%% ME 2016
%% Fall 2007
%%
%% AUTHOR:  Chris Paredis
%%
%% PURPOSE: simulate the motion of a car in a quarter-mile drag race
%%
%% ASSUMPTIONS: 
%%         - the car is described in the function CAR_MODEL with state
%%           [velocity; position];
%%         - at time zero, the car has a position and velocity of zero.

%%
%% define the problem
%%

% the final time is larger than it needs to be -- the simulation will stop
% when the car reaches the finish line
time_interval = [0, 100];
initial_condition = [0;0];

% make sure the races ends when the finish line is reached
options = odeset('Events',@end_of_race_event);

% stop the warnings from engine_model_CJP from showing up
warning off;

%%
%% solve the problem
%%
% solve the car simulation using the Matlab solver ode45
[t,y] = ode45(@car_model,time_interval,initial_condition,options);

%%
%% interpret the results
%%
% plot the velocity as a function of time
figure(1)
plot(t,y(:,1)*3.6);
grid on
xlabel('time [s]');
ylabel('car velocity [km/h]');

figure(2)
plot(t,y(:,2));
grid on
xlabel('time [s]');
ylabel('car position [m]');

fprintf('The finish time is %g seconds\n',t(end));
fprintf('The finish speed is %g km/h\n',y(end,1)*3.6);
fprintf('The average speed is %g km/h\n',y(end,2)/t(end)*3.6);

% the results are:
% The finish time is 15.2551 seconds
% The finish speed is 143.987 km/h
% The average speed is 94.9374 km/h

% note: the results may differ slightly depending on small details in your
% implementation.  For instance, when changing the final time of the
% simulation from 100 to 50 seconds (which should really have no impact on
% the result since the simulation stops after 15-16 seconds) the finish
% time changes to 15.2804 seconds. This is due to the adaptive step-size
% algorithm used by ode45.  The result should still be approximately within
% the default 1e-3 relative tolerance

% Answer to Task 3:  The structure of the program looks like this:
% script car_simulation:
%     - numerical methods: ODE solving -- ode45
%     - function call: car_model
%         - numerical methods: none
%         - function call: resistance_force
%             - numerical methods: none
%             - function call: none
%         - function call: engine_w_torque_converter
%             - numerical method: root finding -- fzero
%             - function call: engine_model_CJP
%                 - numerical method: curve fitting -- polyval
%                 - function call: none
%             - function call: torque_converter
%                 - numerical method: interpolation -- interp1
%                 - function call: none