# Question:Space Balloon Trajectory

## Question:Space Balloon Trajectory

Maple

Dear all.

I am a french ingineering student and I have some problems trying to modelize the ascension of a space balloon (closed balloon full of Helium) from 0 to 11000m in ISA conditions.

I think that my initialization is OK but I'm unfortunately not able to find how to solve my non linear equation. My equation is:

I copy my work below:

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#Atmospheric parameters, initialization
#temperature (K)

Ta := 15-6.5*((1/1000)*z(t))+273.15;

#pressure (Pascal)

Pa := 1013*10^2*(1-3.32*10^(-5)*z(t))^(7/2);

#moleculai mass of air

M := 29;

#thermodynamic constant

R := 8.314;

#volumic mass of air following the altitude

J := M*Pa/(R*Ta);

#Laplace coefficient, initial volume of the balloon, ground pressure:

ga := 1.6665;

V0 := 4.43;

P0 := 1.013*10^2;

#Balloon volume following the altitude (Laplace formula)

Vball1 := (P0/Pa)^(1/ga)*V0;

#Disc surface for the drag force

S1 := 3.14^(1/3)*(3/4)^(2/3)*Vball1^(2/3);

with(DEtools);

Cx := .44; #(turbulent flow)

g := 9.81;

mball := 3; #(balloon mass)

ode1 := J*Vball1*g-mball*g-(1/2)*J*S1*Cx*(diff(z(t), t))^2 = 0;

ics := (D(z))(0) = 0, z(0) = 0:

dsolve(????????);

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The problem is that because of its non linear aspect, i don't know what kind of method I have to use to find the solution with my initial conditions.