Rigid multi-cell structure. The definitive choice?

I’ve seen that NASA has built two balloon prototypes to explore Venus and Titan. Since these two bodies have such different environments, two different design considerations must be carried for each one.

The main issue in Venus (about the design of the balloon structure) is the highly corrosive atmosphere. Since the mission is not expected to last for much time (few Earth days), autonomy and gas leakages are not the main concerns.

The other balloon, intended to explore Titan, is much more similar to this project. Since it will go beyond Saturn, the mission is expected to one year or more. Of course issues like communications and automated decision making algorithms must be carefully designed. What attracted most my attention was the solutions they proposed for increase the lifting properties of the craft.
As in Titan temperatures are about 80-90 K, common materials to prevent gas leakages designed for Earth conditions are not applicable, and in those cryogenic temperatures the lost rate is much bigger than in Earth. So, the device will obtain hydrogen from chemical reactions of the methane widely available in Titan’s atmosphere.

After reading the papers related to those two projects, and since in Earth ambient conditions are not so hard –but in high layers of atmosphere are UV degradation and temperatures of 223 K-, many of the solutions proposed are not directly applicable to this model. Nevertheless, they talked about Mylar supper pressure balloons (rigid structure) used in meteorological observation, which have flown for 744 days.

That gave me the idea of the following design, in order to decrease gas leaks and tensions in the rubber.

Let’s study the performance of a rigid model. Unlike in a flexible model, here the pressure difference must be taken into account. But despite in flexible models pressure differences should not be dramatically high, in the upper layers of the atmosphere outside pressure is very low, the rubber must elongate too much, eventually provoking burst or (which is quite sure) a sudden drop in gas-containing properties.
In addition, a rigid model would be much easier to control in height.

If we calculate the tension that a spherical shaped balloon must bear, we get something like:

This means that the tension supported by the rubber is proportional to the radius of the balloon.

So, maybe there’s a way to reduce the radius of the balloon, but without limiting the gas volume it contains.

Let’s take the following rigid device. It’s composed of an outer spherical structure filled with many small cells (imagine that like a ‘rigid’ balloon filled with smaller ‘rigid’ balloons).

If we make some numbers we can get some interesting information:

The first conclusion is that the radius of the global structure grows with the cube root of the number of cells. This means that in order to decrease the radius of the cells a 50% the number of cells must be increased a 800%.
The good point on that is that the bigger the number of cells is, the better the structure will bear bursts and gas leaks.

But, of course, that also would increase the total surface of the balloon, and hence it’s weight. But would that be limiting?

Assuming a density of boPET film with a thickness of 30 μm of 0.042 Kg/m², we get:

To estimate magnitude orders (which is what I’ve been doing the whole post) let’s suppose a constant difference of density between helium and air of 1 g/m3.

Let’s assume, also, a diameter of 5 m., and the required number of cells to make the small radius equals to 0.5 m. That results in 1000 cells, and the lifting force (expressed in kg.) would be 30 Kg, in contrast to the 60 Kg. of the single-cell structure.

In conclusion, the most suitable design for the balloon (attending to gas leakage, pin holes resistance and reduction of stress) is a multi-cell rigid structure.

Alternatives to helium

While I do some experiments with those home made materials intended to stop helium leaks, and since I’m not sure if they’ll be conclusive, I’ve thinking in other ways to solve that problem. If the cause of helium’s permeability through the rubber is it’s small size, maybe a bigger molecule (less dense than air, of course) won't have that issue. All candidates must pass a final question, and that is “If it’s so good, why is not used in current balloons?”.

So, let’s take a periodic table:

In this table, where transition metals, lanthanides and actinides were removed, are coloured in red those elements heavier than air (remember that its main component is nitrogen, followed by oxygen, both diatomic) and in a darker red those that are metals.

So, those that at first glance might be suitable are left in blank. Let’s discard some of them:

• Hydrogen: Besides it’s highly flammable, it leaks even faster than helium.


• Helium: The same as hydrogen, it’s hard to keep inside a balloon.


