Animation_A1_27-8-2006.html

# Maple 10 sheet for evalution of a ceiling balloon flight over Innsbruck, 27th Aug. 2006;

balloon start site was the University's main weather station called "Villa", observer (theodolite) site was on the roof of the meteorological institute.

created by André Summer

> restart;

> currentdir();

$C:\Dokumente und Einstellungen\MeinBenutzername\Desktop$

# sheet works only if the import data are available in the path above!

Reading measurement data:

> A1_x:=readdata(`Aufstieg1_x.txt`,2);

> A1_y:=readdata(`Aufstieg1_y.txt`,2);

> xdata_A1:=[seq(A1_x[i][2], i=1..nops(A1_x))];

> ydata_A1:=[seq(A1_y[i][2], i=1..nops(A1_y))];

> tdata_A1:=[seq(A1_x[i][1], i=1..nops(A1_x))];

Interpolation:

> with(CurveFitting):

> x1(t):=PolynomialInterpolation(tdata_A1,xdata_A1,t);

> y1(t):=PolynomialInterpolation(tdata_A1,ydata_A1,t);

> pl_A1x:=plot(x1(t),t=0..210,color=blue):

> points_A1x:=stats[statplots,scatterplot](tdata_A1,xdata_A1,color=black,symbol=BOX,symbolsize=15):

> interface(warnlevel=0): with(plots):

> display({pl_A1x,points_A1x},title=`flight path [m] in x-direction (East) as function of t [s]`);

> pl_A1y:=plot(y1(t),t=0..210,color=blue):

> points_A1y:=stats[statplots,scatterplot](tdata_A1,ydata_A1,color=black,symbol=BOX,symbolsize=15):

> display({pl_A1y,points_A1y},title=`flight path [m] in y-direction (North) as function of t [s]`);

Calculation of wind velocity in x- and y-direction:

> diff(x1(t),t);

> diff(y1(t),t);

Animation of balloon ascend 1:

> v:=4: z0:=-44: #z0 ... start height of the balloon in relation to the site of the theodolite

> interface(warnlevel=0): with(plots):

> points:={seq([eval(x1(t),t=time_in_s),eval(y1(t),t=time_in_s),z0+v*time_in_s],time_in_s=0..210,5)}:

> pointplot3d(points,color=blue,symbol=box, axes=normal,labels=[x,y,z],title=`static 3D-model (x,y, and z)`);

# The point of intersection ot the 3 axes is not equivalent to the origin which can be seen at the labelling of the axes)

> balloontrace := pointplot3d(points,color=white,symbol=box, symbolsize=1):

> animate( pointplot3d, [ [[eval(x1(t),t=time),eval(y1(t),t=time),z0+v*time]], color=red, symbol = circle, symbolsize=40, labels=[x,y,z]], time=15..210,digits=3,frames=196, background=balloontrace,axes=normal);

# animated 3D-model (x,y, z, and t)

# Conclusions: Blinding by the sun caused problems during the measurement (the balloon start site was in southern direction related to the theodolite site, so the measurement conditions were only suitable for exercise purposes). At the end the balloon flew fast nearly above our heads which made it difficult to follow it with the theodolite and we had to stop at t = 210 s. So the distance between balloon start site and observer site should not be to close.