1 - 1/6/2010 ECOR 2606 The Big Picture Real World Problem...

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1/6/2010 1 Real World Problem Apply engineering knowledge to get desired ECOR 2606–The Big Picture Formulation for Solution Selection of Appropriate Numerical Method The final solution should be checked. output in terms of known inputs. Computer Solution of Problem Numerical solution Analytical solution Numerical solution obtained using Euler’s Method and 1 sec intervals.
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1/6/2010 2 tMax = 20; % maximum time m = 69.1; g = 9.81; cD = 0.25; % Euler solution n = 21; % number of points (including initial point) deltaT = tMax / (n 1); % interval width The Matlab code used to produce the graph . t = linspace (0, tMax, n); v = zeros (size(t)); fori= 2:n v(i) = v(i 1) + (g ((cD / m) * v(i 1)^2)) * deltaT; end % analytical solution tFine = linspace (0, tMax, 100); vCalc = sqrt(g * m / cD) * tanh(sqrt(g * cD / m) * tFine); plot (t, v, 'r o', tFine, vCalc, 'k'); title ('Skydiver Velocity vs Time'); xlabel ('Time (seconds)'); ylabel ('Velocity (m/s)'); grid on Analytical solution in black, numerical solution (using ode23) in red.
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1 - 1/6/2010 ECOR 2606 The Big Picture Real World Problem...

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