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 calculations for the efficiency of a worm and nut mechanism.
| Identifier | ExFiles\Box 67\4\ scan0332 | |
| Date | 13th July 1927 guessed | |
| contd :- -2- ∴ Fw / Fn = (sin θ cos γ + sin γ cos θ) / cos γ _____________________________________ (cos θ cos γ - sin θ sin γ) / cos γ = sin(θ+γ) / cos(θ+γ) = tan(θ+γ) To find the efficiency when acting as in diagram : Let δ = 'lead' of nut (or worm). Then work done by nut = Fn . δ and work done by worm = 2πr Fw but δ / 2πr = tan θ [Diagram of a right-angled triangle with sides labelled 'δ' (opposite), '2πr' (adjacent), and angle 'θ'] ∴ η = (Fn δ) / (2πr Fw) = (2πr tan θ Fn) / (2πr Fw) = tan θ (Fn / Fw) = tan θ / tan(θ+γ) Efficiency when 'parking' is expressed : by η = tan θ / tan(θ+γ) ____________________ contd :- | ||