vanhees71 said:
Hello vanhees, I've looked at this paper before.
Something I tried to do was treat each wrap of the coil as an individual segment and integrate to get its contribution. I wasn't sure if my results were reasonable. I get a very small terminal velocity.
[CODE lang="matlab" title="coil approximation"]clc
clear all
close all
% magnet dimensions [m]
d = .0127; %magnet height
r = .00238; %magnet radius
%mass of magnet [kg]
m_w = .0017;
% other constants
u_0 = 1.26E-6; % permeability of free space constant T m/A
g = 9.81; % gravitational constant m/s^2
%coil properties [m]
a = .00635; %radius
w = .000635; %width of wire
N = 100; % number of turns
c = pi*a*2; %circumference
wl = c*N; %wire length
cs = pi*(w/2)^2; %cross sectional area
rho = 1.7e-8; % resistivity of copper [ohm/m]
wr = (rho*wl)/cs; % resistance in wire [ohm]
lt = 0.3048; % length of tube
%magnetic properties
sm = 72730000; % magnetic surface charge density [Mx/m^2]
qm = pi*sm*r^2; % total charge Mx
eff_dist = .003175; %effective distance of magnet [m]
%terminal velocity calculation
p = qm*d;
x = d/a;
val = scalingfunction(x);
v = (8*pi*m_w*g*rho*a^2)/(u_0^2*qm^2*w*val); %terminal velocity calculation
%for one ring
flux = [];
z = 0:.00001:eff_dist;
for i = 1:1:length(z) %z varies from zero to effective distance of magnet
flux(end+1) = (u_0*qm*.5)*(((z(i)+d)/sqrt((z(i)+d)^2+a^2))-(z(i)/sqrt(z(i)^2+a^2)));
end
Total_flux = 2*sum(flux);
delta_t = (2*eff_dist)/v;
emf = (N*Total_flux)/delta_t;
function [val] = scalingfunction(x)
fun = @(x,y) ((1./(y.^2+1).^(3/2))-(1./((y+x).^2 + 1)).^(3/2)).^2;
val = integral(@(y) fun(x,y),-Inf,Inf);
end[/CODE]