I am trying to solve for 'h' using the first equation above. My script produces a result, however it is unexpected. The solution of 'h' should increase with 's', yet this is not the case. I have attached the script below, any help would be much appreciated.
clc; clear all; close all;%%%%%%%%%% Physical Parameters %%%%%%%%%%
r=0.1; b=0.15;W=60;Kc=0.99*1000; Kphi=1528.4*1000; n=1.1; c=1.04*1000; phi=28; A1=(Kc/b+Kphi);k=0.6;Beta=0.0872665;kx=0.043*Beta+0.036;%%%%%%%%%% Defining equations %%%%%%%%%%
s=1 syms h syms PhetaPhetaF=acos(1-h/r);PhetaR=acos(1-k*h/r);jx=r*(PhetaF-Pheta-(1-s)*(sin(PhetaF)-sin(Pheta)));Sig=A1*r^n*(cos(Pheta)-cos(PhetaF));Taux=(c+Sig*tand(phi))*(1-exp(-jx/kx));%%%%%%%%%% Solving for h %%%%%%%%%%
fun=Taux*sin(Pheta)+Sig*cos(Pheta);eqn=W==r*b*vpaintegral(fun,Pheta,[PhetaR,PhetaF]);sol=vpasolve(eqn,h,.1)
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