\Box 3\5\  05-page087
Date  8th August 1919 guessed
  
The loss y is to be a minimum
Therefore equate dy{F R Danby}/dz to zero
∴ 2r[2z - x] = 0
∴ 4rz = 2rx
∴ 2z = x
z = ½ x
The loss is therefore a minimum when the current flowing in the resistances is half the output from the armature.
Comparison of S. Smith & Sons Dynamo and Ordinary Shunt Dynamo
S. Smith & Sons/ Output x amps.
If resistance per quadrant = r ohms,
Total loss = ¼ x²r + ¼ x²r = ½ x²r watts.
Ordinary Dynamo/
Total loss = (¼ x² x 2r) + (¼ x² x 2r) = x²r
The loss is therefore twice that in the S.&S. Machine.
  
  


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