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 total engine torque and harmonics for 6, 8, and 12-cylinder engines.
| Identifier | ExFiles\Box 23\5\ Scan074 | |
| Date | 1st February 1923 guessed | |
| contd :- -2- T = A + B sin 1/2 wt + C sin 2 wt + D sin 3/2 wt + E sin 4/2 wt + F sin 5/2 wt + --- etc. Where A is the mean torque for one cylinder and is the only part of the above expression contributing to the H.P. of the cylinder. If we insert the proper phase angles for the other five cylinders, and add up all six series, we get an expression for the total torque of the engine : T₆ = 6 { A + D sin 3/2 wt + G sin 6 wt + J sin 9/2 wt + M sin 6 wt + ---- etc.} In other words the majority of the harmonics disappear, those remaining, only multiples of three, being added together. If we insert the values found graphically for A, D, G etc. and plot the results, we obtain exactly the same torque curve for one revolution as is obtained by adding up three indicated torque diagrams spaced at 120° intervals. By a similar process we may obtain the gas torque of an 8-cyl. engine in the form : T₈ = 8 { A + E sin 2 wt + I sin 4 wt + M sin 6 wt + ---- etc.} the remaining harmonics are multiples of 4. The gas torque of a twin-six becomes : T₁₂ = 12 { A + G sin 3 wt + M sin 6 wt + S sin 9 wt + ---- etc.} the remaining harmonics are multiples of 6. The following tables give the magnitudes, frequencies and amplitudes of the particular harmonics that contd:- | ||