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 calculations for determining the conditions and extent of interference in pitch circles.
| Identifier | ExFiles\Box 28\5\ Scan100 | |
| Date | 28th April 1917 | |
| H.R. 235a (500 T) (S.D. 408. 28-4-17.) Bm. 2/156/13. -2- Contd. Let O1C = r, and O2C = s; be the radii of the pitch circles and a the addendum, then to express the condition of interference mathematically we have:- O2 P1^2 = P1 P2^2 + O2 P2^2 = (r + s)^2 sin^2 θ + s^2 cos^2 θ. = (r^2+2r s) sin^2 θ + s^2 O2K1^2 = (s + a)^2 = a^2 + 2as + s^2 Interference occurs if O2 K1^2 > O2 P1^2 i.e. if (r^2 + 2rs{Sir Henry Royce's Secretary}) sin^2 θ < a^2 + 2as i.e. if sin^2 θ < (a^2 + 2as) / (r^2 + 2rs{Sir Henry Royce's Secretary}) i.e. if sin θ < sqrt((a^2 + 2as) / (r^2 + 2rs{Sir Henry Royce's Secretary})) ================================== To determine the extent of the interference we have:- CK{Mr Clark}1 = P2K1 - P2 C = sqrt(O2K1^2 - O2P2^2) - P2 C = sqrt((s + a)^2 - s^2 cos^2 θ) - s sin θ = sqrt(s^2 sin^2 θ + a(2s + a)) - s sin θ. | ||