Want you build a balloon that will rise in the stratosphere over 30,000 meters?
Then this is the right section for you!
The manufacture of a helium balloon is not too different from a hot air balloon, but we must consider some aspects that are completely different.
First, unlike the hot air balloons, Helium balloons reach great heights, which easily passed the 25,000 meters to get if well designed around 60'000.
Helium is a noble gas, so not flammable, is lighter than air, and provides a thrust 3 times higher than hot-air balloon.
But we need to consider, the high altitude that will reach our balloon, and the respective pressure at that altitude.
In fact, unlike the common hot air balloons, which is unlikely we will see them flying over the 1/2000 meters, the helium balloons, going much higher, will undergo a constant pressure drop, which will result in the expansion of helium in them and consequently an increase of the volume of the balloon.
Now we will design together a balloon that easily exceed 20,000 meters
I have chosen for this guide a balloon that has a middle constructive difficulties so that also is suitable for all those who engage for the first time in their construction.
But if you want to design a larger, following this guide, you can do it! 🙂
First of all we need to know how high we want to go, and the gauge pressure at that height.
To do this we can use very complex calculations regarding the reduction of accruals related pressure at the ground temperature and the geographical position ....
Once you decide how high we want to get, (in our case 20,000 meters) we look at the respective pressure. We will look at the immediately previous or next that makes us more comfortable, then 21'357 m.
In our case the pressure at 21'357 m is 0.0651 ATA (atmospheres absolute)
Now that we have the pressure, we need to calculate how much the balloon will expand at that height, and to do that we use this simple formula.
P = pressure we found in table
1/P = 1/0,0651 = 15,360
This means that at the altitude of 21'357 meters helium in the balloon will be expanded to occupy a volume 15,36 times higher than departure.
We mark the data obtained 15,36 (we need it later).
Now the next step is to decide how much weight to bring. In this guide, our maximum total weight (weight including envelope and basket, the weight that advances will be dedicated to the payload) will be 2 Kg, but of course once you understand how to design, you can change it at will to build the balloon you want.
As is easy to understand, more the weight will be high, and even more increase the envelope size to built, and consequently the work to do.
We obviously want that our "balloon + payload" that has the weight -decided by us- of 2 kg is able to fly... So we have to design a balloon that could raise a higher weight, because if our thrust was 2 kg and the weight too.... we would remain stationary.
Then we divide the weight you want to lift by 0.66
2/0,66 = 3 = Helium cubic m needed to fly
We will use the cubic meters of helium obtained, for sizing the ball, provided that the "balloon payload +" must weigh at most 2 kg decided before.
How to Size the Balloon
What interests us is the maximum size that the ball will reach at the maximum altitude and we get it with the two previous data. The famous 15.36 that i told you to remember and the value of cubic meters of helium needed (3).
Multiplying the two values get the cubic meters (Envelope capacity) needed for reach the decided altitude (21'357 m) with the decided weight ( 2 Kg )
3 * 15,36 = 46 cubic m
To get a little more margin, excess round up the value obtained.
46 cubic m → 50 cubic m
The balloon we're going to design will have a volume of 50 cubic meters.
Knowing now the volume, let's calculate the data for a sphere that has an internal volume of 50 cubic meters. With the formula below we will find the radius.
From the formula, our radius will be:
r = 228,54 cm
Using the radius we now calculate the other parameters.
Diameter = D = r * 2 = 457,08 cm
Circumference = C = D * π = 1435,95 cm
In this project, unlike the hot air balloons, we will not make difference between upper and lower gore, as being a sphere, are equal. But we must decide how many gores do.
More gores we will do, and the spherical shape will be better approximated, but much will also increase the work that we should do. While if we'll make a few we will have a balloon with the wrong volume than that calculated.
A proper number of gores is 10 to 20, but we can get even 30 if we have someone who helps us or even a group of friends whereby divide the tasks and work. We choose the gores number, always equal. In this project we will do 14 gores and being half over, the same as below, we will calculate only one half and then duplicate it.
Gores Number = Nsp = 14
Half-gore height = hss = C / 4 = 1435,95 / 4 = 358,99 cm
Gore Base = C / Nsp = 1435,95 / 14 = 102,56
We choose how many points will be made the gore. Also in this case more gore we will make and more the balloon will be approximate, increasing at the same time the work that we have to do. Correct number that guarantees us a good approximation to the sphere, with a smaller work is 8 points. Wishing we can turn it up to 10 or 12, go up is useless. As for the gores also the points is best are equal. For this project the number of points that I chose is 8.
Np = 8
(For simplicity in the image below I drew a gore with only 3 points, and as you can see is a bit edgy.Realizing it instead with 8 or above, we decreasing this problem)