1. Aug 4, 2013

### pedrobele

Hello to all,
If you know the direction, wind speed, altitude and weight of the radiosonde (values varies by altitude), it is possible to know the approximate track that the radiosonde does?
I have other values ​​such as temperature, pressure, relative humidity and other.
Anyone knows equations for introducing these variables?
Thanks for helping

2. Aug 4, 2013

### voko

You will need to be able to model the shape of the balloon and compute its drag coefficient. That should be enough to have a closed set of equations describing its motion.

3. Aug 5, 2013

### pedrobele

Anyone know any references where I can see the equations?
Sorry for these questions, my basic training is not physics.

4. Aug 5, 2013

### voko

Let $\vec{r}$ be the position of the balloon. Let $\vec{v} = \frac {d \vec{r}} {dt}$ be its velocity. Let $\vec{w}$ be the velocity of wind (relative to the ground). Let $\vec{u} = \vec{w} - \vec{v}$ be the velocity of the wind relative to the balloon. Let $V$ be the total volume of the radiosonde, and $m$ its mass; $g$ the acceleration due to gravity, $\rho$ the density of the atmosphere. All of these values are assumed to be taken at the current location of the radiosonde. Finally, let $\vec{k}$ be the unit vector pointing up. Then the buoyant force acting on the balloon is $\vec{B} = \rho g V \vec {k}$. The force due to the wind is $\vec {A} = c u \vec {u}$, where $c$ is the coefficient related to the shape and material of the aircraft. The general equation is: $m \frac {d \vec{v}} {dt} = \vec{A} + \vec{B} - mg \vec {k}$.

5. Aug 8, 2013

### pedrobele

Hello Voko,
if I understand correctly your answer, in this way I can determine the acceleration of the radiosonde, I should integrate this equation 2 times to determine the equation of motion in x and y (z is not needed). But this is not an easy task, there are other ways?

6. Aug 8, 2013

### voko

You have to "integrate" in 3D (with z), because the force A depends on u, which in turn depends on v, where the vertical motion may be significant.

I am not exactly sure how you should go about solving this. How frequently do you sample all the values?

7. Aug 8, 2013

### pedrobele

Hi Voko,

when I said, I would not need to integrate in z, it is because I do not have the wind speed in the vertical direction.
I have for several altitudes the wind direction and speed (horizontal). You can see an example in the attached file.

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8. Aug 8, 2013

### voko

Are the wind direction and speed absolute (i.e., with respect to the ground) or relative (with respect to the balloon)?

9. Aug 8, 2013

### pedrobele

Upper-air winds (horizontal wind speed and direction) are determined during radiosonde ascents by measuring the position of the radiosonde relative to the earth's surface as the balloon ascends. By measuring the position of the balloon with respect to time and altitude, wind vectors can be computed that represent the layer-averaged horizontal wind speed and wind direction for successive layers. The position data have typically been obtained using radio direction finding techniques or one of the radio navigation networks.

10. Aug 8, 2013

### voko

Now the question is, are these wind velocities just taken to be equal to the velocities of the radiosonde, or is there any kind of trickery that restores the "true" wind velocity?

If the answer is yes to the first option, then things get simplified very significantly.

11. Aug 8, 2013

### pedrobele

The winds are determined by observing the drift of the balloon.
There are two classes:
The first class of wind measurement techniques tracks the balloon externally using one of three
methods:
(1) optical systems use a theodolite to visually track the balloon’s azimuth and elevation;
(2) radio theodolites track a radio signal sent from a transmitter on the radiosonde, again to obtain azimuth and elevation information;
and
(3) radar systems track a radar retroreﬂector suspended from the balloon to obtain slant range, azimuth, and elevation.
The second class of wind measurement techniques uses various navigation systems.

12. Aug 8, 2013

### voko

I understand that the wind velocity is determined through the drift of the balloon. But that does not answer the question in #10.

Regardless, since you said "apprximate track", you can try and assume that the wind velocity is the balloon's velocity. Then we have $$\frac {d\vec{r}} {dt} = \vec{v}(t)$$ with $\vec{v}(t)$ known at $t_0, \ t_1, \ ... \ t_n$.

If that does not work well, then a more complex model could be considered.

13. Aug 8, 2013

### pedrobele

Yes, you're right I did not answer, I need to read more to be able to give you an answer to #10.
Thanks for helping

14. Aug 19, 2013

### pedrobele

Hi Voko, I received an email from Vaisala (vendors of radiosonde RS92-SGP) saying that the radiosonde winds are relative to the earth's surface and taken from the velocities of the moving freely radiosonde. After this response I will try the aproximate solution in #12.
I will compare the path modeled in this way with the real, determined with other methods. Later I give you a feedback. Thank you.

15. Aug 19, 2013

### voko

@pedrobele: good luck with that!

16. Aug 24, 2013

### pedrobele

hi Voko,

I finally had time to finish the program. I used simple equations of motion (#12). The result in my opinion is very good. Figure 2 show the result (using the equations), figure 1 show the true path measured by sensors on the surface (while radiosonde is in the air). This is just one example, I used more cases to validate the results.
Thanks for all the help.

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