Helium balloons are used every day for launching weather probes

Now we will have to calculate all the h steps 1 to 8 with the following formula:

aerostat calc math

If we did everything correctly we will get:

h1 = 199,8 cm

h2 = 171,4 cm

h3 = 142,8 cm

h4 = 114,2 cm

h5 = 85,7 cm

h6 = 57,1 cm

h7 = 28,6 cm

h8 = to this point we will use another formula that will = (r/Np)/2 = 14,3 cm

htop = Now we will calculate a final point not mentioned before with this other formula = [r/(Np*2)]/2 = 7,14

Now that we have all the h points we will use them to find the points A with the following formula:

aerostat formula

The points A need to be calculated each time for each point h

In practice, when in the formula we will use the point h1 we will get A1, when we use h2 we get A2 and so on ....

A1 = 226,72 cm

A2 = 221,28 cm

A3 = 211,84 cm

A4 = 197,88 cm

A5 = 178,40 cm

A6 = 151,12 cm

A7 = 110,70 cm

A8 = 79,57 cm

Atop = 56,67 cm

With all the A points obtained we will now calculate the points L that we will use it in the construction of the balloon, they indicate the width of the gore at certain heights on the same (which we'll see later).

Along with the points L we calculate the h2.n points, which we will then be used to determine where to place on gore points L found.

L1 = ((A1*2)*π) / Sp = 101,75

L2 = ((A2*2)*π) / Sp = 99,31

L3 = 95,07

L4 = 88,80

L5 = 80,06

L6 = 67,82

L7 = 49,68

L8 = 35,71

Ltop = 25,43

h2.1 = (R/Np)*1 = 28,57

h2.2 = (R/Np)*2 = 57,13

h2.3 = 85,70

h2.4 = 114,27

h2.5 = 142,84

h2.6 = 171,40

h2.7 = 199,97

h2.8 = (R/(Np*2))-R = -214,25 >From negative to positive> 214,25   (Applying the above formula only for h2.8)

h2.top = [(R/(Np*2)) / 2] - R = -221,40 >from negative to positive> 221,40    (Applying the above formula only for h2.top)

gores plan

The example image here above shows what L points we have calculated represent on gore, and the H points that will calculate below.

As you can easily understand, the points L indicate the gore width, and H points the distance to L point from the base.

Example: The point L4 tells us the width of the gore at a height from the base equal to H4

Now we calculate the H points using the following formula, in which we will use h2.n points found earlier.

Obviously each point h2.n corresponds to a point Hn, if for example we will use h2.2 get H2, if we use h2.7 get H7 and so on.

aerostat height calc

H1 = 28,64

H2 = 57,74

H3 = 87,84

H4 = 119,66

H5 = 154,29

H6 = 193,80

H7 = 243,48

H8 = 277,74

Htop = 301,71

Now that we have all figured out, we can move on to building 😀