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TrishaMenon_Final_Exam.m
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%% Math 111 Final Exam
% Interceptor Project
%
%
% Your Name: Trisha Menon
% Your Email: [email protected]
%
%
% --- Program Description ---
%
% The objective of this program is to create a program that tracks the
% flight path of a projectile missile from one enemy country to another.
% Once achieved, the program must calculate the flight path for an
% interceptor missile to disrupt Country B's missile's path to Country A,
% with both time and distance from Country A taken into consideration.
%
%
% --- START OF PROGRAM ---
%
clear, clc, clf
format compact
%
% Define the variables...
global t
t = (0:0.04:30); % t is a the time vector in minutes with increments
% of 0.04 minutes from 0 to 30
d = (0:6000); % d is a distance vector in miles between Countries
% A and B with default increments of 1 mile
a0 = 0.127696; % Angles from Station 1 to each point of sighting
a3 = 0.250201; % All angles are in radians
a4 = 0.299485;
b0 = 0.281232; % Angles from Station 2 to each point of sighting
b3 = 0.729737; % All angle are in radians
b4 = 0.972377;
global d1_2
d1_2 = 1500; % Distance between stations 1 and 2
da_1 = 2500; % Distance between Country A and station 1
da_2 = 4000; % Distance between Country A and station 2
da_b = 6000; % Distance between Countries A and B
d2_0 = TrishaMenon_d_from_sight(a0,b0); % Using the d_from_sight function I created,
d2_3 = TrishaMenon_d_from_sight(a3,b3); % these distances are calculated based on
d2_4 = TrishaMenon_d_from_sight(a4,b4); % the angles between the sighting and the 2 stations
ds_b = 2000 - d2_0; % ds_b represents the distance between Country B
% and the first sighting of the projectile
% by Country A's Station 2 based on the
% calculation done to find the distance
% between Station 2 and the position of
% the projectile at the first sighting
x0 = 0; % All the x and y values represent the
y0 = TrishaMenon_y_coor(b0, d2_0); % coordinates of the projectile at each
x3 = 3; % sighting using the function y_coor which
y3 = TrishaMenon_y_coor(b3, d2_3); % finds the y-coordinate based on the angle
x4 = 4; % from Station 2 and the distance between
y4 = TrishaMenon_y_coor(b4, d2_4); % projectile at each sighting and the Station
Vx = d2_3/(x3 - x0); % Vx represents the horizontal velocity of the
% projectile based on the formula given
TrishaMenon_get_time_func(0, y0, 3, y3, 4, y4); % The get_time_func produces the function
% for the flight path of the
% projectile based on time and the 3
% coordinates for the sightings
height = (-288/5)*((t - 25/6).^2)+1000; % height is the given, hard-coded
% function for the interceptor
% flight path as function of time
d_from_s = Vx*t; % d_from_s is the distance from the sighting(t=0) as
% function of time and the calculated velocity of the
% projectile
global a b c % a,b,and c are the cooefficients for the time
% function of the projectile. They are set as
% global because their values are shared bewteen
% this main script and the get_time_func
% function.
% Next, start plotting our flight paths on the 3D plot windows...
plot3(d_from_s, t, a.*(t.^2) + b.*t + c) % Begin by plotting the projectile
% function in terms of time and
% distance in terms of time as
% well
axis([0 6000 0 30 0 1000]) % Axis to contain the distance between the 2 countries
xlabel('Distance from First Sighting(mile)') % distance is the x-axis
ylabel('Time since First Sighting(min)') % time is the y-axis
zlabel('Altitude(mile)') % height is the z-axis
grid on
hold on % ensures that all the plots are to be displayed on the same plot
plot3(d_from_s, t, (-288/5)*((t - 61/6).^2)+1000) % Graph of the interceptor
% flight path in terms
% of time and adjusted
% to be in line with
% Station 2, where it
% is being launched
% from
legend('Projectile Flight Path', 'Interceptor Flight Path', 'AutoUpdate', 'off')
text(d2_0, d2_0/Vx, 0, 'x Station 2')
text((d2_0 + d1_2), (d2_0 + d1_2)/Vx, 0, 'x Station 1') % Labels for each location on the graph
text(da_b - ds_b, (da_b - ds_b)/Vx, 0, 'x Country A')
y = t; % time is the y-axis so it's values will be reassigned for the loop
bob = 0; % trigger to break the while loop when the projectiles meet
count1 = 1; % counter for the projectile's flight path
count2 = 1; % counter for the interceptor's flight path
x = zeros(1, length(t)); % we will create an array for the distance
% that is the same size as the time array
z1 = zeros(1, length(t)); % we will create another empty array of the
z2 = zeros(1, length(t)); % same size for the heights for each projectile
Handle_Point1 = plot3(x,y,z1,'wo'); % plot a baseline from which the data
Handle_Point2 = plot3(x,y,z2,'wo'); % points will be set after being calculated
while count1 <= length(t) % we will need to limit count1 because it
% cannot exceed the length of the time array
if y(count1) > 7 && abs(z2(count2) - z1(count1)) <= 1 % When the projectiles
% come within a
% mile of each
% other...