• Boron: Solid

  a) BH3: Dimerises to B2H6. Almost same density as air (96% density of air, while helium is 14%).
  
  b) BF3: Heavier than air.

• Carbon: Solid
  
  a) CH4 (Methane): Highly flammable.


• Nitrogen:
  
  a)N2: Practically the same density as air.
  
  b) NH3 (Ammonia): Toxic.


• Oxigen
  
  a) O2: Slightly heavier than air.
  
  b) H2O (water): Liquid and even solid at cruise height (what
  a pity, it's the safest and cheapest of all).


• Fluorine
  
  a) F2: Heavier than air. Highly corrosive.
  
  b) HFl: Corrosive. Should be lighter than air, but it makes H–F
  bonds, so it’s heavier.

• Neon
  
  a) Ne: Lighter than air. Not especially expensive (2800 €/m3 while Helium 2500€/m3)

So, the compounds that may be suitable (attending just at their density) are CH4 and NH4, both highly dangerous; they're flammable, corrosive, toxic, or all). I'll try to find out which are the consequences of those properties in materials and how overcome them.

Neon seems to be the most feasible option, but I'm not yet sure if the size of that atom is big enough to avoid leaks.

Helium leakage

Finally I received the GM862-GPS evaluation kit (it was retained for few days in tolls). I have had some problems with the USB-RS232 adapter I bought before I received the package (reading some forums I realised that those adapters hardly work), so while I find a computer with an integrated serial port I’ve been struggling with another problem I didn’t even know it existed.

It seems that in common (well, actually in ALL) balloons helium leaks in a relatively short time. That’s a known fact in toy balloons, but I though the knot was the responsible. I could read that actually helium passes through the rubber of the balloon, no matter if the material is latex (the common coloured balloons that can be filled with either air or water) or foil (in this case the balloon lasts more time to deflate, but it still does in few days).

So the problem is bigger than it seemed at first glance, since or the balloon must land to be re-inflated with helium (which by the way is not especially cheap, about 2500 € per cubic meter) or another way to stop helium leakage must be developed.
Many chemicals companies have developed different materials (with different prices) that claim to retain helium more time. But that idea does not convince me. Or the materials needed are not affordable by a common user or if they are they will need specialized operators for labours such cutting and gluing and related substances (like adhesives). In short, that will imply strong relations with the industry of chemicals and a budget I don’t have.

I've been thinking in a low-cost, home made and light material that can be used in this circumstance. The idea is to keep an extremely thin layer of oil (or any other fluid, preferable less dense than water trapped inside two layers of latex (of toy balloons, for example), and check if that fluid layer can somehow prevent the leakage of the air inside.
If that worked, its density will depend on the thickness of the fluid layer, but anyway it would be much lower than the one of foil, about 30 gr/m2 (to give some numbers, paper density=80 gr/m2; foil=200 gr/m2), for a fluid thickness of 0.01 mm. and a density of 1000 kg/m3 and two plastic layers of 100 gr/m3 density and 0.1 mm thickness.

Ways to control height in a flexible model

In last post simulations showed that a rigid model will have a better behaviour (its equilibrium height is much lower and there are no problems related with rubber burst). In addition, if a system with controlled volume could be easily (and lightly) built, that problem would be solved.
Unfortunately that’s much easier to say than to actually do, besides a rigid model would me much heavier, so I’ll have to manage with a flexible one.

I’ve been thinking in a way to control height without consuming energy (that’s an important issue all the time, but especially at night), and I thought on the following system:

It’s a piston than can compress and expand the gas it contains (helium, for example). When ‘x’ increases, the rest of the gas has more space to fill, so the pressure drops and hence its radius decreases. That increases the system’s density and its lift is much lower. The opposite happens when ‘x’ decreases.

To check its performance in a simulation first is important to create some kind of law to relate ‘x’ as function of current radius, velocity, position and whichever other factors.

