Question
How do you put these arrows into my matlab plot? I need my plot to look exactly like this: here is my code: %x() and
How do you put these arrows into my matlab plot?
I need my plot to look exactly like this:
here is my code:
%x() and y() are the positions of the projectile
%dt = time step
%v_init = initial speed
%theta = launch angle
%B_m = proportional to drag force = B2/m
close all
clear all
clc
%define Variables and Matrices
timeStep = .00001;
initialPositionX = 0;
initialPositionY = 1;
initialVelocity = 110*0.44704; %mph to m/s
positionXNoWind = zeros(1,50);
positionYNoWind = zeros(1,50);
positionXNoWind(1) = initialPositionX;
positionYNoWind(1) = initialPositionY;
theta = 35 * 0.0174533; %degrees to radians
initialVelocityX = initialVelocity * cos(theta);
initialVelocityY = initialVelocity * sin(theta);
vd = 35; %m/s
delta = 5; %m/s
gravity = -9.8;
maxCalculations=100000000;
Bm = .0039 + (.0058)/(1+exp((initialVelocity-vd)/delta)); %B2/m
velocity = initialVelocity;
velocityX = initialVelocityX;
velocityY = initialVelocityY;
velocityWind = 0 * 0.44704; %mph to m/s
for i = 2:maxCalculations
positionXNoWind(i) = positionXNoWind(i-1) + velocityX * timeStep;
positionYNoWind(i) = positionYNoWind(i-1) + velocityY * timeStep;
velocity = sqrt(velocityX^2 + velocityY^2);
Bm = .0039 + (.0058)/(1+exp((velocity-vd)/delta));
%dragForceX = Bm * (velocity - velocityWind) * (velocityX - velocityWind);
%dragForceY = Bm * (velocity - velocityWind) * velocityY;
%dragForceX = Bm * (sqrt((velocityX-velocityWind)^2 + velocityY^2)) * (velocityX - velocityWind);
%dragForceY = Bm * (sqrt((velocityX-velocityWind)^2 + velocityY^2)) * (velocityY);
dragForceX = Bm * (velocity - velocityWind) * (velocityX - velocityWind);
dragForceY = Bm * (velocity) * velocityY;
velocityY = velocityY - (9.8 * timeStep) - (dragForceY * timeStep);
velocityX = velocityX - (dragForceX * timeStep);
%positionX(i) = positionX(i-1) + velocityX * timeStep
%positionY(i) = positionY(i-1) + velocityY * timeStep
%velocityY = velocityY - (9.8 * timeStep) - (dragForce * velocityY * timeStep)
%velocityX = velocityX - (dragForce * velocityX * timeStep)
%initialVelocity = sqrt(initialVelocityX^2 + initialVelocityY^2)
%positionX(i) = positionX(i-1) + (velocityX - (dragForce * velocityX * timeStep)) * timeStep
%positionY(i) = positionY(i-1) + (velocityY - (9.8 * timeStep) - (dragForce * velocityY * timeStep)) * timeStep
%Bm = .0039 + (.0058)/(1+exp((velocity-vd)/delta))
if positionYNoWind(i)
break
end
end
positionXTailWind = zeros(1,50);
positionYTailWind = zeros(1,50);
positionXTailWind(1) = initialPositionX;
positionYTailWind(1) = initialPositionY;
velocity = initialVelocity;
velocityX = initialVelocityX;
velocityY = initialVelocityY;
velocityWind = 10 * 0.44704; %mph to m/s
for i = 2:maxCalculations
positionXTailWind(i) = positionXTailWind(i-1) + velocityX * timeStep;
positionYTailWind(i) = positionYTailWind(i-1) + velocityY * timeStep;
velocity = sqrt(velocityX^2 + velocityY^2);
Bm = .0039 + (.0058)/(1+exp((velocity-vd)/delta));
%dragForceX = Bm * (velocity - velocityWind) * (velocityX - velocityWind);
%dragForceY = Bm * (velocity - velocityWind) * velocityY;
%dragForceX = Bm * (sqrt((velocityX-velocityWind)^2 + velocityY^2)) * (velocityX - velocityWind);
%dragForceY = Bm * (sqrt((velocityX-velocityWind)^2 + velocityY^2)) * (velocityY);
dragForceX = Bm * (velocity - velocityWind) * (velocityX - velocityWind);
dragForceY = Bm * (velocity) * velocityY;
velocityY = velocityY - (9.8 * timeStep) - (dragForceY * timeStep);
velocityX = velocityX - (dragForceX * timeStep);
