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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 2 of a calculation to correct Indicated Horse Power (I.HP) for atmospheric conditions.

Identifier  ExFiles\Box 37\3\  scan 118
Date  20th September 1917 guessed
  
Contd. -2-

therefore for every 100 I.H.P. at N.T.P. k has the value

100 √289 / 29.9 = 1700 / 29.9 = 5.68 so that I = 5.68 P/√T

If we substitute in the above the atmospheric
values of P and T we should obtain a figure to which 100
bears the same ratio as the corrected I.H.P. bears to the
observed I.H.P., and we could therefore correct our I.H.P.
It will, however, be more convenient to find
the % correction to be applied to I to obtain Io, the I.H.P.
at standard state (for corrected I.H.P.) and thence to find
the correction to be applied to B (the B.H.P.) to obtain Bo,
the B.H.P. at standard state (or corrected B.H.P.)
Suppose Po exceeds P by p inches.
To falls short of T by t°C.
(i.e. t°C is the atm. temp. - 16° C).
Io exceeds I by i H.P.
Then:-
Io/I = Po/P x √T/To

or
(I + i)/I = Po/(Po - p) √(To + t)/To

i.e.
1 + i/I = { 1 - p/Po }^-1 { 1 + t/To }^1/2

whence.
≃ 1 + p/Po + t/2To (approx.).

100i/I = 100 p/Po + 50 t/To

Contd.
  
  


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