One control function can be the following (remembering the formula x=1/2*a*t^2):

Being:
h_des=desired height
h= current height
v=current velocity
a=current acceleration
a_crit=desired acceleration

a_crit=(2.*(h_des-h-v*10.)/100.) (making t=10)

And the condition (in pseudocode):
If a>a_crit then increase x
else decrease x
With x between (0,L)

With that control system I run the simulation. First of all it randomly assigned a desired height between 0 m and 9000 m, and tried to reach it. When it’s stabilized at that height it changes the desired height to another one.

The result is shown in the following graph, where both height and diameter were adimensionalized with it’s maximum value so that it’s represented d/dmax and h/hmax as function of the time in hours (max height 8000.09 m and max diameter 3.710571 m.). Since the desired height is chosen randomly in any other simulation the max values may differ.

That system of control seems to work, but further study has to be carried out.

Rigid vs Flexible structure

In previous models I supposed that the main structure will be flexible (like a balloon), and its flexibility will follow some kind of law (in my case that the manometric pressure depends on its radius according to the function 458*ln(1000*x+1) Pa ). Since such airship is much easier to build, there are many other issues that have to be considered; the modelization of the rubber will be always an approximation, and I also have to ensure that its radius won’t exceed some limit value (balloons burst when you inflate them too much).
So a rigid model, with constant (or even better, controllable) volume will be advantageous in some aspects. First of all it’s easier to control (height can be controlled with closed loop control systems that vary volume), it’s models will be more accurate (no strange functions of dubious realism) and the problem of burst is different (now manometric pressure must be checked to ensure that no extreme structural solicitations happen).

I also changed the friction model. Now it’s proportional to the air density and to the square of the velocity and radius. I adjusted the friction coefficient so that a common balloon (mass without helium is 3 grams and its diameter is 20 cm.) will rise at a constant speed of 3 m/s.

So, I modified the last script (and making some corrections that affect to the numeric results) and run it with the following initial conditions:

Total mass without helium:10 Kg.
Diameter (considering spherical shape): 3 m.
Initial height: 1 m.
Standard atmosphere.

To make easier the comparison between rigid and flexible models both results are plotted in the same graph.

After execution these are the results:

In X-axis it’s represented the time in hours. It’s shown that a constant height of 3300 m (10,000 ft.) will be achieved in less than 10 minutes. The lowest temperature is -7 ºC, not bad, since all electronics can work at -40 ºC.

In the flexible model the stationary height is much higher (16000 m.), and what is worse, the temperature at those heights are so low (-56 ºC) that the electronic devices won’t work.

To conclude, these two graphs represent the limit conditions in each case (difference of pressures in the case of a rigid model and diameter in the flexible one):

Satellite communications

Due to the lack of GSM coverage in many parts of the world (many countries and oceans) I looked for what global communications systems are available in the world.
The first I found is the HF Data Link band used by aeroplanes (3-30 MHz). It’s long range and covers the poles. Although it’s transmission speed is quite low it may be an option if permissions can be obtained and the antenna required is not too long.

The other system are satellite links, which allow voice and data exchange. The constellation INMARSAT provides much information about the products and services available. Nevertheless, they are mainly intended for industries, so M2M devices are hard to find (it exists something called IsatM2M that seems to be interesting). The device DMR-800D OEM looks good, since it’s designed for solar powered installations. Nevertheless I couldn’t find any information of prices, and in it’s weights is 190 grams.

With another constellation, called ORBCOMM, was much easier to find M2M devices.
According to Wikipedia the cheapest receivers cost around $100. Since I couldn't find it's exact price, the model I like most, the Stellar DS100, seems to be one of the simplest.
They say in its datasheet that it’s voltage input is 8 to 16 VDC, its max peak current consumption is 2.0 A (transmitting) and it’s nominal consumption receiving is 77 mA. It’s temperature range is also similar to the GM862-GPS (-40ºC to +85ºC).

Those are not the only constellations designed for communications (I also found GlobalStar, for example) but the devices I found in a brief research work with these two systems.

It’s good to know that this technology exists, but it’s still soon to consider the acquisition of any of those devices.

GSM around the world

I found this world map in PDF where places with GSM coverage are coloured in brown (and 3GSM coverage in yellow). It’s a quite big file (21.8 MB), but it seems interesting, since one of the problems the airship will face during its journey will be the lack of coverage (that may determine the route it will follow).


