The mathematical model of the solar balloon is based on 2 characteristics
:

· the top is an half sphere diameter D.

· the bottom is a cone.

The semi angle of the cone is around 40°.

It can be changed . If the angle is increased , the load on balloon bottom
will increase...

Those angles should be expressed in radians in order to use the Excel
97's trigonometric functions.

360° = 2 X Pi radians.

Many characteristics can be modified in the modified in the xls files.

- Pi : Pi = 3,1416
- 360° = 2 X Pi radians
- Sinus of an angle A : sin(A) = opposite side/hypotenuse
- Cosine of an angle A : cos(A) = adjacent side/hypotenuse
- Tangent of an angle A : tang (A) = opposite side / adjacent side
- Cord of an angle A = 2xRxsin(A/2) or Dxsin(A/2)
- Arc of an angle A ( degrees) : arc(A) = (AxPixD)/360
- Arc of an angle A (en radians) : arc(A) = AxR or (AxD)/2
- Perimeter of the circle of half diameter R or circumference : P = 2xPixR or P = PixD
- Surface of circle : S = PixR
^{2}or S = (PixD^{2})/4 - Lateral area of the cylinder : S = 2xPixRxh or S = PixDxh
- Sphere area :

- Sphere volume :

- Lateral area of a cone : (a=length generator line ; alpha=half-angle in
the summit in radians)

- Volume of cone : (h=height of the cone ; alpha=half angle at summit en radians)

- Surface and volume of the balloon :

- The top is an half sphere diameter D
- The bottom is a cone
- Dcc = diameter of the loading circle.
- alpha = half angle en bas off the balloon in radians).