%positionX(i) = positionX(i-1) + velocityX * timeStep
%positionY(i) = positionY(i-1) + velocityY * timeStep
%velocityY = velocityY - (9.8 * timeStep) - (dragForce * velocityY * timeStep)
%velocityX = velocityX - (dragForce * velocityX * timeStep)
%initialVelocity = sqrt(initialVelocityX^2 + initialVelocityY^2)
%positionX(i) = positionX(i-1) + (velocityX - (dragForce * velocityX * timeStep)) * timeStep
%positionY(i) = positionY(i-1) + (velocityY - (9.8 * timeStep) - (dragForce * velocityY * timeStep)) * timeStep
%Bm = .0039 + (.0058)/(1+exp((velocity-vd)/delta))
if positionYTailWind(i)
break
end
end
positionXHeadWind = zeros(1,50);
positionYHeadWind = zeros(1,50);
positionXHeadWind(1) = initialPositionX;
positionYHeadWind(1) = initialPositionY;
velocity = initialVelocity;
velocityX = initialVelocityX;
velocityY = initialVelocityY;
velocityWind = -10 * 0.44704; %mph to m/s
for i = 2:maxCalculations
positionXHeadWind(i) = positionXHeadWind(i-1) + velocityX * timeStep;
positionYHeadWind(i) = positionYHeadWind(i-1) + velocityY * timeStep;
velocity = sqrt(velocityX^2 + velocityY^2);
Bm = .0039 + (.0058)/(1+exp((velocity-vd)/delta));
%dragForceX = Bm * (velocity - velocityWind) * (velocityX - velocityWind);
%dragForceY = Bm * (velocity - velocityWind) * velocityY;
%dragForceX = Bm * (sqrt((velocityX-velocityWind)^2 + velocityY^2)) * (velocityX - velocityWind);
%dragForceY = Bm * (sqrt((velocityX-velocityWind)^2 + velocityY^2)) * (velocityY);
dragForceX = Bm * (velocityX - velocityWind) * (velocityX - velocityWind);
dragForceY = Bm * (velocity) * velocityY;
velocityY = velocityY - (9.8 * timeStep) - (dragForceY * timeStep);
velocityX = velocityX - (dragForceX * timeStep);
%positionX(i) = positionX(i-1) + velocityX * timeStep
%positionY(i) = positionY(i-1) + velocityY * timeStep
%velocityY = velocityY - (9.8 * timeStep) - (dragForce * velocityY * timeStep)
%velocityX = velocityX - (dragForce * velocityX * timeStep)
%initialVelocity = sqrt(initialVelocityX^2 + initialVelocityY^2)
%positionX(i) = positionX(i-1) + (velocityX - (dragForce * velocityX * timeStep)) * timeStep
%positionY(i) = positionY(i-1) + (velocityY - (9.8 * timeStep) - (dragForce * velocityY * timeStep)) * timeStep
%Bm = .0039 + (.0058)/(1+exp((velocity-vd)/delta))
if positionYHeadWind(i)
break
end
end
%a = -positionY(i) / positionY(i-1)
%positionX(i) = (positionX(i) + (a * positionX(i-1))) / (1 + a)
%positionY(i) = 0
%%Plots
figure(1)
hold on
box on
plot(positionXNoWind,positionYNoWind,'-k',positionXTailWind,positionYTailWind,':k',positionXHeadWind,positionYHeadWind,'-.k')
set(gca,'Xtick',linspace(0,150,4),'fontsize',18,'Ytick',linspace(0,50,6))
set(gcf,'Color','w');
set(gcf,'Resize','on');
ylabel('y (m)','fontsize',18)
xlabel ('x (m)','fontsize',18)
text(positionXTailWind(400000),positionYTailWind(95000),'tailwind','fontsize',18)
text(positionXNoWind(492000),positionYNoWind(60000),'no wind','fontsize',18)
text(positionXHeadWind(245000),positionYHeadWind(20000),'headwind','fontsize',18)
title('Trajectory of a batted baseball','fontsize',19)
ylim([0 30])
xlim([0 150])
hold off
Trajectory of a batted basebal 30 tailwind 20 no wind 10 headwind 0 0 50 100 150 x (m) Figure 2.7: Calculated trajectory of a baseball hit at an initial velocity of 110 mph, with the effects of atmospheric drag included. Solid curve: no wind; dotted and dot-dashed curves: a tailwind and headwind of 10 mph. In all cases we assume that the initial velocity makes an angle of 35 with the horizontal
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