In the website where I downloaded that map I also saw an ad about global SIM cards. It’s called MobilityPass, and they claim their rates are much lower than any other roaming service. I haven’t check their rates yet, but this system (or any other similar done by any other company, if exists) can be a solution for the access to GSM.

RC toys

Communications will likely be through the GSM network (especially GPRS where available), but I found interesting to see how common RC toys work, so I opened the receiver to find out who was the responsible of sending and receiving those 27 MHz. when playing. After some time unscrewing I found that:


Two DC-motors connected to a green board. The top right black cable is the antenna, and the disconnected red and black cables at the bottom left is the power source. I didn’t manage to make it work, since I couldn’t find the transmitter and none of my other transmitters worked at the same frequency (I tried, but no positive result). But anyway I could read the name of the IC in the image:


It’s name is RX-2B, and reading it’s datasheet I could see that there’s another chip with similar name; TX-2B (the ‘R’ is from ‘Receiver’ and the ‘T’ is from ‘Transmitter’). It’s designed for cars, since it’s outputs are labelled as ‘right’, ‘left’, ‘turbo’, ‘forward’, etc.

Learning about cameras

I haven’t yet received the GM862-GPS chip, so I’ve been messing around with another important part of the project. Sometimes it will need to be manually controlled it has to carry a webcam. Since I have no idea of how webcams work (except from the view of the user, which is just plugging it to the USB port and start using it) I have to start by finding manuals to understand them.

Soon I found a type of cam that is all I needed; it’s lightweight, cheap, and very low consumption. Those are the so called CMOS Cameras, and they’re widely used in common webcams. Fortunately I had a USB webcam I've never used and that seemed perfect for learning. Once I opened I found the following:


First of all, those six LEDS are not necessary at all (they’re just to illuminate dark rooms). The camera itself is the tiny black square in the middle. Some CMOS cameras available in the Web have integrated lens, but mine not, since it was integrated in the casing. Because of that images are not on focus (unless I put the lens at the right height), but it’s working principle remains the same, so it won’t be a problem to understand how to communicate with it.

Could this airship be passively stabilized?

One of the main concept problems I found is the difficulty to keep the device at a constant height during the night (when solar energy is not available) without spending the scarce electric power stored in a lithium battery. With that issue I remembered a question I asked myself when I was a child and I wondered where did helium balloons go when you release them. Intuitively one could think that it will rise until due to the low outer pressure the balloon eventually explodes, or maybe the coldness of the atmosphere will cool the helium inside the balloon, it's density will rise and an equilibrium will be achieved (now I thing the balloon will just deflate and will fall down at it's limit speed).
I roughly modelized the behaviour of a balloon in an standard atmosphere. First if all I needed to measure how manometric pressure varies inside a balloon as function of its radius. It resulted in something curious, since I could really check how pressure was highest at a given radius, to drop at higher ones and finally keep rising smoothly. Here is the graph I've made.


Hard to modelise that, uh? But I don't need that peak at small radius, so I approximate that graph to a logaritmic function (since it tends to infinite but very slowly). Yes, not precise, but it's mission is just to say that the manometric pressure slightly grows with radius (with high ones). It's analytic expression is 458*ln(1000*x+1) and expressed in mmHg (which means multiplying by 760/101325) is something like that:



So, running a script in Python about the behaviour of a balloon initially filled with 1 kg. of helium at 101325 Pa and (and that's important) ignoring the friction the movement would be like that:
That's funny to see that the balloon would rise up and down all the time at great heights. That's counterintuitive, and probably wrong. That oscillatory movement due to balloon's inertia must be somehow stabilized (losing energy by friction), so an aerodynamic friction term (proportional to it's speed) will be added.


Now we can see how it tends to a stationary solution. No matter how the friction term is (subcritic or supercritic), since after some oscillations it will tend to the same solution. Now I don't care about the numeric results (since the pressure-ratio function was obtained with a common balloon that propably won't be the one used in the real airship), but it's interesting to check how some kind of passive stabilization exists. Now I have to check that all electronic devices will work at those temperatures (since many components won't work below -40ºC).

