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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).
Page of mathematical formulae for calculating the revolutions and deflection of a speedometer drive.

Identifier  ExFiles\Box 59\2\  Scan124
Date  23th March 1931 guessed
  
-4-

The revolutions per minute of the speedometer
drive :-

N = GRS/60

= G/60 (R_oS - bs{A J. Barnes - Assistant Manager}^2) G being the
fixed gear ratio of speedometer drive revs. to wheel revs.

The deflection of the indicating pointer
reckoned in divisions on any proportional miles
per hour scale is :-

d = cN{Mr Chamberain} (c being a constant)

= cG/60 (R_oS - bs{A J. Barnes - Assistant Manager}^2)

In the absence of any speed effect of the tyres
the deflection :-

d_o = cG/60 . R_oS

whence S = 60/cG . d_o/R_o

and cG/60 .bs{A J. Barnes - Assistant Manager}^2 = 60/cG .b d_o^2/R_o^2

and finally d = d_o - 60b/(cGR_o^2) . d_o^2

= d_o - kd_o^2 (k being yet another constant)
  
  


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