text(x(count1) + 100, y(count1), z1(count1), 'BOOM!')
bob = 1; % the demarcation will be displayed
% and the trigger will be
% pulled to break the
% rest of the while loop
else
count1 = count1 + 1; % if not, the counters will continue
count2 = count2 + 1; % and the plot will continue being produced
end
if bob == 1 % here is where the trigger will be
break % felt and it will continue to break the loop
end
x(count1) = Vx*y(count1); % the relationship between the y and x-axes
% is that the x-axis - distance -
% is the time - y-axis - times
% the horizontal velocity of the
% projectile
z1(count1) = a.*(y(count1).^2) + b.*y(count1) + c; % the z-axis is simply
% the height
% function for the
% projectile in
% terms of time
set(Handle_Point1, 'xdata', x, 'ydata', y, 'zdata', z1);
plot3(x(count1), y(count1), z1(count1), 'o') % the new data will be
drawnow % set and plotted
% simultaneously with
% the interceptor
% plot below
x(count2) = Vx*y(count2); % these x and y-axes have the same ratio as above
z2(count2) = (-288/5)*((y(count2) - 61/6).^2)+1000; % height function
% for the interceptor
set(Handle_Point2, 'xdata', x, 'ydata', y, 'zdata', z2);
plot3(x(count2), y(count2), z2(count2), 'o') % set the data for the
drawnow % second base plot
% and draw simultaneously
end
hold off
%
% Now for formatted output display for specifications and formulas to be
% presented...
disp('Trisha Menon ([email protected])')
disp('Math 111-01: Interceptor Project')
fprintf('\n\n\n')
disp('THE INTERCEPTOR FLIGHT PATH FUNCTIONS...')
disp(' 1) The Interceptor flight path function whereby height is a function')
disp(' of horizontal distance from the first sighting is... ')
disp(' I(x) = (-288/5)*(((300*t) - 25/6).^2)+1000')
disp(' 2) The Interceptor flight path function whereby height is a function')
disp(' of time from the first sighting is... ')
disp(' I(x) = (-288/5)*((t - 25/6).^2)+1000')
disp(' ')
disp('THE PROJECTILE FLIGHT PATH FUNCTIONS...')
disp(' 1) The Projectile flight path function whereby height is a function')
disp(' of horizontal distance from the first sighting is... ')
fprintf(' P(x) = %0.3fx^2 + %0.3fx + %0.3f\n', a/300, b/300, c/300)
disp(' 2) The Projectile flight path function whereby height is a function')
disp(' of time from the first sighting is... ')
fprintf(' P(x) = %0.3fx^2 + %0.3fx + %0.3f\n', a, b, c)
disp(' ')
disp('THE ADJUSTED INTERCEPTOR FLIGHT PATH FUNCTIONS...')
disp(' 1) The adjusted Interceptor flight path function whereby height is a function')
disp(' of distance is... ')
disp(' IAdj(x) = (-288/5)*(((300*t) - 61/6).^2)+1000')
disp(' 2) The original time-based Interceptor flight path function remains')
disp(' valid as before...')
disp(' IAdj(x) = (-288/5)*((t - 25/6).^2)+1000')
disp(' ')
disp('FLIGHT TIME REQUIRED TO REACH POINT OF INTERCEPTION...')
disp(' 1) The Projectile will reach the interception point when total')
fprintf(' flight time t = %0.3f minutes after Sighting #1.\n', y(count1))
disp(' 2) The Interceptor will reach the interception point when it')
fprintf(' has achieved a flight time of: %0.3f minutes. \n\n', y(count2))
%
% --- END OF PROGRAM ---