sprftau(R, d, P, n, a, G, v)

function [tau,f] = sprftau(R, d, P, n, a, G, v)
%
% SPRing calculations of F and TAU (sprftau) of a circular cross-section spring,
% where:
% tau = max shear stress produced,
% R = radius of coil measured from spring axis to ctr of section,
% d = diameter of circular section,
% P = load (tensile or compressive),
% f = total stretch or shortening of spring,
% n = number of active turns in spring,
% a = (alpha) pitch angle of spring,
% G = the modulus of rigidity of the material (shear modulus),
% v = poisson's ratio of the material.
%
% Usage:
% 1) If the function is called with no input arguments, then a graphical
% representation of the equations is produced for publication purposes.
% 2) If the function is called with only the first 3 input args (R,d,P),
% then only the value of tau is returned. f is set to -1.
% 3) If the function is called with all 7 input args, then both tau and f
% are returned.
%
% reference 1:
% Roark's Formulas for Stress and Strain, 7th Edition, page 398
% Warren C. Young, Richard G. Budynas
% (c)2002, 1989 by the McGraw-Hill Companies, Inc.
% ISBN 0-07-072542-X
% 
% reference 2:
% Mechancial Springs, 2nd Edition
% A. M. Wahl
% (c)1963, 1944 by the McGraw-Hill Book Company, Inc.
% Congress Catalog Card Number 62-20725
%
% Rev.1 15Apr2008

%%

if nargin >= 7
    f = ((64*P*R^3*n)/(G*d^4))*(1-(3/64)*(d/R)^2+((3+v)/(2*(1+v)))*(tan(a))^2);
else
    f = -1;
end

if nargin >= 3
    tau = ((16*P*R)/(pi*d^3))*(1+(5/8)*(d/R)+(7/32)*(d/R)^2);
else
    tau = -1;
    h1 = figure('Color','w','Position',[100 100 600 300]);
    axis off;
    h2 = text(.5,.25,['$$f = \frac{64PR^3n}{Gd^4} [1-\frac{3}{64}(\frac{d}{R})^2+\frac{3+v}{2(1+v)}(tan\alpha)^2]$$'],...
        'Interpreter','latex','EdgeColor','k','HorizontalAlignment','Center',...
        'BackgroundColor',[.9 .9 .9],'FontSize',20);
    h3 = text(.5,.75,['$$\tau = \frac{16PR}{\pi d^3} [1+\frac{5}{8}\frac{d}{R}+\frac{7}{32}(\frac{d}{R})^2]$$'],...
        'Interpreter','latex','EdgeColor','k','HorizontalAlignment','Center',...
        'BackgroundColor',[.9 .9 .9],'FontSize',20);
end