The calculation of the angular propagation constant for a bend requires the solution of the equation J',(x) Y~(px) -J',(px) Y'v(x) = 0 for v. Methods of solution, which have been proposed, are outlined and their limitations are discussed. A simple computer method, suitable for BAsic language, the main problems of which are those of calculation of cylinder functions of virtually unlimited positive order and argument to a moderate degree of accuracy, is proposed. from which or W.G. OSBORNE B J~,(?rl) J'0'r2) A Y,(?r,) Y'(m)' J'(?rl) Y'(?r2)-J'(?r2) Y;(m)= 0 (Ib) Thus, for propagation in the 0 direction without reflection, (2)
where the angular propagation constant, v, is found by solving equation (lb). Methods for doing this have been developed by a number of workers over a period of many years but most of these have resulted in computational difficulties for bends of moderately small radius. It is proposed in this paper to review briefly the major works and then propose a method of moderate accuracy, which can be used by those with modest computational facilities.
Equation (lb), for convenience, will be rewritten as