Power issues

While I wait for the GM862-GPS Evaluation Kit to arrive I surfed throught some websites trying to find some solution for the power source. Due to autonomy reasons the airship has to be solar powered, and luckily I found a solar panel at home (that belonged to a kind of solar fan). It's composed by three 1,5 v power cells that can be connected in series (to reach higher voltages) or in pararell (to be able to supply more intensity). Besides I measured how the tension was in open circuit with different orientations of the panel. Here are the results (which are kind of disappointing).

In open circuit and parallel connection the voltage varies according to this graph


So, in conclusion, the idea may work, but not with that particular cell. Power is just not enough (and it would be desirable that it was a little more lightweight). I searched the Web trying to find low cost, lightweight and powerful solar panels, and I found something that could be interesting. It's a kind of roll solar cell, so it's light, and it's much powerful that my toy panel I tested at home.

The best way to get started is to stop talking and start doing (Walt Disney)

So, let's go.
I will tackle the part I consider to be the hardest (maybe I’m wrong, who knows), and that’s the electronics part. It comprises both navigation and communications. For that purpose I found at SparkFun this kit to use the GM862-GPS chip. In two lines, the GM862-GPS is a communications chip (43 mm. each side) which is able to receive GPS signal. It has algo a built in Python interpreter (quite limited, though). I have some knowledge of Python, but I’ve never programmed a chip through the serial port. I printed a couple of the official manuals (the Hardware and Software User’s Manual) and I’ll try to figure out what can I do with that. It arrives this Friday, so till then I have some time to read the instructions (and prepare some exams, for September, too).

First doodles

I don’t have yet a complete mental image of the finished airship. At first I imagined something not much bigger than one helium balloon (two at most) but soon I realized that it would hardly carry the not-so-heavy navigation electronics. And since an integrated GSM GPS chip costs 120€ I believe that some extra weight for security systems won’t be a bad idea.

So, many different parts require my attention, and since I can’t solve them all at the same time, I should try to organise myself. Operationally I’ve divided the airship in two different sections that can be split in two subsections each.

1. Aerodynamics
a. Lift
b. Propulsion
2. Electronics
a. Navigation
b. Communications

In a general view, lift will be helium’s job, since I need some way to control height (maybe with vertical propellers or with some system to vary volume), propulsion will be carried out by solar powered and internet controlled propellers. It will navigate using GPS (cheap, precise and global range) and communications will use the GSM network (especially GPRS if available). It will be useful to send image using a CMOS camera, since it has to be manually controlled (on landing).

Welcome!

First of all, thanks for coming!

I created this blog to keep track of the day by day progress of a project that right now seems to be impossible. I am an student of aeronautical engineering in Madrid (Spain) on my fourth course. Since I am quite familiar with aerodynamic issues, electronics and maths, I feel I lack of practical knowledge to carry out real life projects. Well, that would be the project of my life.

It would be interesting to write down what I know at present and keep record of the new skills and knowledge I’ll acquire in the future.

Electronics: I know what a resistor, inductor and condenser are. I took some courses in electric circuits, electrical engineering and two semesters in electronics (Electronics I and II). I found really interesting that world, so I bought a multimeter and later a USB oscilloscope. Apart from some tests I’ve done (build a signal filter, try some diodes, soldering some wires, use some counters, etc.) I have no experience in real projects.

Aerostatics, aerodynamics, thermodynamics…: I have a good base to make physical models of the airship behaviour in a standard atmosphere. It’s important, thought, to be aware that models are just that, models, and real-world testing must be done to be sure. Numerical calculus can also be carried out.

Navigation and communications: Those are vital issues and for that purpose electronics must be mastered. I have basic knowledge of satellite navigation and GSM network.

Materials: I took some courses at university about metals, but not yet about composites. Anyway, those are really expensive solutions, and one of the goals is to make it general user affordable. In the same way, no industrial solutions of fabrication would be desirable (i.e., MIG/TIG welding, CNC Milling machine and so).