Finding the point before landing

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Finnien Mitchell
Finnien Mitchell on 24 May 2020
Commented: Finnien Mitchell on 24 May 2020
I am using a numerical method for finite differences so I can plot the 'x' and 'y' displacement of a projectile neglecting the force of drag. However, as the solutions computed are discrete I can't find the exact point where the projectile lands at (y = 0). So I'm attempting to use the point before/after landing using the code below:
point_before_landing = max(find(fNWy<0));
point_after_landing = max(find(fNWy<0)) + 1;
I am then typing fNWy(point_before_landing) into the command window to find the point. However, when I do this it comes back with the error:
>> fNWy(point_before_landing)
Undefined function or variable 'point_before_landing'.
Would anyone know why this is happening since I believe I defined that variable in my editor section. For reference this is my entire code below as well which is running fine. Any help would be greatly appreciated.
close all
clc
%% Problem Parameters
m = 50*10^-3; % mass in [kg]
radius = 30*10^-3; % radius [m]
a0 = 25; % initial angle [deg]
v0 = 50; % initial velocity [m/s]
y0 = 50; % initial elevation [m]
vy0 = v0*sind(a0); % initial y velocity;
x0 = 0; %initial horizontal
vx0 = v0*cosd(a0); % inital x velocity;
Cdrag = 0.8; % coefficient of drag
Area = 0.0028274334; %cross section area [m^2]
rho = 1.183; % density of air
g = 9.81; % gravity
t = 6.02007; % simulation time [s]
dt = 0.01; % timestep [s]
Niter = floor(t/dt); %iteration
%% Numerical Without Drag (NW)
% To neglect drag Cdrag is set to be equal to 0
Cdrag = 0.00;
NWx(1) = x0;
NWx(2) = x0 + dt*vx0;
NWy(1) = y0;
NWy(2) = y0 + dt*vy0;
NWVx(1) = vx0;
NWVx(2) = vx0;
for i = 3:Niter
NWxNow = NWx(i - 1);
NWxPre = NWx(i - 2);
NWyNow = NWy(i - 1);
NWyPre = NWy(i - 2);
fNWx = @(NWxNex)m*((NWxNex-2*NWxNow+NWxPre)/(dt^2))+((Cdrag*rho*Area)/2) ...
* sqrt(((NWxNow-NWxPre)/dt)^2+ ((NWyNow-NWyPre)/dt)^2) * ...
((NWxNex-NWxPre)/(2*dt));
NWxNex = fzero(fNWx,NWxNow);
NWx(i) = NWxNex;
fNWy = @(NWyNex)m*((NWyNex-2*NWyNow+NWyPre)/(dt^2))+((Cdrag*rho*Area)/2)...
* sqrt(((NWxNow-NWxPre)/dt)^2 +((NWyNow-NWyPre)/dt)^2) * ...
((NWyNex-NWyPre)/(2*dt))+ m*g ;
NWyNex =fzero(fNWy,NWyNow);
NWy(i) = NWyNex;
end
point_before_landing = max(find(fNWy<0));
point_after_landing = max(find(fNWy<0)) + 1;

Answers (1)

Thiago Henrique Gomes Lobato
You used the function, not the calculated variables to find the index. Your point definiton was also a bit off. This version of your code works:
close all
clc
%% Problem Parameters
m = 50*10^-3; % mass in [kg]
radius = 30*10^-3; % radius [m]
a0 = 25; % initial angle [deg]
v0 = 50; % initial velocity [m/s]
y0 = 50; % initial elevation [m]
vy0 = v0*sind(a0); % initial y velocity;
x0 = 0; %initial horizontal
vx0 = v0*cosd(a0); % inital x velocity;
Cdrag = 0.8; % coefficient of drag
Area = 0.0028274334; %cross section area [m^2]
rho = 1.183; % density of air
g = 9.81; % gravity
t = 6.02007; % simulation time [s]
dt = 0.01; % timestep [s]
Niter = floor(t/dt); %iteration
%% Numerical Without Drag (NW)
% To neglect drag Cdrag is set to be equal to 0
Cdrag = 0.00;
NWx(1) = x0;
NWx(2) = x0 + dt*vx0;
NWy(1) = y0;
NWy(2) = y0 + dt*vy0;
NWVx(1) = vx0;
NWVx(2) = vx0;
for i = 3:Niter
NWxNow = NWx(i - 1);
NWxPre = NWx(i - 2);
NWyNow = NWy(i - 1);
NWyPre = NWy(i - 2);
fNWx = @(NWxNex)m*((NWxNex-2*NWxNow+NWxPre)/(dt^2))+((Cdrag*rho*Area)/2) ...
* sqrt(((NWxNow-NWxPre)/dt)^2+ ((NWyNow-NWyPre)/dt)^2) * ...
((NWxNex-NWxPre)/(2*dt));
NWxNex = fzero(fNWx,NWxNow);
NWx(i) = NWxNex;
fNWy = @(NWyNex)m*((NWyNex-2*NWyNow+NWyPre)/(dt^2))+((Cdrag*rho*Area)/2)...
* sqrt(((NWxNow-NWxPre)/dt)^2 +((NWyNow-NWyPre)/dt)^2) * ...
((NWyNex-NWyPre)/(2*dt))+ m*g ;
NWyNex =fzero(fNWy,NWyNow);
NWy(i) = NWyNex;
end
[~,point_before_landing] = min(NWy(NWy>0));
point_after_landing = point_before_landing+1;
fNWy(point_before_landing)

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