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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).
The mathematical formulas for calculating valve spring wave velocity.

Identifier  ExFiles\Box 56\2\  Scan111
Date  22th November 1930 guessed
  
X290.

VALVE SPRING WAVE VELOCITY.

The wave velocity = √e/m

e = force for unit compression in unit length
= force for unit strain (poundals)
m = mass per unit length (pounds per inch)

Dimensionally √e/m = √((lbs inch² sec⁻²) / lbs)
= inch sec⁻¹

e = WgL where

W = rate of spring (lbw. per inch)
g = gravity (inches per sec²)
L = length of spring (inches)

Since W = (Cd⁴) / (8D³ k¹L) where k¹ = number of turns per unit length.

e = (Cd⁴g) / (8D³ k¹)

m = (k¹L + 1) πD x (π/4) .d² w ÷ L
= ((k¹L + 1) π² Dd² w) / (4L)
  
  


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