1. SINGLE OBJECT RANGE DETECTION (SAMPLE ASSIGNMENT)
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Trebuchet Range Simulation and Optimization
This sample assignment shows a Model of a simple trebuchet that predicts projectile range based on
fulcrum position & launch angle.
plot_treb.m
% Plot the projectile range for a simplified trebuchet over a
range of
% design variable values. Illustrates the nonsmoothness in
objective
% function that results from discrete events in the
simulation.
%
% Model corresponds to an example video created for ME
149 (Engineering
% System Design Optimization), a graduate course taught
in the mechanical
% engineering department at Tufts University. The video
can be viewed at:
%
% http://www.youtube.com/watch?v=3QUJNEzloDo
%
% Author: James T. Allison, Ph.D.
clear
% Define points for full-factorial numerical sampling
x1 = pi/2:0.1/2:pi; % theta_r
x2 = 0.6:0.005:0.99; % l1
range = zeros(length(x1),length(x2));
for i=1:length(x1)
for j=1:length(x2)
% evaluate projectile range
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2. range(i,j) = treb([x1(i),x2(j)]);
end
end
% Plot range as a function of release angle and fulcrum
position
figure(2);
surf(x2,x1,range);
xlabel('l1 (m)')
ylabel('theta_r (rad)')
zlabel('range (m)')
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