# Parachute Simulation using ODE45

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Viper224 on 4 Dec 2016
Answered: Tamir Suliman on 4 Dec 2016
I've been asked to create a falling parachute simulation that must incorporate the ODE45 function to determine the location, velocity, and acceleration vs time. I have hardly any experience when it comes to MatLab so I'm not really sure how to do this. I have some rough code right now with equations,the initial locations, and a density function. I'm just not sure how to incorporate the location, density, and velocity equations into ODE45.
g = 32.174; %Acceleration due to gravity
A = 3; %Payload characteristic area
CP = 2; %Payload Drag Coefficient
CS = 0.5; %Payload Side Force Coefficient
S = 20; %Aerodynamic area of canopy
WS = 10; %Canopy wing span
CDi = 0.01; %Initial canopy Drag Coefficient
CLi = 0.0; %Initial canopy Lift Coefficient
CD = 0.2; %Inflated canopy Drag Coefficient
CL = 1.0; %Inflated canopy Lift Coefficient
CR= CL + CD; %Resultant Coefficient
e = 1.0; %Oswald Efficiency Factor
delTi = 5; %Inflation time
[lat,lon,h] = geodetic2enu(68.6719,44.8831,15000,68.6719,44.8831,0,wgs84Ellipsoid);
function[rho,T,P]=density(h)
if h<= 16000 % troposphere
T = 59 - 0.00356.*h; %deg F Temperature
P = 2116.*((T+459.7)./518.6).^5.256; %lbs/ft^2 pressure
end
rho = P/(1718.*(T+459.7)); %slugs/ft^3 density
end
V = ((2*W)/(rho*S))^2*(1/(CR^2)^.25); %Velocity
L = (1/2*rho*V^2*S*CL); %Inflated Lift force
D = (1/2*rho*V^2*S*CD); %Inflated Drag force
D = (1/2*rho*V^2*A*CP); %Payload Drag force
R = (L^2+D^2)^.5; %Inflated Resultant force
gamma = atand(CD/CL); %Flight Path Angle
Vh = V*cos(gamma); %Horizontal veloctiy
Vv = V*sin(gamma); %Vertical velocity
%Force Equations
Fh = L*sin(gamma)-D*cos(gamma); %Horizontal force
Fv = L*cos(gamma)+D*sin(gamma)-W; %Vertical force

Tamir Suliman on 4 Dec 2016
You will have to construct the model you trying to solve
ode45 is used to solve differential equation . You will have to find the model differential equation for the falling parachute problem, For example The motion of the skydiver is governed by Newton's Second Law of Motion. Balancing the forces of acceleration, gravity, and air resistance yields the second-order (linear) initial value problem mx'' = -mg - kx' x(0) = x0 and x'(0) = 0